Partition of Unity Methods

11 XFEM Modeling of Cracked Elastic-Plastic Solids

Emilio Martínez-Pañeda

Department of Civil and Environmental Engineering, Imperial College London, London, UK

11.1 Introduction

The eXtended finite element method (XFEM) was developed initially for elastic solids and its applications have been mostly limited to the context of linear elastic fracture mechanics (Moës et al., 1999, Li et al., 2018). Previous chapters exploited this approximation. However, most materials exhibit inelastic behavior, particularly in the vicinity of cracks and other stress concentrators. For example, characterizing the local crack tip behavior in metals inevitably requires taking into consideration the role of dislocation densities and plastic deformations (Martínez-Pañeda et al., 2019). A variety of material models can be used to characterize metallic fracture and several of them have been successfully coupled with the XFEM, including conventional von Mises plasticity (Elguedj et al., 2006, Martin et al., 2015), Lemaitre’s damage-plasticity model (Broumand and Khoei, 2013), and strain gradient plasticity (Martínez-Pañeda et al., 2017). This chapter describes some of these endeavors and provides an introduction to the modeling of fracture problems in elastic-plastic solids using XFEM.

11.2 Conventional von Mises Plasticity

We shall start by the constitutive model that is arguably the most widely used to describe material deformation in elastic-plastic solids: von Mises J2 plasticity theory (Dunne ...