An improved stress recovery technique for the unfitted finite element analysis of discontinuous gradient fields

Abstract

Stress analysis is an all‐pervasive practice in engineering design. With displacement‐based finite element analysis, directly‐calculated stress fields are obtained in a post‐processing step by computing the gradient of the displacement field—therefore less accurate. In enriched finite element analysis (EFEA), which provides unprecedented versatility by decoupling the finite element mesh from material interfaces, cracks, and structural boundaries, stress recovery is further aggravated when such discontinuities get arbitrarily close to nodes of the mesh; the presence of small area integration elements often yields overestimated stresses, which could have a detrimental impact on nonlinear analyses (e.g., damage or plasticity) since stress concentrations are just a nonphysical numerical artifact. In this article, we propose a stress recovery procedure for enhancing the stress field in problems where the field gradient is discontinuous. The formulation is based on a stress improvement procedure (SIP) initially proposed for low‐order standard finite elements. Although generally applicable to all EFEA, we investigate the technique with the Interface‐enriched Generalized Finite Element Method and compare the procedure to other post‐processing smoothing techniques. We demonstrate that SIP for EFEA provides an enhanced stress field that is more accurate than directly‐calculated stresses—even when compared with standard FEM with fitted meshes.

An interface-enriched generalized finite element formulation for locking-free coupling of non-conforming discretizations and contact

“…As enriched nodes are only placed along the contact/coupling interfaces, we conjecture that the presence of sliver integration elements does not adversely affect the gradient field accuracy and thus the method can properly recover strains and stresses. It is worth noting that there is work [104] that aims at improving the accuracy of recovered gradient fields from enriched FEMs (and in fact unfitted FEMs in general).…”

A novel application of recovered stresses in stress intensity factors extraction methods for the generalized/extended finite element method

“…This modification, in general, doesn't penalize the recovered stresses description but enhances the computational efficiency. Other works where recovery‐based error estimators are proposed under the G/XFEM approach can be found in References 38‐46.…”