Brittle crack propagation intersecting a contact interface within the framework of Arbitrary Lagrangian-Eulerian description of motion

Abstract

Configurational mechanics provides the theoretical basis for modelling thermodynamically consistent crack propagation in brittle materials. Using the Arbitrary Lagrangian-Eulerian (ALE) formulation, material kinematics that describe crack surface increment are coupled with spatial kinematics that describe elastic body deformation. To include the contact interaction into the model, a mortar-like formulation was exploited. While the crack surface is distant from the contact interface, contact elements act only in the spatial domain. However, once the crack surface is in the proximity of the contact zone, additional considerations are needed. Firstly, mesh cutting and mesh smoothing due to evolution of the crack surface affect the position of nodes in the material domain, requiring reconstruction of contact elements. Secondly, once the crack front reaches the contact interface, contact pressure provides an additional contribution to configurational forces driving the crack propagation. Therefore, topological changes due to crack propagation and evolution of contact surfaces are strongly coupled. Here we present for the first time the solution of this coupled problem using a monolithic approach. Examples are considered demonstrating the robustness of the proposed framework and evaluating the effect of the contact loading on the crack propagation.