Isotropic Damage Model (Plane Stress)

Isotropic damage model in 2D plane stress problems

function [Material_State2,D_crco]=Isotropic_Damage_Model(Material,Material_State,e)

Input:

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Material: A variable containing material properties Material.E (modulus of elasticity), Material.v (poisson ratio), Material.f_t (tensile strength) and Material.g_f (fracture energy divided by element size)

Material_State: A history variable containing material state variables at previous increment or iteration. it includes Material_State.s (stress vector) , Material_State.e (strain vector),Material_State.e_eq (equivalent strain) ,Material_State.k (hardening parameter) and Material_State.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:

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

D_crco: Tangent constitutive matrix

References:

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