Fixed Crack Model (Plane Stress)

Fixed crack model in 2D plane stress problems

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

Input:

--------

Material: A variable containing material properties Material.E (modulus of elasticity) ,

Material.v (poisson ratio), Material.f_t (tensile strength), Material.g_f (fracture energy divided by element size) and Material.beta (shear retention factor)

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) and Material.e_cr_l (crack strain vector), Material.e_cr_n_max (Maximium reached normal crack strain) and Material.theta (angle perpendicular to crack)

Initial values for these history variables should be zeros except for theta it is NaN

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_crco: 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.