Applications of a phase-field fracture model to materials with inclusions

Abstract

Fracture in materials with inclusions is considered in the computational model of this contribution which allows prediction of crack propagation. The inclusions cause that cracks may appear inside the materials or along matrix-inclusion interfaces. The presented model can treat them both using two internal variables in a fashion of damage mechanics so that fracture is a consequence of the damage. The first variable is defined at the interface represented by a thin degradable adhesive layer so that an appropriate stress-strain relationship can be obtained as in cohesive zone models. The second variable is defined in the structural domains as a phase-field fracture variable which causes elastic properties degradation in a narrow material strip that forms a smeared crack. Both these damaging schemes are expressed in a unique quasi-static energy evolution process. The numerical solution approach is thus rendered from a variational form with a staggered time stepping procedure related to a separation of deformation variables from the damage ones and using non-linear programming algorithms implemented together within an own MATLAB finite element code. The numerical simulations with the model include simplified structural and material elements.