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

Abstract

Here, 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 into new regions of the domain, elements are split into several copies that contain pieces of the domain on either side of the crack. 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.

Authors:
 [1]; ORCiD logo [2];  [3]; ORCiD logo [2]
  1. COMAC Shanghai Aircraft Design and Research Institute, Shanghai (China)
  2. Idaho National Lab. (INL), Idaho Falls, ID (United States)
  3. Duke Univ., Durham, NC (United States)
Publication Date:
Research Org.:
Idaho National Lab. (INL), Idaho Falls, ID (United States)
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE)
OSTI Identifier:
1473961
Report Number(s):
INL/JOU-17-42013-Rev000
Journal ID: ISSN 0178-7675
Grant/Contract Number:  
AC07-05ID14517
Resource Type:
Accepted Manuscript
Journal Name:
Computational Mechanics
Additional Journal Information:
Journal Volume: 62; Journal Issue: 2; Journal ID: ISSN 0178-7675
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; extended finite element method; plasticity; moment fitting

Citation Formats

Zhang, Ziyu, Jiang, Wen, Dolbow, John E., and Spencer, Benjamin W. A modified moment-fitted integration scheme for X-FEM applications with history-dependent material data. United States: N. p., 2018. Web. doi:10.1007/s00466-018-1544-2.
Zhang, Ziyu, Jiang, Wen, Dolbow, John E., & Spencer, Benjamin W. A modified moment-fitted integration scheme for X-FEM applications with history-dependent material data. United States. doi:10.1007/s00466-018-1544-2.
Zhang, Ziyu, Jiang, Wen, Dolbow, John E., and Spencer, Benjamin W. Mon . "A modified moment-fitted integration scheme for X-FEM applications with history-dependent material data". United States. doi:10.1007/s00466-018-1544-2. https://www.osti.gov/servlets/purl/1473961.
@article{osti_1473961,
title = {A modified moment-fitted integration scheme for X-FEM applications with history-dependent material data},
author = {Zhang, Ziyu and Jiang, Wen and Dolbow, John E. and Spencer, Benjamin W.},
abstractNote = {Here, 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 into new regions of the domain, elements are split into several copies that contain pieces of the domain on either side of the crack. 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.},
doi = {10.1007/s00466-018-1544-2},
journal = {Computational Mechanics},
number = 2,
volume = 62,
place = {United States},
year = {2018},
month = {1}
}

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