ABAQUS user subroutines for the simulation of viscoplastic - loicz

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