General Consistency of Strong Discontinuity Kinematics in Embedded Finite Element Method (E-FEM) Formulations

Abstract

This paper performs an in-depth study of the theoretical basis behind the strong discontinuity methods to improve local fracture simulations using the Embedded Finite Element Method (E-FEM). The process starts from a review of the elemental enhancement functions found in current E-FEM literature, providing the reader a solid context of E-FEM fundamentals. A set of theoretical pathologies is then discussed, which prevent current frameworks from attaining full kinematic consistency and introduce unintended mesh dependencies. Based on this analysis, a new proposal of strong discontinuity enhancement functions is presented considering generalised fracture kinematics in a full tridimensional setting and a more robust definition of internal auxiliary functions. Element-level simulations are performed to compare the outputs within a group of selected E-FEM approaches, including the novel proposal. Simulations show that the new element formulation grants a wider level of basic kinematic coherence between the local fracture outputs and element kinematics, demonstrating an increase in robustness that might drive the usefulness of E-FEM techniques for fracture simulations to a higher level.

On the Use of Drilling Degrees of Freedom to Stabilise the Augmented Finite Element Method

“…The AFEM differs significantly from other strong discontinuity approaches, such as the numerous embedded finite element methods (EFEM) or the extended finite element method (XFEM) (see, e.g., Refs. [15,[30][31][32][33][34][35][36][37]). Indeed, the cohesive internal tractions are treated similarly to the external tractions, and no discontinuous displacement or strain field is introduced.…”