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Tham khảo tài liệu 'mechanics of materials 2010 part 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 21 19.9 fCase Stu Dian dy J2 Plasticity von Mises Plasticity 2. Consistency condition F r.i A 0 9s dq dA 19.119 from which we solve the plastic multiplier 2Gs e A 2Gs s ị -Ạ- ơy Epepffw3s s 19.120 3. Tangential stress-strain relation deviatoric s G ep e 19.121 where G 2GTa 2Gs 0 s 1 Gep 2G I 4 - ------ ------- 1 Gs s ay Epepff ự3s s 19.122 67 Note that isotropic hardening softening is a poor representation of plastic behavior under cyclic loading because of the Bauschinger effect. 19.9.2 Kinematic Hardening Softening J2 plasticity 68 Kinematic hardening softening developed by Prager 1956 involves a shift of the origin of the yield surface see figure 19.14 . Here kinematic hardening softening captures the Bauschinger effect in a more realistic manner than the isotropic hardening softening. 1. Yield function F s a 1 s a s a 19.123 3 G 0 2. Consistency condition plastic multiplier 2G s a e s a s a 2G C 19.124 Victor Saouma Mechanics of Materials II 3D PLASTICITY iaj LU where C Ep 19.125 and C is related to a the backstress by a Ce XC s - a 19.126 For perfectly plastic behavior C 0 and a 0. 3. Tangential stress-strain relation deviatoric s Gep e 19.127 where G _2G G- 2G s - a 0 s - a 1 19128 Gep 2G I4 s - a s - a 2G C 19.128 19.10 Computer Implementation Written by Eric Hansen SUBROUTINE pd_strain Outfid Logfid Pstfid Lclfid PD_STRAIN - Strain controlled parabolic Drucker-Prager model Variables required ----------------- Outfid Output file ID Logfid Log file ID Pstfid Post file ID Lclfid Localization file ID Variables returned none Subroutine called by -------------------- p_drucker.f90 Parabolic Drucker-Rrager model Functions subroutines called --------.------------------ alloc8.f90 Allocate memory space in array Kmn el_ten1.f90 Construct 4th order elastic stiffness tensor Variable definition Eo_ten Et_ten alpha alpha_bar phi_inc tr_sig tr_eps phibar_inc w_ten wbar_ten y_hat_pr Elastic stiffness tensor Continuum tangent stiffness tensor Inverse damage-effect tensor .
