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.
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Acknowledgements
The bulk of the work presented in this manuscript was performed while first author Ziyu Zhang was a graduate research assistant in the Duke Computational Mechanics Laboratory. The support of Duke University is gratefully acknowledged. All authors would also like to acknowledge the support of the Idaho National Laboratory’s Laboratory Directed Research and Development (LDRD) program (Project 13-071) and the Consortium for Advanced Simulation of Light Water Reactors (CASL), an Energy Innovation Hub under the U.S. Department of Energy. This manuscript has been authored by Battelle Energy Alliance, LLC under Contract No. DE-AC07-05ID14517 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.
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Zhang, Z., Jiang, W., Dolbow, J.E. et al. A modified moment-fitted integration scheme for X-FEM applications with history-dependent material data. Comput Mech 62, 233–252 (2018). https://doi.org/10.1007/s00466-018-1544-2
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DOI: https://doi.org/10.1007/s00466-018-1544-2