A quasi-static computational model for interface and phase-field fracture in domains with inclusions

Abstract

A computational model fracture in materials with inclusions is considered. The proposed model allows to predict crack initiation and growth in quasi-brittle materials. The inclusions cause that cracks may appear inside the matrix materials or along matrix-inclusion interfaces. The model can treat them both using two internal variables in a form considered in damage mechanics so that crack formation process is a consequence of a material degradation. The first of the damage variables is defined at matrix-inclusion interfaces and it is related to by a thin degradable adhesive layer so that an adequate stress-strain relation is rendered as in common cohesive zone models. The second variable is defined in the structural domains, matrix plus inclusions, as a phase-field fracture variable which causes domain elastic properties degradation in a narrow material strip that results in a diffuse form of a 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 obtained by a staggered time-stepping procedure related to a separation of deformation variables from the damage ones, and by using sequential quadratic programming algorithms implemented within a MATLAB finite element code. The numerical simulations with the model include simplified structural and material elements with inclusions.