An adaptive spacetime discontinuous Galerkin method for cohesive models of elastodynamic fracture

This paper describes an adaptive numerical framework for cohesive fracture models based on a space- time discontinuous Galerkin (SDG) method for elastodynamics with elementwise momentum balance. Discontinuous basis functions and jump conditions written with respect to target traction values simplify the implementation of cohesive traction-separation laws in the SDG framework; no special cohesive elements or other algorithmic devices are required. We use unstructured spacetime grids in a h-adaptive implementation to adjust simultaneously the spatial and temporal resolutions. Two independent error indicators drive the adaptive refinement. One is a dissipation-based indicator that controls the accuracy of the solution in the bulk material; the second ensures the accuracy of the discrete rendering of the cohesive law. Applications of the SDG cohesive model to elastodynamic fracture demonstrate the effectiveness of the proposed method and reveal a new solution feature: an unexpected quasi-singular structure in the velocity response. Numerical examples demonstrate the use of adaptive analysis methods in resolving this structure, as well as its importance in reliable predictions of fracture kinetics.