Puck Criteria (2D)

HyperView Composite libraries expose different flavors of the general criterion of PUCK failure theory for 2D plane stress.

Simple Puck

Fiber Failure
F fiber = σ 1 X MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaBaaaleaapeGaamOzaiaadMgacaWGIbGaamyzaiaa dkhaa8aabeaak8qacqGH9aqpdaabdaWdaeaapeWaaSaaa8aabaWdbi aabo8apaWaaSbaaSqaa8qacaaIXaaapaqabaaakeaapeGaamiwaaaa aiaawEa7caGLiWoaaaa@43BF@
Where X = X T MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGybGaeyypa0Jaamiwa8aadaWgaaWcbaWdbiaadsfaa8aabeaa aaa@3A04@ or X = X C MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGybGaeyypa0Jaamiwa8aadaWgaaWcbaWdbiaadoeaa8aabeaa aaa@39F3@ if σ 1 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGdpWdamaaBaaaleaapeGaaGymaaWdaeqaaOWdbiabgwMiZkaa icdaaaa@3B0B@ or σ 1 < 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGdpWdamaaBaaaleaapeGaaGymaaWdaeqaaOWdbiabgYda8iaa icdaaaa@3A49@
Matrix Failure
F matrix = σ 2 Y 2 + τ 12 S 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaBaaaleaapeGaamyBaiaadggacaWG0bGaamOCaiaa dMgacaWG4baapaqabaGcpeGaeyypa0ZaaeWaa8aabaWdbmaalaaapa qaa8qacaqGdpWdamaaBaaaleaapeGaaGOmaaWdaeqaaaGcbaWdbiaa dMfaaaaacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiaaikdaaaGccq GHRaWkdaqadaWdaeaapeWaaSaaa8aabaWdbiaabs8apaWaaSbaaSqa a8qacaaIXaGaaGOmaaWdaeqaaaGcbaWdbiaadofaaaaacaGLOaGaay zkaaWdamaaCaaaleqabaWdbiaaikdaaaaaaa@4C1A@
Where Y = Y T MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGzbGaeyypa0Jaamywa8aadaWgaaWcbaWdbiaadsfaa8aabeaa aaa@3A09@ or Y=X Y C MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGzbGaeyypa0JaamiwaiaadMfapaWaaSbaaSqaa8qacaWGdbaa paqabaaaaa@3AD5@ if σ 2 0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaHdpWCpaWaaSbaaSqaa8qacaaIYaaapaqabaGcpeGaeyyzImRa aGimaaaa@3B87@ or
The final failure is given as:
F index =max F fiber , F matrix MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaBaaaleaapeGaamyAaiaad6gacaWGKbGaamyzaiaa dIhaa8aabeaak8qacqGH9aqpciGGTbGaaiyyaiaacIhadaWadaWdae aapeGaamOra8aadaWgaaWcbaWdbiaadAgacaWGPbGaamOyaiaadwga caWGYbaapaqabaGcpeGaaiilaiaadAeapaWaaSbaaSqaa8qacaWGTb GaamyyaiaadshacaWGYbGaamyAaiaadIhaa8aabeaaaOWdbiaawUfa caGLDbaaaaa@4F71@

Modified Puck

Fiber Failure
F fiber = σ 1 X MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaBaaaleaapeGaamOzaiaadMgacaWGIbGaamyzaiaa dkhaa8aabeaak8qacqGH9aqpdaabdaWdaeaapeWaaSaaa8aabaWdbi abeo8aZ9aadaWgaaWcbaWdbiaaigdaa8aabeaaaOqaa8qacaWGybaa aaGaay5bSlaawIa7aaaa@4439@
Where X = X T MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGybGaeyypa0Jaamiwa8aadaWgaaWcbaWdbiaadsfaa8aabeaa aaa@3A04@ or X = X C MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGybGaeyypa0Jaamiwa8aadaWgaaWcbaWdbiaadoeaa8aabeaa aaa@39F3@ if σ 1 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGdpWdamaaBaaaleaapeGaaGymaaWdaeqaaOWdbiabgwMiZkaa icdaaaa@3B0B@ or σ 1 < 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGdpWdamaaBaaaleaapeGaaGymaaWdaeqaaOWdbiabgYda8iaa icdaaaa@3A49@
Matrix Failure
F matrix = σ 2 2 Y T Y C + τ 12 S 2 + 1 Y T 1 Y C σ 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaBaaaleaapeGaamyBaiaadggacaWG0bGaamOCaiaa dMgacaWG4baapaqabaGcpeGaeyypa0ZaaSaaa8aabaWdbiaabo8apa Waa0baaSqaa8qacaaIYaaapaqaa8qacaaIYaaaaaGcpaqaa8qacaWG zbWdamaaBaaaleaapeGaamivaaWdaeqaaOWdbiaadMfapaWaaSbaaS qaa8qacaWGdbaapaqabaaaaOWdbiabgUcaRmaabmaapaqaa8qadaWc aaWdaeaapeGaaeiXd8aadaWgaaWcbaWdbiaaigdacaaIYaaapaqaba aakeaapeGaam4uaaaaaiaawIcacaGLPaaapaWaaWbaaSqabeaapeGa aGOmaaaakiabgUcaRmaabmaapaqaa8qadaWcaaWdaeaapeGaaGymaa WdaeaapeGaamywa8aadaWgaaWcbaWdbiaadsfaa8aabeaaaaGcpeGa eyOeI0YaaSaaa8aabaWdbiaaigdaa8aabaWdbiaadMfapaWaaSbaaS qaa8qacaWGdbaapaqabaaaaaGcpeGaayjkaiaawMcaaiaabo8apaWa aSbaaSqaa8qacaaIYaaapaqabaaaaa@59DA@
The final failure is given as:
F index =max F fiber , F matrix MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaBaaaleaapeGaamyAaiaad6gacaWGKbGaamyzaiaa dIhaa8aabeaak8qacqGH9aqpciGGTbGaaiyyaiaacIhadaWadaWdae aapeGaamOra8aadaWgaaWcbaWdbiaadAgacaWGPbGaamOyaiaadwga caWGYbaapaqabaGcpeGaaiilaiaadAeapaWaaSbaaSqaa8qacaWGTb GaamyyaiaadshacaWGYbGaamyAaiaadIhaa8aabeaaaOWdbiaawUfa caGLDbaaaaa@4F71@

Puck2D

Fiber Failure
F fiber = σ 1 X MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaBaaaleaapeGaamOzaiaadMgacaWGIbGaamyzaiaa dkhaa8aabeaak8qacqGH9aqpdaabdaWdaeaapeWaaSaaa8aabaWdbi abeo8aZ9aadaWgaaWcbaWdbiaaigdaa8aabeaaaOqaa8qacaWGybaa aaGaay5bSlaawIa7aaaa@4439@
Where X = X T MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGybGaeyypa0Jaamiwa8aadaWgaaWcbaWdbiaadsfaa8aabeaa aaa@3A04@ or X = X C MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGybGaeyypa0Jaamiwa8aadaWgaaWcbaWdbiaadoeaa8aabeaa aaa@39F3@ if σ 1 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGdpWdamaaBaaaleaapeGaaGymaaWdaeqaaOWdbiabgwMiZkaa icdaaaa@3B0B@ or σ 1 < 0 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGdpWdamaaBaaaleaapeGaaGymaaWdaeqaaOWdbiabgYda8iaa icdaaaa@3A49@
Matrix Failure
Three failures modes are developed:
Mode A
When σ 2 >0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaHdpWCpaWaaSbaaSqaa8qacaaIYaaapaqabaGcpeGaeyOpa4Ja aGimaaaa@3AC9@
F matrix A = τ 12 S 2 + 1 P || + Y T S 2 σ 2 Y T 2 + P || + σ 2 S MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaDaaaleaapeGaamyBaiaadggacaWG0bGaamOCaiaa dMgacaWG4baapaqaa8qacaWGbbaaaOGaeyypa0ZaaOaaa8aabaWdbm aabmaapaqaa8qadaWcaaWdaeaapeGaaeiXd8aadaWgaaWcbaWdbiaa igdacaaIYaaapaqabaaakeaapeGaam4uaaaaaiaawIcacaGLPaaapa WaaWbaaSqabeaapeGaaGOmaaaakiabgUcaRmaabmaapaqaa8qacaaI XaGaeyOeI0Iaamiua8aadaqhaaWcbaWdbiabgwQiEjaacYhacaGG8b aapaqaa8qacqGHRaWkaaGcdaWcaaWdaeaapeGaamywa8aadaWgaaWc baWdbiaadsfaa8aabeaaaOqaa8qacaWGtbaaaaGaayjkaiaawMcaa8 aadaahaaWcbeqaa8qacaaIYaaaaOWaaeWaa8aabaWdbmaalaaapaqa a8qacaqGdpWdamaaBaaaleaapeGaaGOmaaWdaeqaaaGcbaWdbiaadM fapaWaaSbaaSqaa8qacaWGubaapaqabaaaaaGcpeGaayjkaiaawMca a8aadaahaaWcbeqaa8qacaaIYaaaaaqabaGccqGHRaWkcaWGqbWdam aaDaaaleaapeGaeyyPI4LaaiiFaiaacYhaa8aabaWdbiabgUcaRaaa kmaalaaapaqaa8qacaqGdpWdamaaBaaaleaapeGaaGOmaaWdaeqaaa GcbaWdbiaadofaaaaaaa@6617@
Mode B
When σ 2 <0 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaHdpWCpaWaaSbaaSqaa8qacaaIYaaapaqabaGccqGH8aappeGa aGimaaaa@3AC5@ and 0 σ 2 τ 12 R A τ 21 c MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaaIWaGaeyizIm6aaqWaa8aabaWdbmaalaaapaqaa8qacaqGdpWd amaaBaaaleaapeGaaGOmaaWdaeqaaaGcbaWdbiaabs8apaWaaSbaaS qaa8qacaaIXaGaaGOmaaWdaeqaaaaaaOWdbiaawEa7caGLiWoacqGH KjYOdaWcaaWdaeaapeGaamOua8aadaqhaaWcbaWdbiabgwQiEjabgw QiEbWdaeaapeGaamyqaaaaaOWdaeaapeWaaqWaa8aabaWdbiaabs8a paWaaSbaaSqaa8qacaaIYaGaaGymaiaadogaa8aabeaaaOWdbiaawE a7caGLiWoaaaaaaa@5076@
F matrix B = 1 S τ 12 2 + P || σ 2 2 + P || σ 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaDaaaleaapeGaamyBaiaadggacaWG0bGaamOCaiaa dMgacaWG4baapaqaa8qacaWGcbaaaOGaeyypa0ZaaSaaa8aabaWdbi aaigdaa8aabaWdbiaadofaaaWaaeWaa8aabaWdbmaakaaapaqaa8qa caqGepWdamaaDaaaleaapeGaaGymaiaaikdaa8aabaWdbiaaikdaaa GccqGHRaWkdaqadaWdaeaapeGaamiua8aadaqhaaWcbaWdbiabgwQi EjaacYhacaGG8baapaqaa8qacqGHsislaaGccaqGdpWdamaaBaaale aapeGaaGOmaaWdaeqaaaGcpeGaayjkaiaawMcaa8aadaahaaWcbeqa a8qacaaIYaaaaaqabaGccqGHRaWkcaWGqbWdamaaDaaaleaapeGaey yPI4LaaiiFaiaacYhaa8aabaWdbiabgkHiTaaakiaabo8apaWaaSba aSqaa8qacaaIYaaapaqabaaak8qacaGLOaGaayzkaaaaaa@5BBE@
Mode C
Otherwise
F matrix C = τ 12 2 1+ P S 2 + σ 2 Y C 2 Y C σ 2 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGgbWdamaaDaaaleaapeGaamyBaiaadggacaWG0bGaamOCaiaa dMgacaWG4baapaqaa8qacaWGdbaaaOGaeyypa0ZaamWaa8aabaWdbm aabmaapaqaa8qadaWcaaWdaeaapeGaaeiXd8aadaWgaaWcbaWdbiaa igdacaaIYaaapaqabaaakeaapeGaaGOmamaabmaapaqaa8qacaaIXa Gaey4kaSIaamiua8aadaqhaaWcbaWdbiabgwQiEjabgwQiEbWdaeaa peGaeyOeI0caaaGccaGLOaGaayzkaaGaam4uaaaaaiaawIcacaGLPa aapaWaaWbaaSqabeaapeGaaGOmaaaakiabgUcaRmaabmaapaqaa8qa daWcaaWdaeaapeGaae4Wd8aadaWgaaWcbaWdbiaaikdaa8aabeaaaO qaa8qacaWGzbWdamaaBaaaleaapeGaam4qaaWdaeqaaaaaaOWdbiaa wIcacaGLPaaapaWaaWbaaSqabeaapeGaaGOmaaaaaOGaay5waiaaw2 faamaalaaapaqaa8qacaWGzbWdamaaBaaaleaapeGaam4qaaWdaeqa aaGcbaWdbiabgkHiTmaabmaapaqaa8qacaqGdpWdamaaBaaaleaape GaaGOmaaWdaeqaaaGcpeGaayjkaiaawMcaaaaaaaa@612B@
Where, for all the above equations we define:
R A = S 2 P || 1+2 P || Y C S 1 MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGsbWdamaaDaaaleaapeGaeyyPI4LaeyyPI4fapaqaa8qacaWG bbaaaOGaeyypa0ZaaSaaa8aabaWdbiaadofaa8aabaWdbiaaikdaca WGqbWdamaaDaaaleaapeGaeyyPI4LaaiiFaiaacYhaa8aabaWdbiab gkHiTaaaaaGcdaqadaWdaeaapeWaaOaaa8aabaWdbiaaigdacqGHRa WkcaaIYaGaamiua8aadaqhaaWcbaWdbiabgwQiEjaacYhacaGG8baa paqaa8qacqGHsislaaGcdaWcaaWdaeaapeGaamywa8aadaWgaaWcba Wdbiaadoeaa8aabeaaaOqaa8qacaWGtbaaaaWcbeaakiabgkHiTiaa igdaaiaawIcacaGLPaaaaaa@534E@
τ 21c =S 1+2 P MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaqGepWdamaaBaaaleaapeGaaGOmaiaaigdacaWGJbaapaqabaGc peGaeyypa0Jaam4uamaakaaapaqaa8qacaaIXaGaey4kaSIaaGOmai aadcfapaWaa0baaSqaa8qacqGHLkIxcqGHLkIxa8aabaWdbiabgkHi Taaaaeqaaaaa@4426@
P = P || R A S MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacaWGqbWdamaaDaaaleaapeGaeyyPI4LaeyyPI4fapaqaa8qacqGH sislaaGccqGH9aqpcaWGqbWdamaaDaaaleaapeGaeyyPI4LaaiiFai aacYhaa8aabaWdbiabgkHiTaaakmaalaaapaqaa8qacaWGsbWdamaa DaaaleaapeGaeyyPI4LaeyyPI4fapaqaa8qacaWGbbaaaaGcpaqaa8 qacaWGtbaaaaaa@4935@
Being and , in Puck’s theory, the inclination parameters respectively on the tension and compression side.
The following values are used:
GFRP CFRP OTHERWISE
0.25 0.30 0.2
0.30 0.35 0.3

Syntax

PuckFT(tensor,xt,xc,yt,yc,s,criterion,output2d,sets,plies,elems,parts,props,pool_name,layer_index,opt_str)

Arguments

tensor
Stress table
xt
Allowable tensile stress in ply material direction 1
xc
Allowable compressive stress in ply material direction 1
yt
Allowable tensile stress in ply material direction 2
yc
Allowable compressive stress in ply material direction 2
s
Allowable in-plane shear stress
criterion
Puck Criterion: simple, modified, General2D, Glass2D, Carbon2D (D=simple)
output2d
Puck 2D output mode: value or mode (0=fiber failure, 1,2,3=matrix failure mode A,B,C) (D=value)
sets
Set table (D=NULL)
plies
Ply table (D=NULL)
elems
Element table (D)
parts
Part table (D)
props
Property table (D)
pool_name
Pool name (D=@current_pool)
layer_index
Layer index (D=@current_slice_index)
opt_str
This is an optional argument, which can passed if needed (D=option).