Energy consistent framework for continuously evolving 3D crack propagation

Abstract

This paper presents an enhanced theoretical formulation and associated computational framework for brittle fracture in elastic solids within the context of configurational mechanics, building on the authors’ previous paper, Kaczmarczyk et al. (2014). The local form of the first law of thermodynamics provides an equilibrium condition for the crack front, expressed in terms of the configurational forces. Applying the principle of maximal energy dissipation, it is shown that the direction of the crack propagation is given by the direction of the configurational forces. In combination with a fracture criterion, these are utilised to determine the position of the continuously evolving crack front. This exploitation of the crack front equilibrium condition leads to a completely new, implicit, crack propagation formulation. A monolithic solution strategy is adopted, solving simultaneously for both the material displacements (i.e. crack extension) and the spatial displacements. The resulting crack path is resolved as a discrete displacement discontinuity, where the material displacements of the nodes on the crack front change continuously, without the need for mesh splitting or the use of enrichment techniques. In order to trace the dissipative loading path, an arc-length procedure is adopted that controls the incremental crack area growth. In order to maintain mesh quality, smoothing of the mesh is undertaken as a continuous process, together with face flipping, node merging and edge splitting where necessary. Hierarchical basis functions of arbitrary polynomial order are adopted to increase the order of approximation without the need to change the finite element mesh. Performance of the formulation is demonstrated by means of three representative numerical simulations, demonstrating both accuracy and robustness.