On Implementation of a Computational Approach of Phase-Field Fracture to Elasto-Plastic Materials

Computational analysis of fracture in elasto-plastic materials is considered. The computational model introduces internal variables to treat with the nonlinear phenomena: a plastic strain and a damage-like variable. The former includes also plastic kinematic hardening and is commonly initiated first. The latter enables to represent fracture by mechanical damage. Additionally, the damage-parameter character is based on the theory of phase-field fracture which causes material elastic properties degradation only in a narrow material band which forms a diffused crack. Both these internal variables together with a displacement field define a structure state inside a unique quasi-static energy evolution process which allows to formulate a novel computational approach in a variational form. The evolution is approximated by a staggered time stepping procedure related to a separation of strain variables, including the plastic strain, from the damage one. Both the strain solution and damage solution at each instant are resolved by nonlinear programming algorithms implemented in an in-house MATLAB computational code whose numerical treatment incorporates approximation by finite elements. The computations with the proposed model include a simplified material element which enables to assess mutual influences of plasticity and damage processes resulting in crack nucleation and propagation.