Extended finite element simulation of quasi-brittle fracture in functionally graded materials

The paper addresses the simulation of fracture processes in quasi-brittle functionally graded materials (FGMs), endowed with elastic and toughness properties which gradually vary in space. To avoid strong stress gradients, reference is made to FGMs with a weak gradation. An ad hoc extended finite element formulation, accounting for material gradation, is developed to follow the propagation of cohesive cracks in the graded medium. The effectiveness of the proposed methodology is checked simulating four points bending tests on notched beams, made of a glass-filled epoxy composite material, featuring a mechanical gradient parallel and perpendicular to the notch.