Asynchronous Spacetime Discontinuous Galerkin Formulation for a Hyperbolic Time-Delay Bulk Damage Model

Abstract

A bulk damage formulation is presented for failure analysis of brittle materials under dynamic loading. A time-delay ordinary differential equation (ODE) is used to model damage evolution. The evolution is driven by the difference between a target static damage value and the instantaneous damage value. A damage length scale is introduced from the model’s intrinsic relaxation time and elastic wave speeds. This length scale addresses the mesh sensitivity problem of some existing damage formulations for dynamic fracture, with less computational effort than some other existing remedies. The authors use the asynchronous spacetime discontinuous Galerkin (aSDG) method for the solution of the resulting hyperbolic system of equations. Local and asynchronous solution process, linear complexity of the solution versus the number of elements, local recovery of balance properties, and high spatial and temporal orders of accuracy are some of the main advantages of the aSDG method. Several numerical examples are presented to demonstrate mesh insensitivity of the method and the effect of boundary conditions on dynamic fracture patterns.