/MAT/LAW122 (MODIFIED_LADEVEZE)

Block Format Keyword A simple unidirectional composite ply model, accounting for orthotropic elasticity and plasticity. Fiber and matrix damage are considered, including strain rate effect.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW122/mat_ID/unit_ID or /MAT/MODIFIED_LADEVEZE/mat_ID/unit_ID
mat_title
ρ i
E 1T MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaajugybiaadw eakmaaBaaaleaacaaIXaGaamivaaqabaaaaa@3ACF@ E 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaajugybiaadw eakmaaBaaaleaacaaIYaaabeaaaaa@39F7@ E 3 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaajugybiaadw eakmaaBaaaleaacaaIYaaabeaaaaa@39F7@ G 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbWaaS baaSqaaiaaigdacaaIYaaabeaaaaa@39DB@ G 23 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbWaaS baaSqaaiaaigdacaaIYaaabeaaaaa@39DB@
G 13 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbWaaS baaSqaaiaaigdacaaIYaaabeaaaaa@39DB@ ν 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH9oGBda WgaaWcbaGaaGymaiaaikdaaeqaaaaa@3AC7@ ν 23 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH9oGBda WgaaWcbaGaaGymaiaaikdaaeqaaaaa@3AC7@ ν 31 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH9oGBda WgaaWcbaGaaGymaiaaikdaaeqaaaaa@3AC7@
E 1C MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaajugybiaadw eakmaaBaaaleaacaaIXaGaaGimaiaadoeaaeqaaaaa@3B78@ γ ISH ITR IRES
σ Y0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadMfacaaIWaaabeaaaaa@397B@ β M A
ε f ti MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWG0bGaamyAaaaaaaa@3A99@ ε f tu MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWG0bGaamyDaaaaaaa@3AA5@ d f tu MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaDa aaleaacaWGMbaabaGaamiDaiaadwhaaaaaaa@39E7@
ε f c i MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWG0bGaamyAaaaaaaa@3A99@ ε f c u MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWG0bGaamyDaaaaaaa@3AA5@ d f c u MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaDa aaleaacaWGMbaabaGaamiDaiaadwhaaaaaaa@39E7@ IBUCK
IFUNCD1 d sat1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGZbGaamyyaiaadshacaaIXaaabeaaaaa@3A9A@ Y 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaaIWaaabeaaaaa@37B7@ Y C MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaWGdbaabeaaaaa@37C5@ b
DMAX Y R MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaWGsbaabeaaaaa@37D4@ Y S MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaWGsbaabeaaaaa@37D4@
IFUNCD2 d sat2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGZbGaamyyaiaadshacaaIYaaabeaaaaa@3A9B@ Y 0 ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaaIWaaabeaakiaacEcaaaa@386C@ Y C ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaWGdbaabeaakiaacEcaaaa@387A@
IFUNCD2C d sat2C MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGZbGaamyyaiaadshacaaIYaGaam4qaaqabaaaaa@3B63@ Y 0C ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaaIWaGaam4qaaqabaGccaGGNaaaaa@3934@ Y CC ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaWGdbGaam4qaaqabaGccaGGNaaaaa@3942@
ε ˙ 11 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbai aadaWgaaWcbaGaaGymaiaaigdaaeqaaaaa@3945@ D 11 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaaIXaGaaGymaaqabaaaaa@385E@ n 11 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaaBa aaleaacaaIXaGaaGymaaqabaaaaa@3888@ D 11U MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaaIXaGaaGymaiaadwfaaeqaaaaa@3938@ n 11U MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaaBa aaleaacaaIXaGaaGymaiaadwfaaeqaaaaa@3962@
ε ˙ 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbai aadaWgaaWcbaGaaGymaiaaigdaaeqaaaaa@3945@ D 22 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaaIXaGaaGymaaqabaaaaa@385E@ n 22 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaaBa aaleaacaaIXaGaaGymaaqabaaaaa@3888@ D 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbWaaS baaSqaaiaaigdacaaIYaaabeaaaaa@39DB@ n 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaaBa aaleaacaaIXaGaaGOmaaqabaaaaa@3889@
ε ˙ R0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbai aadaWgaaWcbaGaamOuaiaaicdaaeqaaaaa@3960@ D R0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWGsbGaaGimaaqabaaaaa@3879@ n R0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaaBa aaleaacaWGsbGaaGimaaqabaaaaa@38A3@ LTYPE11 LTYPE12 LTYPER0
FCUT

Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

unit_ID (Optional) Unit identifier.

(Integer, maximum 10 digits)

mat_title Material title.

(Character, maximum 100 characters)

ρ i Initial density.

(Real)

[ kg m 3 ]
E 1 T MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaajugybiaadw eakmaaBaaaleaacaaIXaGaamivaaqabaaaaa@3ACF@ Young’s modulus in fiber direction 1 for tension.

(Real)

[ Pa ]
E 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaajugybiaadw eakmaaBaaaleaacaaIYaaabeaaaaa@39F7@ Young’s modulus in matrix direction 2.

(Real)

[ Pa ]
E 3 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaajugybiaadw eakmaaBaaaleaacaaIYaaabeaaaaa@39F7@ Young’s modulus in matrix direction 3.

(Real)

[ Pa ]
G 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbWaaS baaSqaaiaaigdacaaIYaaabeaaaaa@39DB@ Shear modulus in the plane 12.

(Real)

[ Pa ]
G 23 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbWaaS baaSqaaiaaigdacaaIYaaabeaaaaa@39DB@ Shear modulus in the plane 23.

(Real)

[ Pa ]
G 13 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbWaaS baaSqaaiaaigdacaaIYaaabeaaaaa@39DB@ Shear modulus in the plane 13.

(Real)

[ Pa ]
ν 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH9oGBda WgaaWcbaGaaGymaiaaikdaaeqaaaaa@3AC7@ Poisson’s ratio in the plane 12.

(Real)

ν 23 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH9oGBda WgaaWcbaGaaGymaiaaikdaaeqaaaaa@3AC7@ Poisson’s ratio in the plane 23.

(Real)

ν 31 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH9oGBda WgaaWcbaGaaGymaiaaikdaaeqaaaaa@3AC7@ Poisson’s ratio in the plane 31.

(Real)

E 1 C MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaajugybiaadw eakmaaBaaaleaacaaIXaGaaGimaiaadoeaaeqaaaaa@3B78@ Young’s modulus in fiber direction 1 for compression.

(Real)

[ Pa ]
γ Compressive factor of the modulus correction.

(Real)

P a 1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaaca GGqbGaaiyyaaGaay5waiaaw2faamaaCaaaleqabaGaeyOeI0IaaGym aaaaaaa@3B71@
ISH Shear matrix damage flag.
= 1 (Default)
Linear function
= 2
Exponential function
= 3
Tabulated function

(Integer)

ITR Transverse matrix damage flag.
= 1 (Default)
Linear function
= 2
Exponential function
= 3
Tabulated function

(Integer)

IRES Return mapping algorithm flag.
= 1
NICE (Next Increment Correct Error) explicit algorithm.
= 2 (Default)
Cutting plane semi-implicit algorithm.

(Integer)

σ Y 0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadMfacaaIWaaabeaaaaa@397B@ Initial yield stress.

Default = 1020 (Real)

[ Pa ]
β Hardening modulus.

(Real)

[ Pa ]
M Hardening exponent.

(Real)

A Shear and transverse plasticity coupling factor.

(Real)

ε f t i MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWG0bGaamyAaaaaaaa@3A99@ Tensile initial damage strain in fiber direction 1.

Default = 1020 (Real)

ε f t u MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWG0bGaamyDaaaaaaa@3AA5@ Tensile ultimate damage strain in fiber direction 1.

Default = 2*1020 (Real)

d f t u MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaDa aaleaacaWGMbaabaGaamiDaiaadwhaaaaaaa@39E7@ Tensile ultimate damage in fiber direction 1.

(Real)

ε f c i MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWG0bGaamyAaaaaaaa@3A99@ Compression initial damage strain in fiber direction 1.

Default = 1020 (Real)

ε f c u MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWG0bGaamyDaaaaaaa@3AA5@ Compression ultimate damage strain in fiber direction 1.

Default = 2*1020 (Real)

d f c u MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaDa aaleaacaWGMbaabaGaamiDaiaadwhaaaaaaa@39E7@ Compression ultimate damage in fiber direction 1.

(Real)

IBUCK Buckling damage matrix on fiber in compression flag.
= 1 (Default)
No compression damage due to buckling effect.
= 2
Compression damage due to buckling effect activated.

(Integer)

IFUNCD1 Matrix shear tabulated damage function identifier.

(Integer)

d s a t 1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGZbGaamyyaiaadshacaaIXaaabeaaaaa@3A9A@ Damage saturation for matrix shear exponential damage.

(Real)

Y 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaaIWaaabeaaaaa@37B7@ Initial matrix shear damage threshold / Abscissa scale factor for tabulated damage.

Default = 1020 or 1.0 (Real)

Y C MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaWGdbaabeaaaaa@37C5@ Critical matrix shear damage limit.

(Real)

b Shear/transverse matrix damage coupling factor.

Default = E 2 / G 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcgaqaa4 GaamyraSWaaSbaaeaacaaIYaaabeaaaOqaaiaadEeadaWgaaWcbaGa aGymaiaaikdaaeqaaaaaaaa@3BBB@ (Real)

DMAX Damage maximum allowed value.

(Real)

Y R MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaWGsbaabeaaaaa@37D4@ Elementary shear damage value.

Default = 1020 (Real)

Y S MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaWGsbaabeaaaaa@37D4@ Brittle damage limit for fiber-matrix interface.

Default = 1020 (Real)

IFUNCD2 Tension transverse matrix tabulated damage function identifier.

(Integer)

d s a t 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGZbGaamyyaiaadshacaaIYaaabeaaaaa@3A9B@ Damage saturation for transverse matrix exponential damage in tension.

(Real)

Y 0 ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaaIWaaabeaakiaacEcaaaa@386C@ Initial transverse matrix damage threshold in tension / Abscissa scale factor for tabulated damage.

Default = 1020 or 1.0 (Real)

Y C ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaWGdbaabeaakiaacEcaaaa@387A@ Critical transverse matrix damage limit in tension.

(Real)

IFUNCDC2 Compression transverse matrix tabulated damage (shells only) function identifier.

(Integer)

d s a t 2 C MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGZbGaamyyaiaadshacaaIYaGaam4qaaqabaaaaa@3B63@ Damage saturation for compression transverse matrix exponential damage (shells only).

(Real)

Y 0 C ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaaIWaGaam4qaaqabaGccaGGNaaaaa@3934@ Initial transverse damage threshold in compression / Abscissa scale factor for tabulated damage (shells only).

(Real)

Y C C ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaWGdbGaam4qaaqabaGccaGGNaaaaa@3942@ Critical transverse damage limit in compression (shells only).

(Real)

ε ˙ 11 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbai aadaWgaaWcbaGaaGymaiaaigdaaeqaaaaa@3945@ Reference strain rate for fiber direction 1.

Default = 1.0 (Real)

[ 1 s ]
D 11 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaaIXaGaaGymaaqabaaaaa@385E@ First parameter for Young’s modulus strain rate dependency in fiber direction 1.

(Real)

n 11 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaaBa aaleaacaaIXaGaaGymaaqabaaaaa@3888@ Second parameter for Young’s modulus strain rate dependency in fiber direction 1.

(Real)

D 11 U MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaaIXaGaaGymaiaadwfaaeqaaaaa@3938@ First parameter for rupture strain rate dependency in fiber direction 1.

(Real)

n 11 U MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaaBa aaleaacaaIXaGaaGymaiaadwfaaeqaaaaa@3962@ Second parameter for rupture strain rate dependency in fiber direction 1.

(Real)

ε ˙ 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbai aadaWgaaWcbaGaaGymaiaaigdaaeqaaaaa@3945@ Reference strain rate for shear and transverse directions.

Default = 1.0 (Real)

[ 1 s ]
D 22 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaaIXaGaaGymaaqabaaaaa@385E@ First parameter for Young’s modulus strain rate dependency in matrix transverse direction 2.

(Real)

n 22 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaaBa aaleaacaaIXaGaaGymaaqabaaaaa@3888@ Second parameter for Young’s modulus strain rate dependency in matrix transverse direction 2.

(Real)

D 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGhbWaaS baaSqaaiaaigdacaaIYaaabeaaaaa@39DB@ First parameter for shear modulus strain rate dependency in plane 12.

(Real)

n 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaaBa aaleaacaaIXaGaaGOmaaqabaaaaa@3889@ Second parameter for shear modulus strain rate dependency in plane 12.

(Real)

ε ˙ R 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbai aadaWgaaWcbaGaamOuaiaaicdaaeqaaaaa@3960@ Reference strain rate for initial yield stress.

Default = 1.0 (Real)

[ 1 s ]
D R 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaWGsbGaaGimaaqabaaaaa@3879@ First parameter for initial yield stress strain rate dependency.

(Real)

n R 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaaBa aaleaacaWGsbGaaGimaaqabaaaaa@38A3@ Second parameter for initial yield stress strain rate dependency.

(Real)

LTYPE11 Strain rate dependency law type for fiber direction 1.
= 1 (Default)
Power law
= 2
Linear law
= 3
Logarithmic law
= 4
Tangent hyperbolic law

(Integer)

LTYPE12 Strain rate dependency law type for shear and transverse directions.
= 1 (Default)
Power law
= 2
Linear law
= 3
Logarithmic law
= 4
Tangent hyperbolic law

(Integer)

LTYPER0 Strain rate dependency law type for initial yield stress.
= 1 (Default)
Power law
= 2
Linear law
= 3
Logarithmic law
= 4
Tangent hyperbolic law

(Integer)

FCUT Equivalent strain rate cutoff frequency.

Default = 5 kHz (Real)

[ 1 s ]

Example (Steel)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
Test unit
                  Mg                  mm                   s
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW122/1/1
Steel                                                                                               
#        Init. dens.
              1.8E-9
#                 E1                  E2                  E3                 G12                 G23
              135000                1000                1000                4000                4000
#                G31                NU12                NU23                NU31
                4000                0.33                 0.1                0.33 
#                E1C               GAMMA                 ISH                 ITR                IRES
              138000              1.7E-4                   0                   0                   2
#              SIGY0                BETA                   M                   A
                  20              0.7986              0.5166                0.33
#            EPS_FTI             EPS_FTU                DFTU
               0.002              0.0025                 1.0
#            EPS_FCI             EPS_FCU                DCFU               IBUCK
              0.0104              0.0105                 1.0                   1
#            IFUNCD1               DSAT1                  Y0                  YC                   B
                                                       0.158                0.05                
#               DMAX                  YR                 YSP
                0.95              1.5811              1.0e20
#            IFUNCD2               DSAT2                 Y0P                 YCP
                                                       0.158                0.05 
#           IFUNCD2C              DSAT2C                Y0PC                YCPC
                                                       0.158                0.05 
#             EPSD11                 D11                 N11                D11U                N11U                                     

#             EPSD12                 D22                 N22                 D12                 N12                                     

#             EPSDR0                 DR0                 NR0             LTYPE11   LTYPE12   LTYPER0                                     

#               FCUT
 
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. The modified Ladeveze model considers a unidirectional composite ply where fibers are to be oriented in the direction 1, and the matrix in the transverse directions 2 and 3. This material orientation will then be identified as x MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaaaa@36F0@ , y MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaaaa@36F0@ , z MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaaaa@36F0@ (Figure 1). The “out of plane” transverse direction will then correspond to z MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaaaa@36F0@ -axis for shell and thickshell elements.
    Figure 1. Unidirectional ply and its material orientation considered by /MAT/LAW122


  2. The elastic behavior is assumed to be orthotropic. Under 2D plane stress conditions, for shells, the stress/strain relationship is given by:

    σ xx = C 11 ε xx e + C 12 ε yy e σ yy = C 21 ε xx e + C 22 ε yy e σ xy = G 12 ε xy e σ yz =κ G 23 ε yz e σ zx =κ G 13 ε zx e MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaaiqaaqaabe qaaiabeo8aZnaaBaaaleaacaWG4bGaamiEaaqabaGccqGH9aqpcaWG dbWaaSbaaSqaaiaaigdacaaIXaaabeaakiabew7aLnaaDaaaleaaca WG4bGaamiEaaqaaiaadwgaaaGccqGHRaWkcaWGdbWaaSbaaSqaaiaa igdacaaIYaaabeaakiabew7aLnaaDaaaleaacaWG5bGaamyEaaqaai aadwgaaaaakeaacqaHdpWCdaWgaaWcbaGaamyEaiaadMhaaeqaaOGa eyypa0Jaam4qamaaBaaaleaacaaIYaGaaGymaaqabaGccqaH1oqzda qhaaWcbaGaamiEaiaadIhaaeaacaWGLbaaaOGaey4kaSIaam4qamaa BaaaleaacaaIYaGaaGOmaaqabaGccqaH1oqzdaqhaaWcbaGaamyEai aadMhaaeaacaWGLbaaaaGcbaGaeq4Wdm3aaSbaaSqaaiaadIhacaWG 5baabeaakiabg2da9iaadEeadaWgaaWcbaGaaGymaiaaikdaaeqaaO GaeqyTdu2aa0baaSqaaiaadIhacaWG5baabaGaamyzaaaaaOqaaiab eo8aZnaaBaaaleaacaWG5bGaamOEaaqabaGccqGH9aqpcqaH6oWAca WGhbWaaSbaaSqaaiaaikdacaaIZaaabeaakiabew7aLnaaDaaaleaa caWG5bGaamOEaaqaaiaadwgaaaaakeaacqaHdpWCdaWgaaWcbaGaam OEaiaadIhaaeqaaOGaeyypa0JaeqOUdSMaam4ramaaBaaaleaacaaI XaGaaG4maaqabaGccqaH1oqzdaqhaaWcbaGaamOEaiaadIhaaeaaca WGLbaaaaaakiaawUhaaaaa@87C0@ with C = 1 1 ν 12 ν 21 E 1 ν 12 E 2 ν 21 E 1 E 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaGaaC4qaiabg2 da9maalaaabaGaaGymaaqaaiaaigdacqGHsislcqaH9oGBdaWgaaWc baGaaGymaiaaikdaaeqaaOGaeqyVd42aaSbaaSqaaiaaikdacaaIXa aabeaaaaGcdaWadaqaauaabeqaciaaaeaacaWGfbWaaSbaaSqaaiaa igdaaeqaaaGcbaGaeqyVd42aaSbaaSqaaiaaigdacaaIYaaabeaaki aadweadaWgaaWcbaGaaGOmaaqabaaakeaacqaH9oGBdaWgaaWcbaGa aGOmaiaaigdaaeqaaOGaamyramaaBaaaleaacaaIXaaabeaaaOqaai aadweadaWgaaWcbaGaaGOmaaqabaaaaaGccaGLBbGaayzxaaaaaa@50BA@

    Where, E 1 = E 1 T if ε x x 0 E 1 C 1 + γ E 1 C ε x x if ε x x < 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaaoiaadweada WgaaWcbaGaaGymaaGdbeaacqGH9aqpdaGabaqaauaabeqacmaaaeaa caWGfbWcdaqhaaqaaiaaigdaaeaacaWGubaaaaGdbaGaaeyAaiaabA gaaeaacqaH1oqzlmaaBaaabaGaamiEaiaadIhaaeqaa4GaeyyzImRa aGimaaqaamaalaaabaGaamyraSWaa0baaeaacaaIXaaabaGaam4qaa aaa4qaaiaaigdacqGHRaWkcqaHZoWzcaWGfbWcdaqhaaqaaiaaigda aeaacaWGdbaaa4WaaqWaaeaacqaH1oqzlmaaBaaabaGaamiEaiaadI haaeqaaaGdcaGLhWUaayjcSdaaaaqaaiaabMgacaqGMbaabaGaeqyT du2cdaWgaaqaaiaadIhacaWG4baabeaaoiabgYda8iaaicdaaaaaca GL7baaaaa@5D04@ .

    This nonlinear evolution of compression Young’s modulus in fiber direction is used to represent the effect of fiber micro buckling and misalignment. κ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqOqFfpeea0xe9vq=Jb9 vqpeea0xd9q8qiYRWxGi6xij=hbba9q8aq0=yq=He9q8qiLsFr0=vr 0=vr0db8meaabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaH6oWAaa a@391E@ is the shear factor used for shells only and defined in the property.

    For 3D stress conditions (solid elements and thickshells), the inverse of compliance matrix is used to link the stresses with the strains:

    σ x x σ y y σ z z σ x y σ y z σ z x = 1 E 1 - ν 12 E 1 - ν 13 E 1 - ν 12 E 1 1 E 2 - ν 23 E 2 - ν 13 E 1 - ν 23 E 2 1 E 3 1 G 12 1 G 23 1 G 13 - 1 ε x x e ε y y e ε z z e ε x y e ε y z e ε z x e

    The same non-linearity of fiber direction Young’s modulus in compression is used.

  3. In fiber directions 1 (or x MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiEaaaa@36F0@ -axis), the behavior remains purely elastic until damage occurs (detailed below). However, the plastic behavior of the matrix is considered under transverse and shear loadings. The elastic limit is introduced through a yield function that differs from solids to shells:
    • For Shells:
      f = σ x y 2 + A σ y y 2 σ Y MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiabg2 da9maakaaabaGaeq4Wdm3aa0baaSqaaiaadIhacaWG5baabaGaaGOm aaaakiabgUcaRiaadgeacqaHdpWCdaqhaaWcbaGaamyEaiaadMhaae aacaaIYaaaaaqabaGccqGHsislcqaHdpWCdaWgaaWcbaGaamywaaqa baaaaa@46B9@
    • For Solids:
      f = σ x y 2 + σ y z 2 + σ z y 2 + A σ y y 2 + σ z z 2 σ Y MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiabg2 da9maakaaabaGaeq4Wdm3aa0baaSqaaiaadIhacaWG5baabaGaaGOm aaaakiabgUcaRiabeo8aZnaaDaaaleaacaWG5bGaamOEaaqaaiaaik daaaGccqGHRaWkcqaHdpWCdaqhaaWcbaGaamOEaiaadMhaaeaacaaI YaaaaOGaey4kaSIaamyqamaabmaabaGaeq4Wdm3aa0baaSqaaiaadM hacaWG5baabaGaaGOmaaaakiabgUcaRiabeo8aZnaaDaaaleaacaWG 6bGaamOEaaqaaiaaikdaaaaakiaawIcacaGLPaaaaSqabaGccqGHsi slcqaHdpWCdaWgaaWcbaGaamywaaqabaaaaa@5917@

    Where, A MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyqaaaa@36B9@ is a coupling factor whose value can be set to 0.33 for an isotropic resin. In this equation, the yield function is defined as:

    σ Y = σ Y 0 + β ε p m MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaadMfaaeqaaOGaeyypa0Jaeq4Wdm3aaSbaaSqaaiaadMfa caaIWaaabeaakiabgUcaRiabek7aIjabew7aLnaaDaaaleaacaWGWb aabaGaamyBaaaaaaa@439F@

    This describes an isotropic hardening following a power law. The hardening modulus β is numerically bounded by the value max E , 2 G 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaciyBaiaacg gacaGG4bWaaeWaaeaacaWGfbGaaiilaiaaikdacaWGhbWaaSbaaSqa aiaaigdacaaIYaaabeaaaOGaayjkaiaawMcaaaaa@3EFF@ to avoid stability issues.

  4. Like elasticity or plasticity, the damage behavior is assumed to be orthotropic. Three damage variables are then defined: d f MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGMbaabeaaaaa@37F3@ , d MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaaaa@36DC@ and d ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaacE caaaa@3787@ which respectively describes the fiber rupture, the shear matrix damage, and the transverse matrix damage.
    • Fiber damage d f MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGMbaabeaaaaa@37F3@ affects the behavior along the fiber direction 1. Under tension loading condition, fiber damage evolves following the equations.
      d f = 0 if ε f e q ε f t i d f t u ε f e q ε f t i ε f t u ε f t i if ε f t i < ε f e q ε f t u 1 1 d f t u ε f t u ε f e q if ε f e q > ε f t u MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGMbaabeaakiabg2da9maaceaabaqbaeqabmWaaaqaaiaa icdaaeaacaqGPbGaaeOzaaqaaiabew7aLnaaDaaaleaacaWGMbaaba GaamyzaiaadghaaaGccqGHKjYOcqaH1oqzdaqhaaWcbaGaamOzaaqa aiaadshacaWGPbaaaaGcbaGaamizamaaDaaaleaacaWGMbaabaGaam iDaiaadwhaaaGcdaWcaaqaaiabew7aLnaaDaaaleaacaWGMbaabaGa amyzaiaadghaaaGccqGHsislcqaH1oqzdaqhaaWcbaGaamOzaaqaai aadshacaWGPbaaaaGcbaGaeqyTdu2aa0baaSqaaiaadAgaaeaacaWG 0bGaamyDaaaakiabgkHiTiabew7aLnaaDaaaleaacaWGMbaabaGaam iDaiaadMgaaaaaaaGcbaGaaeyAaiaabAgaaeaacqaH1oqzdaqhaaWc baGaamOzaaqaaiaadshacaWGPbaaaOGaeyipaWJaeqyTdu2aa0baaS qaaiaadAgaaeaacaWGLbGaamyCaaaakiabgsMiJkabew7aLnaaDaaa leaacaWGMbaabaGaamiDaiaadwhaaaaakeaacaaIXaGaeyOeI0Yaae WaaeaacaaIXaGaeyOeI0IaamizamaaDaaaleaacaWGMbaabaGaamiD aiaadwhaaaaakiaawIcacaGLPaaadaWcaaqaaiabew7aLnaaDaaale aacaWGMbaabaGaamiDaiaadwhaaaaakeaacqaH1oqzdaqhaaWcbaGa amOzaaqaaiaadwgacaWGXbaaaaaaaOqaaiaabMgacaqGMbaabaGaeq yTdu2aa0baaSqaaiaadAgaaeaacaWGLbGaamyCaaaakiabg6da+iab ew7aLnaaDaaaleaacaWGMbaabaGaamiDaiaadwhaaaaaaaGccaGL7b aaaaa@91AF@
      Where, ε f t i MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWG0bGaamyAaaaaaaa@3A9A@ is the strain at the onset of damage, ε f t u MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWG0bGaamyDaaaaaaa@3AA6@ is the ultimate strain, d f t u MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaDa aaleaacaWGMbaabaGaamiDaiaadwhaaaaaaa@39E7@ is the ultimate damage value and ε f e q MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTdu2aa0 baaSqaaiaadAgaaeaacaWGLbGaamyCaaaaaaa@3A92@ is the equivalent fiber strain defined by:
      • For Shells:
        ε f e q   =   ε x x e +   ν 21 ε y y e
      • For Solids:
        ε f e q   =   1 - ν 23 ν 32 ε x x e +   ν 23 ν 31 + ν 21 ε y y e + ν 21 ν 32 + ν 31 ε z z e

      The compression damage on fiber due to matrix buckling can be activated with the IBUCK flag and is described with a similar equation:

      d f = 0 if ε f e q ε f c i d f c u ε f e q ε f c i ε f c u ε f c i if ε f c i < ε f e q ε f c u 1 1 d f c u ε f c u ε f e q if ε f e q > ε f c u MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGMbaabeaakiabg2da9maaceaabaqbaeqabmWaaaqaaiaa icdaaeaacaqGPbGaaeOzaaqaamaaemaabaGaeqyTdu2aa0baaSqaai aadAgaaeaacaWGLbGaamyCaaaaaOGaay5bSlaawIa7aiabgsMiJkab ew7aLnaaDaaaleaacaWGMbaabaGaam4yaiaadMgaaaaakeaacaWGKb Waa0baaSqaaiaadAgaaeaacaWGJbGaamyDaaaakmaalaaabaWaaqWa aeaacqaH1oqzdaqhaaWcbaGaamOzaaqaaiaadwgacaWGXbaaaaGcca GLhWUaayjcSdGaeyOeI0IaeqyTdu2aa0baaSqaaiaadAgaaeaacaWG JbGaamyAaaaaaOqaaiabew7aLnaaDaaaleaacaWGMbaabaGaam4yai aadwhaaaGccqGHsislcqaH1oqzdaqhaaWcbaGaamOzaaqaaiaadoga caWGPbaaaaaaaOqaaiaabMgacaqGMbaabaGaeqyTdu2aa0baaSqaai aadAgaaeaacaWGJbGaamyAaaaakiabgYda8maaemaabaGaeqyTdu2a a0baaSqaaiaadAgaaeaacaWGLbGaamyCaaaaaOGaay5bSlaawIa7ai abgsMiJkabew7aLnaaDaaaleaacaWGMbaabaGaam4yaiaadwhaaaaa keaacaaIXaGaeyOeI0YaaeWaaeaacaaIXaGaeyOeI0IaamizamaaDa aaleaacaWGMbaabaGaam4yaiaadwhaaaaakiaawIcacaGLPaaadaWc aaqaaiabew7aLnaaDaaaleaacaWGMbaabaGaam4yaiaadwhaaaaake aadaabdaqaaiabew7aLnaaDaaaleaacaWGMbaabaGaamyzaiaadgha aaaakiaawEa7caGLiWoaaaaabaGaaeyAaiaabAgaaeaadaabdaqaai abew7aLnaaDaaaleaacaWGMbaabaGaamyzaiaadghaaaaakiaawEa7 caGLiWoacqGH+aGpcqaH1oqzdaqhaaWcbaGaamOzaaqaaiaadogaca WG1baaaaaaaOGaay5Eaaaaaa@A0AF@

      This fiber damage then affects the stress computation as:

      σ x x d a m   =   1 - d f C 11 ε x x e + 1 - d f 1 - d ' C 12 ε y y e

      Where, d' is the transverse matrix damage described below.
      Note: This new damage variable is introduced to consider coupling damage effect between fiber and matrix. Similar coupling is used if direction z is considered (for solid elements).
      Figure 2 shows the expected behavior in tension/compression along the fiber direction. The dashed line allows to highlight the nonlinear Young’s modulus in compression.
      Figure 2. Tension/compression test in fiber direction showing fiber damage effect on stress


      Note: Along fiber direction, the behavior is purely elastic and damaging.
    • Shear matrix damage d MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaaaa@36DC@ is introduced to represent the debonding between matrix and fibers. Its evolution is influenced by the energy release rate often used in Lemaitre-type damage model. Two elastic energy rates are considered in this model.
      • For Shells:
        Z d = 1 2 σ 12 2 G 12 + σ 13 2 G 13 Z d ' = 1 2 σ 22 + 2 E 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGAb WaaSbaaSqaaiaadsgaaeqaaOGaeyypa0ZaaSaaaeaacaaIXaaabaGa aGOmaaaadaqadaqaamaalaaabaGaeq4Wdm3aa0baaSqaaiaaigdaca aIYaaabaGaaGOmaaaaaOqaaiaadEeadaWgaaWcbaGaaGymaiaaikda aeqaaaaakiabgUcaRmaalaaabaGaeq4Wdm3aa0baaSqaaiaaigdaca aIZaaabaGaaGOmaaaaaOqaaiaadEeadaWgaaWcbaGaaGymaiaaioda aeqaaaaaaOGaayjkaiaawMcaaaqaaiaadQfadaqhaaWcbaGaamizaa qaaiaacEcaaaGccqGH9aqpdaWcaaqaaiaaigdaaeaacaaIYaaaamaa bmaabaWaaSaaaeaadaaadaqaaiabeo8aZnaaBaaaleaacaaIYaGaaG OmaaqabaaakiaawMYicaGLQmcadaqhaaWcbaGaey4kaScabaGaaGOm aaaaaOqaaiaadweadaWgaaWcbaGaaGOmaaqabaaaaaGccaGLOaGaay zkaaaaaaa@5A00@

        Where, + MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaaWaaeaaai aawMYicaGLQmcadaWgaaWcbaGaey4kaScabeaaaaa@38D1@ are the Macauley’s brackets that only considers the positive values of σ 22 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS baaSqaaiaaikdacaaIYaaabeaaaaa@395A@ . However, if compression damage described below is considered (for shells only), these brackets becomes simple parenthesis.

      • For Solids:
        Z d = 1 2 σ 12 2 G 12 + σ 23 2 G 23 + σ 13 2 G 13 Z d ' = 1 2 σ 22 + 2 E 2 + σ 33 + 2 E 3 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGAb WaaSbaaSqaaiaadsgaaeqaaOGaeyypa0ZaaSaaaeaacaaIXaaabaGa aGOmaaaadaqadaqaamaalaaabaGaeq4Wdm3aa0baaSqaaiaaigdaca aIYaaabaGaaGOmaaaaaOqaaiaadEeadaWgaaWcbaGaaGymaiaaikda aeqaaaaakiabgUcaRmaalaaabaGaeq4Wdm3aa0baaSqaaiaaikdaca aIZaaabaGaaGOmaaaaaOqaaiaadEeadaWgaaWcbaGaaGOmaiaaioda aeqaaaaakiabgUcaRmaalaaabaGaeq4Wdm3aa0baaSqaaiaaigdaca aIZaaabaGaaGOmaaaaaOqaaiaadEeadaWgaaWcbaGaaGymaiaaioda aeqaaaaaaOGaayjkaiaawMcaaaqaaiaadQfadaqhaaWcbaGaamizaa qaaiaacEcaaaGccqGH9aqpdaWcaaqaaiaaigdaaeaacaaIYaaaamaa bmaabaWaaSaaaeaadaaadaqaaiabeo8aZnaaBaaaleaacaaIYaGaaG OmaaqabaaakiaawMYicaGLQmcadaqhaaWcbaGaey4kaScabaGaaGOm aaaaaOqaaiaadweadaWgaaWcbaGaaGOmaaqabaaaaOGaey4kaSYaaS aaaeaadaaadaqaaiabeo8aZnaaBaaaleaacaaIZaGaaG4maaqabaaa kiaawMYicaGLQmcadaqhaaWcbaGaey4kaScabaGaaGOmaaaaaOqaai aadweadaWgaaWcbaGaaG4maaqabaaaaaGccaGLOaGaayzkaaaaaaa@6B63@

        This then leads to the following computation:

        Y = S u p t τ Z d + b Z d ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywaiabg2 da9iaadofacaWG1bGaamiCamaaBaaaleaacaWG0bGaeyizImQaeqiX dqhabeaakmaakaaabaGaamOwamaaBaaaleaacaWGKbaabeaakiabgU caRiaadkgacaWGAbWaa0baaSqaaiaadsgaaeaacaGGNaaaaaqabaaa aa@45BE@

        Where, b MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaaaa@36DC@ is a coupling factor.

      Depending on the value of the flag ISH, the shear matrix damage can evolve with different shapes.
      • ISH = 1: linear shape (Figure 3)
        d = 0 if Y ( t ) Y 0 Y ( t ) Y 0 Y C if d < d M A X , Y ( t ) < Y S , 1 ( 1 d M A X ) Y ( t Δ t ) Y ( t ) otherwise Y ( t ) < Y R MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiabg2 da9maaceaabaqbaeqabmWaaaqaaiaaicdaaeaacaqGPbGaaeOzaaqa aiaadMfacaGGOaGaamiDaiaacMcacqGHKjYOcaWGzbWaaSbaaSqaai aaicdaaeqaaaGcbaWaaSaaaeaacaWGzbGaaiikaiaadshacaGGPaGa eyOeI0IaamywamaaBaaaleaacaaIWaaabeaaaOqaaiaadMfadaWgaa WcbaGaam4qaaqabaaaaaGcbaGaaeyAaiaabAgaaeaacaWGKbGaeyip aWJaamizamaaBaaaleaacaWGnbGaamyqaiaadIfaaeqaaOGaaiilai aadMfacaGGOaGaamiDaiaacMcacqGH8aapcaWGzbWaaSbaaSqaaiaa dofaaeqaaOGaaiilaaqaaiaaigdacqGHsislcaGGOaGaaGymaiabgk HiTiaadsgadaWgaaWcbaGaamytaiaadgeacaWGybaabeaakiaacMca daWcaaqaaiaadMfacaGGOaGaamiDaiabgkHiTiabfs5aejaadshaca GGPaaabaGaamywaiaacIcacaWG0bGaaiykaaaaaeaacaqGVbGaaeiD aiaabIgacaqGLbGaaeOCaiaabEhacaqGPbGaae4Caiaabwgaaeaaaa aacaGL7baacaWGzbGaaiikaiaadshacaGGPaGaeyipaWJaamywamaa BaaaleaacaWGsbaabeaaaaa@7986@
        Figure 3. Shear test showing shear matrix damage effect with a linear shape
      • ISH = 2: exponential shape (Figure 4)
        d = d s a t 1 1 exp Y 0 Y t Y C if Y t > Y 0 0 otherwise MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiabg2 da9maaceaabaqbaeqabiWaaaqaaiaadsgadaWgaaWcbaGaam4Caiaa dggacaWG0bGaaGymaaqabaGcdaqadaqaaiaaigdacqGHsislciGGLb GaaiiEaiaacchadaqadaqaamaalaaabaGaamywamaaBaaaleaacaaI WaaabeaakiabgkHiTiaadMfadaqadaqaaiaadshaaiaawIcacaGLPa aaaeaacaWGzbWaaSbaaSqaaiaadoeaaeqaaaaaaOGaayjkaiaawMca aaGaayjkaiaawMcaaaqaaiaabMgacaqGMbaabaGaamywamaabmaaba GaamiDaaGaayjkaiaawMcaaiabg6da+iaadMfadaWgaaWcbaGaaGim aaqabaaakeaacaaIWaaabaGaae4BaiaabshacaqGObGaaeyzaiaabk hacaqG3bGaaeyAaiaabohacaqGLbaabaaaaaGaay5Eaaaaaa@5E97@
        Figure 4. Shear test showing shear matrix damage effect with an exponential shape
      • ISH = 3: tabulated shape (Figure 5)

        d = f D 1 Y t Y 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiabg2 da9iaadAgadaWgaaWcbaGaamiraiaaigdaaeqaaOWaaeWaaeaadaWc aaqaaiaadMfadaqadaqaaiaadshaaiaawIcacaGLPaaaaeaacaWGzb WaaSbaaSqaaiaaicdaaeqaaaaaaOGaayjkaiaawMcaaaaa@414E@

        Where, f D 1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaaBa aaleaacaWGebGaaGymaaqabaaaaa@388E@ is the function identified by IFUNCD1.
        Figure 5. Shear test showing shear matrix damage effect with a tabulated shape
      The shear matrix damage then affects the stresses computation as:
      • For Shells:
        σ x y d a m = 1 d σ x y σ y z d a m = min 1 d , 1 d ' σ y z σ z x d a m = min 1 d , 1 d ' σ z x MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqaHdp WCdaqhaaWcbaGaamiEaiaadMhaaeaacaWGKbGaamyyaiaad2gaaaGc cqGH9aqpdaqadaqaaiaaigdacqGHsislcaWGKbaacaGLOaGaayzkaa Gaeq4Wdm3aaSbaaSqaaiaadIhacaWG5baabeaaaOqaaiabeo8aZnaa DaaaleaacaWG5bGaamOEaaqaaiaadsgacaWGHbGaamyBaaaakiabg2 da9iGac2gacaGGPbGaaiOBamaabmaabaGaaGymaiabgkHiTiaadsga caGGSaGaaGymaiabgkHiTiaadsgacaGGNaaacaGLOaGaayzkaaGaeq 4Wdm3aaSbaaSqaaiaadMhacaWG6baabeaaaOqaaiabeo8aZnaaDaaa leaacaWG6bGaamiEaaqaaiaadsgacaWGHbGaamyBaaaakiabg2da9i Gac2gacaGGPbGaaiOBamaabmaabaGaaGymaiabgkHiTiaadsgacaGG SaGaaGymaiabgkHiTiaadsgacaGGNaaacaGLOaGaayzkaaGaeq4Wdm 3aaSbaaSqaaiaadQhacaWG4baabeaaaaaa@72D1@
      • For Solids:
        σ x y d a m = 1 d σ x y σ y z d a m = 1 d σ y z σ z x d a m = 1 d σ z x MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqaHdp WCdaqhaaWcbaGaamiEaiaadMhaaeaacaWGKbGaamyyaiaad2gaaaGc cqGH9aqpdaqadaqaaiaaigdacqGHsislcaWGKbaacaGLOaGaayzkaa Gaeq4Wdm3aaSbaaSqaaiaadIhacaWG5baabeaaaOqaaiabeo8aZnaa DaaaleaacaWG5bGaamOEaaqaaiaadsgacaWGHbGaamyBaaaakiabg2 da9maabmaabaGaaGymaiabgkHiTiaadsgaaiaawIcacaGLPaaacqaH dpWCdaWgaaWcbaGaamyEaiaadQhaaeqaaaGcbaGaeq4Wdm3aa0baaS qaaiaadQhacaWG4baabaGaamizaiaadggacaWGTbaaaOGaeyypa0Za aeWaaeaacaaIXaGaeyOeI0IaamizaaGaayjkaiaawMcaaiabeo8aZn aaBaaaleaacaWG6bGaamiEaaqabaaaaaa@6555@
    • Transverse matrix damage d ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaacE caaaa@3787@ allows to represent the microcracking of the matrix. Its evolution is very similar to shear matrix damage, except from the fact that a different elastic energy release rate is used:
      Y ' = S u p t τ Z d ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaCa aaleqabaGaai4jaaaakiabg2da9iaadofacaWG1bGaamiCamaaBaaa leaacaWG0bGaeyizImQaeqiXdqhabeaakmaakaaabaGaamOwamaaDa aaleaacaWGKbaabaGaai4jaaaaaeqaaaaa@42D9@
      Then, like shear matrix damage, three different evolution shapes are available depending on the ITR flag value.
      • ITR = 1: linear shape (Figure 6)
        d ' = 0 if Y ' ( t ) Y 0 ' Y ' ( t ) Y 0 ' Y C ' if d < d M A X , Y ' ( t ) < Y S , 1 ( 1 d M A X ) Y ' ( t Δ t ) Y ' ( t ) otherwise Y ' ( t ) < Y R MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaacE cacqGH9aqpdaGabaqaauaabeqadmaaaeaacaaIWaaabaGaaeyAaiaa bAgaaeaacaWGzbGaai4jaiaacIcacaWG0bGaaiykaiabgsMiJkaadM fadaWgaaWcbaGaaGimaaqabaGccaGGNaaabaWaaSaaaeaacaWGzbGa ai4jaiaacIcacaWG0bGaaiykaiabgkHiTiaadMfadaWgaaWcbaGaaG imaaqabaGccaGGNaaabaGaamywamaaBaaaleaacaWGdbaabeaakiaa cEcaaaaabaGaaeyAaiaabAgaaeaacaWGKbGaeyipaWJaamizamaaBa aaleaacaWGnbGaamyqaiaadIfaaeqaaOGaaiilaiaadMfacaGGNaGa aiikaiaadshacaGGPaGaeyipaWJaamywamaaBaaaleaacaWGtbaabe aakiaacYcaaeaacaaIXaGaeyOeI0IaaiikaiaaigdacqGHsislcaWG KbWaaSbaaSqaaiaad2eacaWGbbGaamiwaaqabaGccaGGPaWaaSaaae aacaWGzbGaai4jaiaacIcacaWG0bGaeyOeI0IaeuiLdqKaamiDaiaa cMcaaeaacaWGzbGaai4jaiaacIcacaWG0bGaaiykaaaaaeaacaqGVb GaaeiDaiaabIgacaqGLbGaaeOCaiaabEhacaqGPbGaae4Caiaabwga aeaaaaaacaGL7baacaWGzbGaai4jaiaacIcacaWG0bGaaiykaiabgY da8iaadMfadaWgaaWcbaGaamOuaaqabaaaaa@8033@
        Figure 6. Tensile test in transverse direction showing transverse matrix damage effect with a linear shape


      • ITR = 2: exponential shape (Figure 7)
        d ' = d s a t 2 1 exp Y 0 ' Y ' t Y C ' if Y ' t > Y 0 ' 0 otherwise MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaacE cacqGH9aqpdaGabaqaauaabeqacmaaaeaacaWGKbWaaSbaaSqaaiaa dohacaWGHbGaamiDaiaaikdaaeqaaOWaaeWaaeaacaaIXaGaeyOeI0 IaciyzaiaacIhacaGGWbWaaeWaaeaadaWcaaqaaiaadMfadaWgaaWc baGaaGimaaqabaGccaGGNaGaeyOeI0IaamywaiaacEcadaqadaqaai aadshaaiaawIcacaGLPaaaaeaacaWGzbWaaSbaaSqaaiaadoeaaeqa aOGaai4jaaaaaiaawIcacaGLPaaaaiaawIcacaGLPaaaaeaacaqGPb GaaeOzaaqaaiaadMfacaGGNaWaaeWaaeaacaWG0baacaGLOaGaayzk aaGaeyOpa4JaamywamaaBaaaleaacaaIWaaabeaakiaacEcaaeaaca aIWaaabaGaae4BaiaabshacaqGObGaaeyzaiaabkhacaqG3bGaaeyA aiaabohacaqGLbaabaaaaaGaay5Eaaaaaa@629A@
        Figure 7. Tensile test in transverse direction showing transverse matrix damage effect with an exponential shape


      • ITR = 3: tabulated shape (Figure 8)

        d ' = f D 2 Y ' t Y 0 ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaacE cacqGH9aqpcaWGMbWaaSbaaSqaaiaadseacaaIYaaabeaakmaabmaa baWaaSaaaeaacaWGzbGaai4jamaabmaabaGaamiDaaGaayjkaiaawM caaaqaaiaadMfadaWgaaWcbaGaaGimaaqabaGccaGGNaaaaaGaayjk aiaawMcaaaaa@4350@

        Where, f D 2 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaaBa aaleaacaWGebGaaGOmaaqabaaaaa@388F@ is the function identified by IFUNCD2.
        Figure 8. Tensile test in transverse direction showing transverse matrix damage effect with a tabulated shape
        This damage variable is supposed to occur in tension only. In compression, the microcracks of the matrix are assumed too close to recover the initial undamaged stiffness (Figure 9). However, for shells only, a specific transverse matrix damage evolution in compression can be described the same way using parameters: Y 0 C ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaaIWaGaam4qaaqabaGccaGGNaaaaa@3934@ , Y C C ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaWGdbGaam4qaaqabaGccaGGNaaaaa@3942@ , d s a t 2 C MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizamaaBa aaleaacaWGZbGaamyyaiaadshacaaIYaGaam4qaaqabaaaaa@3B63@ or IFUNCD2C.
        Figure 9. Tension/compression test in transverse direction


        This last damage variable affects the stress computation with:
        σ y y d a m   =   1 - d '   1 - d f C 12 ε x x e + 1 - d ' C 22 ε y y e                   i f     ε y y 0                                                           σ y y                                                                               i f       ε y y < 0
        Note: That additional terms are introduced when z direction is considered (for solid elements only), and a similar formula is used for the computation of the corresponding stress component σ z z . One can also notice that the coupling effect with fiber damage is similar to the one used for σ x x computation described above.
  5. The last phenomenon represented in the modified Ladeveze model is the strain rate dependency. Once again, it is assumed that the viscous effects are not the same for the fibers and the matrix.
    • In fiber direction, the viscosity affects the Young’s modulus through the introduction of a rate factor denoted F 11 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaIXaGaaGymaaqabaaaaa@3860@ :
      E 1 v i s = E 1 1 + F 11 ε ˙ ε ˙ 11 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaDa aaleaacaaIXaaabaGaamODaiaadMgacaWGZbaaaOGaeyypa0Jaamyr amaaBaaaleaacaaIXaaabeaakmaabmaabaGaaGymaiabgUcaRiaadA eadaWgaaWcbaGaaGymaiaaigdaaeqaaOWaaeWaaeaadaWcaaqaaiqb ew7aLzaacaaabaGafqyTduMbaiaadaWgaaWcbaGaaGymaiaaigdaae qaaaaaaOGaayjkaiaawMcaaaGaayjkaiaawMcaaaaa@4993@

      Where, ε ˙ is the equivalent strain rate and ε ˙ 11 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbai aadaWgaaWcbaGaaGymaiaaigdaaeqaaaaa@3945@ is the reference strain rate in direction 1.

      The rate factor equation can take different shape depending on the value of the flag LTYPE11:
      • LTYPE11 = 1: power law
        F 11 ε ˙ ε ˙ 11 = D 11 ε ˙ ε ˙ 11 n 11 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaIXaGaaGymaaqabaGcdaqadaqaamaalaaabaGafqyTduMb aiaaaeaacuaH1oqzgaGaamaaBaaaleaacaaIXaGaaGymaaqabaaaaa GccaGLOaGaayzkaaGaeyypa0JaamiramaaBaaaleaacaaIXaGaaGym aaqabaGcdaqadaqaamaalaaabaGafqyTduMbaiaaaeaacuaH1oqzga GaamaaBaaaleaacaaIXaGaaGymaaqabaaaaaGccaGLOaGaayzkaaWa aWbaaSqabeaacaWGUbWaaSbaaWqaaiaaigdacaaIXaaabeaaaaaaaa@4BF2@
      • LTYPE11 = 2: linear law
        F 11 ε ˙ ε ˙ 11 = D 11 ε ˙ ε ˙ 11 + n 11 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaIXaGaaGymaaqabaGcdaqadaqaamaalaaabaGafqyTduMb aiaaaeaacuaH1oqzgaGaamaaBaaaleaacaaIXaGaaGymaaqabaaaaa GccaGLOaGaayzkaaGaeyypa0JaamiramaaBaaaleaacaaIXaGaaGym aaqabaGcdaqadaqaamaalaaabaGafqyTduMbaiaaaeaacuaH1oqzga GaamaaBaaaleaacaaIXaGaaGymaaqabaaaaaGccaGLOaGaayzkaaGa ey4kaSIaamOBamaaBaaaleaacaaIXaGaaGymaaqabaaaaa@4CA6@
      • LTYPE11 = 3: logarithmic law
        F 11 ε ˙ ε ˙ 11 = D 11 ln ε ˙ ε ˙ 11 + + log n 11 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaIXaGaaGymaaqabaGcdaqadaqaamaalaaabaGafqyTduMb aiaaaeaacuaH1oqzgaGaamaaBaaaleaacaaIXaGaaGymaaqabaaaaa GccaGLOaGaayzkaaGaeyypa0JaamiramaaBaaaleaacaaIXaGaaGym aaqabaGcdaaadaqaaiGacYgacaGGUbWaaeWaaeaadaWcaaqaaiqbew 7aLzaacaaabaGafqyTduMbaiaadaWgaaWcbaGaaGymaiaaigdaaeqa aaaaaOGaayjkaiaawMcaaaGaayzkJiaawQYiamaaBaaaleaacqGHRa WkaeqaaOGaey4kaSIaciiBaiaac+gacaGGNbGaamOBamaaBaaaleaa caaIXaGaaGymaaqabaaaaa@5442@
      • LTYPE11 = 4: tangent hyperbolic law
        F 11 ε ˙ ε ˙ 11 = D 11 tanh n 11 ε ˙ ε ˙ 11 + MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaIXaGaaGymaaqabaGcdaqadaqaamaalaaabaGafqyTduMb aiaaaeaacuaH1oqzgaGaamaaBaaaleaacaaIXaGaaGymaaqabaaaaa GccaGLOaGaayzkaaGaeyypa0JaamiramaaBaaaleaacaaIXaGaaGym aaqabaGcciGG0bGaaiyyaiaac6gacaGGObWaaeWaaeaacaWGUbWaaS baaSqaaiaaigdacaaIXaaabeaakmaaamaabaGafqyTduMbaiaacqGH sislcuaH1oqzgaGaamaaBaaaleaacaaIXaGaaGymaaqabaaakiaawM YicaGLQmcadaWgaaWcbaGaey4kaScabeaaaOGaayjkaiaawMcaaaaa @5350@

      The fibers failure can also be affected by strain rate through the introduction of the factor, F 11 R MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaIXaGaaGymaiaadkfaaeqaaaaa@3937@ whose evolution will also depend on the flag LTYPE11 using parameters D 11 R MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacaaIXaGaaGymaiaadkfaaeqaaaaa@3935@ and n 11 R MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaaBa aaleaacaaIXaGaaGymaiaadkfaaeqaaaaa@395F@ :

      ε f t i v i s = ε f t i 1 + F 11 R ε ˙ ε ˙ 11 ε f t u v i s = ε f t u 1 + F 11 R ε ˙ ε ˙ 11 ε f c i v i s = ε f c i 1 + F 11 R ε ˙ ε ˙ 11 ε f c u v i s = ε f c u 1 + F 11 R ε ˙ ε ˙ 11 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqaH1o qzdaqhaaWcbaGaamOzaaqaaiaadshacaWGPbaaaOWaaWbaaSqabeaa caWG2bGaamyAaiaadohaaaGccqGH9aqpcqaH1oqzdaqhaaWcbaGaam OzaaqaaiaadshacaWGPbaaaOWaaeWaaeaacaaIXaGaey4kaSIaamOr amaaBaaaleaacaaIXaGaaGymaiaadkfaaeqaaOWaaeWaaeaadaWcaa qaaiqbew7aLzaacaaabaGafqyTduMbaiaadaWgaaWcbaGaaGymaiaa igdaaeqaaaaaaOGaayjkaiaawMcaaaGaayjkaiaawMcaaaqaaiabew 7aLnaaDaaaleaacaWGMbaabaGaamiDaiaadwhaaaGcdaahaaWcbeqa aiaadAhacaWGPbGaam4Caaaakiabg2da9iabew7aLnaaDaaaleaaca WGMbaabaGaamiDaiaadwhaaaGcdaqadaqaaiaaigdacqGHRaWkcaWG gbWaaSbaaSqaaiaaigdacaaIXaGaamOuaaqabaGcdaqadaqaamaala aabaGafqyTduMbaiaaaeaacuaH1oqzgaGaamaaBaaaleaacaaIXaGa aGymaaqabaaaaaGccaGLOaGaayzkaaaacaGLOaGaayzkaaaabaGaeq yTdu2aa0baaSqaaiaadAgaaeaacaWGJbGaamyAaaaakmaaCaaaleqa baGaamODaiaadMgacaWGZbaaaOGaeyypa0JaeqyTdu2aa0baaSqaai aadAgaaeaacaWGJbGaamyAaaaakmaabmaabaGaaGymaiabgUcaRiaa dAeadaWgaaWcbaGaaGymaiaaigdacaWGsbaabeaakmaabmaabaWaaS aaaeaacuaH1oqzgaGaaaqaaiqbew7aLzaacaWaaSbaaSqaaiaaigda caaIXaaabeaaaaaakiaawIcacaGLPaaaaiaawIcacaGLPaaaaeaacq aH1oqzdaqhaaWcbaGaamOzaaqaaiaadogacaWG1baaaOWaaWbaaSqa beaacaWG2bGaamyAaiaadohaaaGccqGH9aqpcqaH1oqzdaqhaaWcba GaamOzaaqaaiaadogacaWG1baaaOWaaeWaaeaacaaIXaGaey4kaSIa amOramaaBaaaleaacaaIXaGaaGymaiaadkfaaeqaaOWaaeWaaeaada Wcaaqaaiqbew7aLzaacaaabaGafqyTduMbaiaadaWgaaWcbaGaaGym aiaaigdaaeqaaaaaaOGaayjkaiaawMcaaaGaayjkaiaawMcaaaaaaa@A044@

      The expected behavior is detailed below in Figure 10.
      Figure 10. Strain rate effect on fibers direction behavior


    • In matrix direction, the shear and transverse behavior are affected by strain rate, as well. The elasticity is then modified with the introduction of the factors F 22 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaIYaGaaGOmaaqabaaaaa@3862@ and F 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaaIYaGaaGOmaaqabaaaaa@3862@ as follows:
      E 2 v i s = E 2 1 + F 22 ε ˙ ε ˙ 12 E 3 v i s = E 3 1 + F 22 ε ˙ ε ˙ 12 G 12 v i s = G 12 1 + F 12 ε ˙ ε ˙ 12 G 23 v i s = G 23 1 + F 12 ε ˙ ε ˙ 12 G 13 v i s = G 13 1 + F 12 ε ˙ ε ˙ 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGfb Waa0baaSqaaiaaikdaaeaacaWG2bGaamyAaiaadohaaaGccqGH9aqp caWGfbWaaSbaaSqaaiaaikdaaeqaaOWaaeWaaeaacaaIXaGaey4kaS IaamOramaaBaaaleaacaaIYaGaaGOmaaqabaGcdaqadaqaamaalaaa baGafqyTduMbaiaaaeaacuaH1oqzgaGaamaaBaaaleaacaaIXaGaaG OmaaqabaaaaaGccaGLOaGaayzkaaaacaGLOaGaayzkaaaabaGaamyr amaaDaaaleaacaaIZaaabaGaamODaiaadMgacaWGZbaaaOGaeyypa0 JaamyramaaBaaaleaacaaIZaaabeaakmaabmaabaGaaGymaiabgUca RiaadAeadaWgaaWcbaGaaGOmaiaaikdaaeqaaOWaaeWaaeaadaWcaa qaaiqbew7aLzaacaaabaGafqyTduMbaiaadaWgaaWcbaGaaGymaiaa ikdaaeqaaaaaaOGaayjkaiaawMcaaaGaayjkaiaawMcaaaqaaiaadE eadaqhaaWcbaGaaGymaiaaikdaaeaacaWG2bGaamyAaiaadohaaaGc cqGH9aqpcaWGhbWaaSbaaSqaaiaaigdacaaIYaaabeaakmaabmaaba GaaGymaiabgUcaRiaadAeadaWgaaWcbaGaaGymaiaaikdaaeqaaOWa aeWaaeaadaWcaaqaaiqbew7aLzaacaaabaGafqyTduMbaiaadaWgaa WcbaGaaGymaiaaikdaaeqaaaaaaOGaayjkaiaawMcaaaGaayjkaiaa wMcaaaqaaiaadEeadaqhaaWcbaGaaGOmaiaaiodaaeaacaWG2bGaam yAaiaadohaaaGccqGH9aqpcaWGhbWaaSbaaSqaaiaaikdacaaIZaaa beaakmaabmaabaGaaGymaiabgUcaRiaadAeadaWgaaWcbaGaaGymai aaikdaaeqaaOWaaeWaaeaadaWcaaqaaiqbew7aLzaacaaabaGafqyT duMbaiaadaWgaaWcbaGaaGymaiaaikdaaeqaaaaaaOGaayjkaiaawM caaaGaayjkaiaawMcaaaqaaiaadEeadaqhaaWcbaGaaGymaiaaioda aeaacaWG2bGaamyAaiaadohaaaGccqGH9aqpcaWGhbWaaSbaaSqaai aaigdacaaIZaaabeaakmaabmaabaGaaGymaiabgUcaRiaadAeadaWg aaWcbaGaaGymaiaaikdaaeqaaOWaaeWaaeaadaWcaaqaaiqbew7aLz aacaaabaGafqyTduMbaiaadaWgaaWcbaGaaGymaiaaikdaaeqaaaaa aOGaayjkaiaawMcaaaGaayjkaiaawMcaaaaaaa@9CA9@

      You can notice that the two factors are using the same strain rate reference value ε ˙ 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGafqyTduMbai aadaWgaaWcbaGaaGymaiaaikdaaeqaaaaa@3946@ and that E 3 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyramaaBa aaleaacaaIZaaabeaaaaa@37A6@ , G 23 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa aaleaacaaIYaGaaG4maaqabaaaaa@3864@ and G 13 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa aaleaacaaIYaGaaG4maaqabaaaaa@3864@ are only modified for solids. The shape of the factors F 22 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa aaleaacaaIYaGaaG4maaqabaaaaa@3864@ and F 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa aaleaacaaIYaGaaG4maaqabaaaaa@3864@ will be fixed by the flag LTYPE12, and will depend respectively on the values of D 22 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa aaleaacaaIYaGaaG4maaqabaaaaa@3864@ , n 22 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaaBa aaleaacaaIYaGaaGOmaaqabaaaaa@388A@ and D 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4ramaaBa aaleaacaaIYaGaaG4maaqabaaaaa@3864@ , n 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOBamaaBa aaleaacaaIYaGaaGOmaaqabaaaaa@388A@ .

      The fracture energy is increased with strain rate, as well, using the same factors:
      Y 0 v i s = Y 0 1 + F 12 ε ˙ ε ˙ 12 Y C v i s = Y C 1 + F 12 ε ˙ ε ˙ 12 Y 0 ' v i s = Y 0 ' 1 + F 22 ε ˙ ε ˙ 12 Y C ' v i s = Y C ' 1 + F 22 ε ˙ ε ˙ 12 Y 0 C ' v i s = Y 0 C ' 1 + F 22 ε ˙ ε ˙ 12 Y C C ' v i s = Y C C ' 1 + F 22 ε ˙ ε ˙ 12 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGzb Waa0baaSqaaiaaicdaaeaacaWG2bGaamyAaiaadohaaaGccqGH9aqp caWGzbWaaSbaaSqaaiaaicdaaeqaaOWaaeWaaeaacaaIXaGaey4kaS IaamOramaaBaaaleaacaaIXaGaaGOmaaqabaGcdaqadaqaamaalaaa baGafqyTduMbaiaaaeaacuaH1oqzgaGaamaaBaaaleaacaaIXaGaaG OmaaqabaaaaaGccaGLOaGaayzkaaaacaGLOaGaayzkaaaabaGaamyw amaaDaaaleaacaWGdbaabaGaamODaiaadMgacaWGZbaaaOGaeyypa0 JaamywamaaBaaaleaacaWGdbaabeaakmaabmaabaGaaGymaiabgUca RiaadAeadaWgaaWcbaGaaGymaiaaikdaaeqaaOWaaeWaaeaadaWcaa qaaiqbew7aLzaacaaabaGafqyTduMbaiaadaWgaaWcbaGaaGymaiaa ikdaaeqaaaaaaOGaayjkaiaawMcaaaGaayjkaiaawMcaaaqaaiaadM fadaWgaaWcbaGaaGimaaqabaGccaGGNaWaaWbaaSqabeaacaWG2bGa amyAaiaadohaaaGccqGH9aqpcaWGzbWaaSbaaSqaaiaaicdaaeqaaO Gaai4jamaabmaabaGaaGymaiabgUcaRiaadAeadaWgaaWcbaGaaGOm aiaaikdaaeqaaOWaaeWaaeaadaWcaaqaaiqbew7aLzaacaaabaGafq yTduMbaiaadaWgaaWcbaGaaGymaiaaikdaaeqaaaaaaOGaayjkaiaa wMcaaaGaayjkaiaawMcaaaqaaiaadMfadaWgaaWcbaGaam4qaaqaba GccaGGNaWaaWbaaSqabeaacaWG2bGaamyAaiaadohaaaGccqGH9aqp caWGzbWaaSbaaSqaaiaadoeaaeqaaOGaai4jamaabmaabaGaaGymai abgUcaRiaadAeadaWgaaWcbaGaaGOmaiaaikdaaeqaaOWaaeWaaeaa daWcaaqaaiqbew7aLzaacaaabaGafqyTduMbaiaadaWgaaWcbaGaaG ymaiaaikdaaeqaaaaaaOGaayjkaiaawMcaaaGaayjkaiaawMcaaaqa aiaadMfadaWgaaWcbaGaaGimaiaadoeaaeqaaOGaai4jamaaCaaale qabaGaamODaiaadMgacaWGZbaaaOGaeyypa0JaamywamaaBaaaleaa caaIWaGaam4qaaqabaGccaGGNaWaaeWaaeaacaaIXaGaey4kaSIaam OramaaBaaaleaacaaIYaGaaGOmaaqabaGcdaqadaqaamaalaaabaGa fqyTduMbaiaaaeaacuaH1oqzgaGaamaaBaaaleaacaaIXaGaaGOmaa qabaaaaaGccaGLOaGaayzkaaaacaGLOaGaayzkaaaabaGaamywamaa BaaaleaacaWGdbGaam4qaaqabaGccaGGNaWaaWbaaSqabeaacaWG2b GaamyAaiaadohaaaGccqGH9aqpcaWGzbWaaSbaaSqaaiaadoeacaWG dbaabeaakiaacEcadaqadaqaaiaaigdacqGHRaWkcaWGgbWaaSbaaS qaaiaaikdacaaIYaaabeaakmaabmaabaWaaSaaaeaacuaH1oqzgaGa aaqaaiqbew7aLzaacaWaaSbaaSqaaiaaigdacaaIYaaabeaaaaaaki aawIcacaGLPaaaaiaawIcacaGLPaaaaaaa@B656@
      Note: The compression damage parameter for transverse directions Y 0 C ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaaIWaGaam4qaaqabaGccaGGNaaaaa@3934@ and Y C C ' MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamywamaaBa aaleaacaWGdbGaam4qaaqabaGccaGGNaaaaa@3942@ are only modified for shells.
    • Finally, the last parameter affected by viscous effect is the initial yield stress, with the use of factor F R 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaWGsbGaaGimaaqabaaaaa@387B@ .
      σ Y 0 v i s = σ Y 0 1 + F R 0 ε ˙ ε ˙ R 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aa0 baaSqaaiaadMfacaaIWaaabaGaamODaiaadMgacaWGZbaaaOGaeyyp a0Jaeq4Wdm3aaSbaaSqaaiaadMfacaaIWaaabeaakmaabmaabaGaaG ymaiabgUcaRiaadAeadaWgaaWcbaGaamOuaiaaicdaaeqaaOWaaeWa aeaadaWcaaqaaiqbew7aLzaacaaabaGafqyTduMbaiaadaWgaaWcba GaamOuaiaaicdaaeqaaaaaaOGaayjkaiaawMcaaaGaayjkaiaawMca aaaa@4D75@

      Similarly, the shape of factor F R 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaWGsbGaaGimaaqabaaaaa@387B@ is dictated by the flag LTYPER0 using parameters D R 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaWGsbGaaGimaaqabaaaaa@387B@ and n R 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOramaaBa aaleaacaWGsbGaaGimaaqabaaaaa@387B@ .

      The expected behavior for transverse matrix direction (which is similar for tension and shear) is detailed below in Figure 11.
      Figure 11. Strain rate effect on matrix transverse (or shear) direction behavior


  6. The different damage variable can be output using /H3D/ELEM/DAMG/ID=Mat_ID with the keyword MODE (=I or ALL). The correspondences between modes and damage variables are:
    • Mode 1: Fiber damage d MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaaaa@36E0@
    • Mode 2: Shear matrix damage d MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaaaa@36E0@
    • Mode 3: Transverse matrix damage d' MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamizaiaacE caaaa@378B@

    The global damage index is obtained by using /H3D/ELEM/DAMG/(ID=Mat_ID) without specifying any mode. It corresponds to the maximum between the 3 damage variables.

1 P. Ladeveze, E. LeDantec, Damage modelling of the elementary ply for laminated composites, Composites Science and Technology, Volume 43, Issue 3, 1992, Pages 257-267, ISSN 0266-3538