Combination of the material force concept and the extended finite element method for mixed mode crack growth simulations

A novel approach to simulate crack growth within an extended finite element framework is presented. The introduced approach combines the material force concept and the extended finite element method (xFEM) that is not straight forward and faces the major problem that a crack tip node, which is required for the evaluation of the material force, is not available within an xFEM framework. The introduced concept enables an efficient single step evaluation of the crack state and the crack growth direction based on a continuum mechanics approach and represents an alternative to the common procedure of using the stress intensity factor solution within a stress or energy‐based empirical formulation for the determination of the crack growth direction. Two different approaches are introduced that evaluate the crack tip material force within the xFEM based on a domain or contour approach, both providing equivalent results. After an evaluation of the method, a major focus is set on crack growth investigations with increased complexity, including mixed mode loading and crack interaction with other discontinuities. The influence of different evaluation parameters is studied by comparing the results with empirical, experimental and alternative numerical solutions and confirms the applicability and capability of the proposed combination of both concepts. Copyright © 2010 John Wiley & Sons, Ltd.