A modified moment-fitted integration scheme for X-FEM applications with history-dependent material data

TitleA modified moment-fitted integration scheme for X-FEM applications with history-dependent material data
Publication TypeJournal Article
Year of Publication2018
AuthorsZ Zhang, W Jiang, JE Dolbow, and BW Spencer
JournalComputational Mechanics
Volume62
Issue2
Start Page233
Pagination233 - 252
Date Published08/2018
Abstract

We present a strategy for the numerical integration of partial elements with the eXtended finite element method (X-FEM). The new strategy is specifically designed for problems with propagating cracks through a bulk material that exhibits inelasticity. Following a standard approach with the X-FEM, as the crack propagates new partial elements are created. We examine quadrature rules that have sufficient accuracy to calculate stiffness matrices regardless of the orientation of the crack with respect to the element. This permits the number of integration points within elements to remain constant as a crack propagates, and for state data to be easily transferred between successive discretizations. In order to maintain weights that are strictly positive, we propose an approach that blends moment-fitted weights with volume-fraction based weights. To demonstrate the efficacy of this simple approach, we present results from numerical tests and examples with both elastic and plastic material response.

DOI10.1007/s00466-018-1544-2
Short TitleComputational Mechanics