A robust interface finite element formulation for modeling brittle material failure problems

Abstract

Failure of many brittle materials and structures can be modeled using interface-oriented finite elements combined with intrinsic cohesive zone models. The discontinuous Galerkin (DG) finite element method provides an innovative framework for modeling brittle crack propagation with zero-thickness interface elements, which can accommodate extrinsic cohesive laws to avoid the artificial compliance required in intrinsic cohesive models. However, robust formulations and implementations of DG methods are critical in alleviating the well-known convergence issues for both crack nucleation and propagation with reduced instability. This paper presents a robust interface element formulation by modifying the incomplete interior penalty Galerkin (IIPG) method, which successfully avoids the initial element interface penetration across elements that occurs prior to crack nucleation, and thereby greatly reduces the instability issue as cracks open. We further verified and validated our implementation by using a bar tension test and a beam fracturing benchmark. The robustness of our proposed interface element method was demonstrated by a micromechanics fiber/matrix debonding problem with 64 fibers embedded in a bulk matrix.