Two dimensional configurational-force-driven crack propagation using the discontinuous Galerkin method with rp-adaptivity.

Abstract

This paper presents a quasi-static configurational force (CF) brittle fracture propagation method, [1], using the discontinuous Galerkin (dG) symmetric interior penalty (SIP) method, [2]. The method is derived from the first law of thermodynamics with consideration of the Griffith fracture criterion [1]. The criterion is evaluated by finding the difference between the power applied to the domain and the rate of internal energy change at every point in the domain. If a node within the element mesh satisfies the criterion, a crack will propagate in the CF direction. Around the crack tip the advantage of element specific degrees of freedom in dG methods enables simple p-adaptivity to determine the CF in the spatial domain. In the material domain r-adaptivity is implemented, where the CF direction is used to align element edges, which are then split to propagate the crack.