Elastic Plastic Model with Ductile Damage

Elastic plastic model with ductile damage in 3D problems

[Material_State2,D]=Elastic_Plastic_Ductile_Damage_Model(Material,Material_State,e)

Input:

Material: A variable containing material properties Material.E (modulus of elasticity), Material.v (poisson ratio), Material.f_y (yield stress), Material.g_f (normalized fracture energy), Material.Ep_eqv_0 (equivelent plastic strain at which damage initiates)

Material_State: A history variable containing material state variables at previous increment or iteration. it includes Material_State.s (stress vector) , Material_State.s_eff (effective stress), Material_State.e (strain vector), Material_State.k (hardening parameter), Material.k_D (maximium equivalent plastic strain) and Material.d (damage).

Initial values for these history variables should be zeros

IMPORTANT: for this model, this variable should be called from the last converged state of material ((i.e. end of previous increment not from the last iteration) in order to avoid spurious unloading. See Section 6.2 in Crisfrield book [1]

e: Strain vector in the current iteration.

Output:

Material_State2: A history variable containing material state variables at current iteration

D: Tangent constitutive matrix

References:

[1] Crisfield, Michael A. Non-linear finite element analysis of solids and structures. Vol. 1. Wiley, 1993.

[2] Sena-Cruz, José, Joaquim AO Barros, and Álvaro FM Azevedo. Elasto-plastic multi-fixed smeared crack model for concrete. Universidade do Minho. Departamento de Engenharia Civil (DEC), 2004.o Minho. Departamento de Engenharia Civil (DEC), 2004.