Appendix Here are the equations and functions used in the AMM. Data Preparation: Young's Module Smooth Add Mean Curve Fitting Table 1. Curve Fitting Equations Voce σ = K 0 + Q ( 1 − e − B ∈ p l ) MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaaJecqaHdp WCcqGH9aqpcaWGlbGaaGimaiabgUcaRiaadgfacaGGOaGaaGymaiab gkHiTiaadwgadaahaaWcbeqaaiabgkHiTiaadkeacqGHiiIZaaGcda ahaaWcbeqaamaaBaaameaacaWGWbGaamiBaaqabaaaaOGaaiykaaaa @45EB@ Swift σ=Α ε pl + ε 0 n MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaey ypa0JaeuyKde0aaeWaaeaacqaH1oqzdaWgaaWcbaGaamiCaiaadYga aeqaaOGaey4kaSIaeqyTdu2aaSbaaSqaaiaaicdaaeqaaaGccaGLOa GaayzkaaWaaWbaaSqabeaacaWGUbaaaaaa@4405@ Sherby σ=Qs−(Qs−Q0) e −m( ε n ) MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaey ypa0JaamyuaiaadohacqGHsislcaGGOaGaamyuaiaadohacqGHsisl caWGrbGaaGimaiaacMcacaWGLbWaaWbaaSqabeaacqGHsislcaWGTb Gaaiikaiabew7aLnaaCaaameqabaGaamOBaaaaliaacMcaaaaaaa@4841@ Ghosh σ = K ( ε o − ε p l ) n − p MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaey ypa0Jaam4saiaacIcacqaH1oqzdaWgaaWcbaGaam4BaaqabaGccqGH sislcqaH1oqzdaWgaaWcbaGaamiCaiaadYgaaeqaaOGaaiykamaaCa aaleqabaGaamOBaiabgkHiTiaadchaaaaaaa@456C@ EIMagd σ = Q 0 + A ∗ ε p l + B ( 1 − e ) − c ∗ ε p l MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaey ypa0JaamyuaiaaicdacqGHRaWkcaWGbbGaey4fIOIaeqyTdu2aaSba aSqaaiaadchacaWGSbaabeaakiabgUcaRiaadkeacaGGOaGaaGymai abgkHiTiaadwgacaGGPaWaaWbaaSqabeaacqGHsislcaWGJbGaey4f IOIaeqyTdu2aaSbaaWqaaiaadchacaWGSbaabeaaaaaaaa@4CE9@ Johnson σ=A+B∗ ε pl n MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaey ypa0JaamyqaiabgUcaRiaadkeacqGHxiIkcqaH1oqzdaqhaaWcbaGa amiCaiaadYgaaeaacaWGUbaaaaaa@40CB@ Gsell σ=A+B(1− e (−c∗ ε pl ) )∗(1+d∗ ε pl +f∗ ε pl 2 ) MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaey ypa0JaamyqaiabgUcaRiaadkeacaGGOaGaaGymaiabgkHiTiaadwga daahaaWcbeqaaiaacIcacqGHsislcaWGJbGaey4fIOIaeqyTdu2aaS baaWqaaiaadchacaWGSbaabeaaliaacMcaaaGccaGGPaGaey4fIOIa aiikaiaaigdacqGHRaWkcaWGKbGaey4fIOIaeqyTdu2aaSbaaSqaai aadchacaWGSbaabeaakiabgUcaRiaadAgacqGHxiIkcqaH1oqzdaWg aaWcbaGaamiCaiaadYgaaeqaaOWaaWbaaSqabeaacaaIYaaaaOGaai ykaaaa@5825@ Polymer σ = A + B * ε p l c + D * ε p l E * e - F * ε p l Spline Strain Rate Table 2. Strain Rate Equations Johnson & Cook σ = ( A + B ∗ ε p l n ) ∗ ( 1 + c 1 n ε ˙ ε ˙ 0 ) MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaey ypa0JaaiikaiaadgeacqGHRaWkcaWGcbGaey4fIOIaeqyTdu2aa0ba aSqaaiaadchacaWGSbaabaGaamOBaaaakiaacMcacqGHxiIkcaGGOa GaaGymaiabgUcaRiaadogacaaIXaGaamOBamaalaaabaGafqyTduMb aiaaaeaacuaH1oqzgaGaamaaBaaaleaacaaIWaaabeaaaaGccaGGPa aaaa@4D09@ Cowper Symonds σ=(A+B∗ ε pl n )∗ 1+ ε ˙ C 1 p MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaey ypa0JaaiikaiaadgeacqGHRaWkcaWGcbGaey4fIOIaeqyTdu2aa0ba aSqaaiaadchacaWGSbaabaGaamOBaaaakiaacMcacqGHxiIkdaqada qaaiaaigdacqGHRaWkdaWcaaqaaiqbew7aLzaacaaabaGaam4qaaaa aiaawIcacaGLPaaadaahaaWcbeqaamaalaaabaGaaGymaaqaaiaadc haaaaaaaaa@4AB8@ FOSTA σ = A + C ∗ ε p l m − n m MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4WdmNaey ypa0JaamyqaiabgUcaRiaadoeacqGHxiIkcqaH1oqzdaWgaaWcbaGa amiCaiaadYgaaeqaaOWaaWbaaSqabeaacaWGTbGaeyOeI0IaamOBaa aakmaaCaaaleqabaWaaWbaaWqabeaacaWGTbaaaaaaaaa@4438@ Failure Table 3. Failure Equations Johnson&Cook εf=D1+D2∗exp(D3∗σ*) MathType@MTEF@5@5@+= feaahGart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyTduMaam Ozaiabg2da9iaadseacaaIXaGaey4kaSIaamiraiaaikdacqGHxiIk ciGGLbGaaiiEaiaacchacaGGOaGaamiraiaaiodacqGHxiIkcqaHdp WCcaGGQaGaaiykaaaa@4783@ BiQuad