Phase-field modeling of brittle fracture using automatically oriented exponential finite elements

In the recent decade, there has been a growing interest in using the phase-field approach to model fracture processes in various materials. Conventional phase-field implementations can simulate fracture processes using bi-linear finite element (LFE) shape functions but at the expense of a very fine mesh. In contrast, exponential finite element (EFE) shape functions can predict sharp gradients in solution variables with coarse meshes due to their exponential nature. A potential advantage lies in reducing the number of elements in the problem without losing accuracy in the solution. However, EFE shape functions do not yield a good approximation unless they are oriented relative to the expected crack propagation path. This study uses an approximate analysis using LFE shape functions to orient the EFE shape functions before the computations. Computational advantages are reported in terms of accuracy in predicted load responses and the computational times incurred.