A thermodynamically consistent discontinuous Galerkin formulation for interface separation

Abstract

This paper describes the formulation of an interface damage model, based on the discontinuous Galerkin (DG) method, for the simulation of failure and crack propagation in laminated structures. The DG formulation avoids common difficulties associated with cohesive elements. Specifically, it does not introduce any artificial interfacial compliance and, in explicit dynamic analysis, it leads to a stable time increment size which is unaffected by the presence of stiff massless interfaces. The proposed method is implemented in a finite element setting. Convergence and accuracy are demonstrated in Mode I and mixed-mode delamination in both static and dynamic analyses. Significantly, numerical results obtained using the proposed interface model are found to be independent of the value of the penalty factor that characterizes the DG formulation. By contrast, numerical results obtained using a classical cohesive method are found to be dependent on the cohesive penalty stiffnesses. As a result of this notable advantage, the proposed approach is shown to yield more accurate predictions pertaining to crack propagation under mixed-mode fracture. Furthermore, in explicit dynamic analysis, the stable time increment size calculated with the proposed method is found to be an order of magnitude larger than the maximum allowable value for classical cohesive elements.