8 - The embedded finite element method (E-FEM) for multicracking of quasi-brittle materials

Abstract

Dealing with brittle or quasi-brittle failure within a finite element (FE) context is a well-known problem and basically requires to implement new methods since the finite element method (FEM) has originally been thought for continuum media, i.e., without discontinuities. The models using traditional FEM and based on the linear fracture mechanics require mesh refinements in order to model the singularity of the stress field around the crack tip. Several numerical schemes have been used in this view: the double noding technique, local or general remeshing, boundary elements, cohesive zone models, smeared cracks models, and models with embedded discontinuities. The latter family is the most physically based because cracks are nothing else but real discontinuities within the material itself. Moreover the released energy corresponding to the crack opening process is dissipated onto the discontinuity. Thus no mesh dependency is observed and no numerical treatments of the strain localization are required. Their numerical implementations can be made according to two main ways: the extended finite element method (X-FEM), which corresponds to a global kinematic enrichment, and the embedded finite element method (E-FEM), which is a local enhancement.