Assumed enhanced strain and the extended finite element methods: A unification of concepts

We present strong and weak forms of boundary-value problems for a solid with a cohesive–frictional crack. Two commonly used techniques for enhancing the finite element (FE) interpolation are considered: the assumed enhanced strain (AES) and the extended FE methods. We compare and contrast the FE approximations involved in these techniques. The AES method employs a piecewise constant interpolation of slip that is discontinuous across element boundaries. In contrast, the extended FE method interpolates slip continuously across element boundaries. Through numerical examples, we discuss the implications of these approximations to the calculated overall deformation field in the regime of infinitesimal deformation. With only a Heaviside enrichment, we find the AES method to predict larger slip (i.e., softer response) compared to the extended FE solution. We ascribe the discrepancy to the lack of higher-order crack tip enhancement in the extended FE solution. Finally, we compare the slip predicted by the above FE enhancement techniques to that calculated by classical nonlinear contact mechanics algorithm for the case where the crack traverses the element sides.