ABAQUS user subroutines for the simulation of viscoplastic - loicz

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R ∞ Wi Z I , Z D Zij 6 saturated yield stress for isotropic hardening in CHABOCHE's model specific work of inelastic strain in the BODNER-PARTOM model internal variables for isotropic and kinematic hardening in the BODNER-PARTOM model material parameters (i = 1, 2, 3; j = 1, 2, 3, 4), eqs. (22a,b) β, βi material parameters for damage evolution, eqs. (3b, 4) ε i e εi η i eigen-values (i = 1, 2, 3) of total strain tensor E eigen-values (i = 1, 2, 3) of elastic strain tensor E e orientation function φ(p) material function for kinematic hardening in CHABOCHE's model φ ∞ ˆ σ i vectors e i c ei saturated value of φ(p) , material parameter for kinematic hardening in CHABOCHE's model eigen-values (i = 1, 2, 3) of damage-active stress tensor ˆ S orthogonal unit vectors (i = 1, 2, 3), reference base, e i ⋅ e j = δ ij lattice vectors (i = 1, 2, 3) e εe e n , ni eigen-vectors (i = 1, 2, 3) of total and elastic strain tensors, E and E , respectively i s n ˆ i eigen-vectors (i = 1, 2, 3) of damage-active stress tensor ˆ S second order tensors B internal variable for kinematic hardening in the BODNER-PARTOM model D damage tensor Da E, E e active damage tensor total and elastic strain tensor E + , E e+ positive projections of total and elastic strain tensors, E and E e , eqs. (11a,b) E Ý i inelastic strain rate tensor in unified models H ε , H εe spectral tensors, eqs. (8a,b) I second order identity tensor
S CAUCHY stress tensor ˜ S effective stress tensor ˆ S damage-active stress tensor ˜ ′ S deviator of the damage-active stress Y D thermodynamic force conjugate to damage tensor D X backstress tensor 7
Page 1 and 2: Technical Note GKSS/WMS/01/5 intern
Page 4 and 5: 0. Nomenclature 3 1. Introduction 7
Page 8 and 9: W internal variable, eq. (20b) four
Page 10 and 11: where S is the CAUCHY stress tensor
Page 12 and 13: 12 0 for x ≤ xm 1 h(x) = 2 1− c
Page 14 and 15: flow rule: E Ý i = p Ý ˜ S ′
Page 16 and 17: 16 −1 −1 D1 = 0 , L1 = 0, Z i1
Page 18 and 19: parameters of Tables 2 and 3, and t
Page 20 and 21: 20 Fig. 1. Experiments and model pr
Page 22 and 23: 22 Fig. 3. Contour plots of the max
Page 24 and 25: 24 Fig. 5. Contour plots of directi
Page 26 and 27: 26 Fig. 6. FE-mesh and loading cond
Page 28 and 29: 28 Fig. 13. FE-mesh and loading con
Page 30 and 31: proove that the model performs well
Page 33 and 34: 6. References AI, S.H.; LUPINC, V.
Page 35 and 36: 7. Appendices: ABAQUS-Inputfiles 7.
Page 37 and 38: ** auflagerung ** *BOUNDARY, OP=NEW
Page 39 and 40: ** E, nu, Do, n, K1, K2, K3, m1 149
Page 41 and 42: ** ====== 2. load ein ** *STEP, INC
Page 43 and 44: 7.3 Appendix 3: Single crystal plat
Page 45 and 46: *NODE FILE, FREQUENCY=0 *EL FILE, F
Page 47 and 48: 7.4 Appendix 4: TiAl turbine blade
Page 49 and 50: *AMPLITUDE, NAME=CYCLEONE, DEFINITI

ABAQUS user subroutines for the simulation of viscoplastic - loicz

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