A variational multiscale discontinuous Galerkin formulation for both implicit and explicit dynamic modeling of interfacial fracture

Abstract

A stabilized Discontinuous Galerkin method is presented for modeling interfacial debonding under dynamic conditions. The method’s distinctive feature is its treatment of the inelastic gap at the interface as an internal variable that is evolved through a traction–separation constitutive model, enabling initially perfect adhesion to be captured. Numerical stability is derived using Variational Multiscale ideas, and comparisons are drawn with both the intrinsic cohesive zone method and hybrid Discontinuous Galerkin-cohesive zone method to expose subtle differences. The proposed formulation is applied to model the nonlinear response of a composite unit cell under impact loading. Both explicit and implicit time integration schemes provide similar accuracy and stability, and the critical time step for explicit analyses is only slightly reduced below the value for the continuous Galerkin mesh without an interface. Further studies of mesh refinement and adjustments to the initial elastic interface stiffness in the reference cohesive zone model reveal the improved accuracy of the Variational Multiscale Discontinuous Galerkin method on coarser grids.