Partition of Unity Methods

6 Recovery-Based Error Estimation and Bounding in XFEM

Octavio Andrés González-Estrada¹, Juan José Ródenas García² and Stéphane P. A. Bordas³

¹Universidad Industrial de Santander, Colombia Universidad Politécnica de Valencia, Valencia, Spain² Univesity of Luxembourg, Luxembourg, UK³

6.1 Introduction

Engineering structures, in particular in aerospace engineering, are intended to operate with flawless components, especially for safety critical parts. However, there is always a possibility that cracking will occur during operation, risking catastrophic failure, and associated casualties.

The mission of damage tolerance assessment (DTA) is to assess the influence of these defects, cracks, and damage on the ability of a structure to perform safely and reliably during its service life. An important goal of DTA is to estimate the fatigue life of a structure, i.e., the time during which it remains safe given a pre-existing flaw.

DTA relies on the ability to accurately predict crack paths and growth rates in complex structures. Since the simulation of three-dimensional (3D) crack growth is either not supported by commercial software, or requires significant effort and time for the analysts and is generally not coupled to robust error indicators, reliable, quality-controlled, industrial DTA is still a major challenge in engineering practice.

The extended finite element method (XFEM) (Moës et al., 1999) is now one of many successful numerical methods to solve fracture mechanics problems. ...