skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

On the elimination of quadrature subcells for discontinuous functions in the eXtended Finite-Element Method
journal, January 2006

  • Ventura, G.
  • International Journal for Numerical Methods in Engineering, Vol. 66, Issue 5
  • DOI: 10.1002/nme.1570

Appropriate extended functions for X-FEM simulation of plastic fracture mechanics
journal, January 2006

  • Elguedj, T.; Gravouil, A.; Combescure, A.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issue 7-8
  • DOI: 10.1016/j.cma.2005.02.007

A finite element method for crack growth without remeshing
journal, September 1999


Moderate Degree Symmetric Quadrature Rules for the Triangle
journal, January 1975

  • Lyness, J. N.; Jespersen, D.
  • IMA Journal of Applied Mathematics, Vol. 15, Issue 1
  • DOI: 10.1093/imamat/15.1.19

A new Crack tip Enrichment Function in the Extended Finite Element Method for General Inelastic Materials
journal, January 2012


A method for dynamic crack and shear band propagation with phantom nodes
journal, January 2006

  • Song, Jeong-Hoon; Areias, Pedro M. A.; Belytschko, Ted
  • International Journal for Numerical Methods in Engineering, Vol. 67, Issue 6
  • DOI: 10.1002/nme.1652

Modeling crack discontinuities without element-partitioning in the extended finite element method: MODELING CRACKS WITHOUT ELEMENT-PARTITIONING IN THE X-FEM
journal, October 2016

  • Chin, E. B.; Lasserre, J. B.; Sukumar, N.
  • International Journal for Numerical Methods in Engineering, Vol. 110, Issue 11
  • DOI: 10.1002/nme.5436

Incremental kinematics for finite element applications
journal, December 1993

  • Rashid, M. M.
  • International Journal for Numerical Methods in Engineering, Vol. 36, Issue 23
  • DOI: 10.1002/nme.1620362302

About the use of standard integration schemes for X-FEM in solid mechanics plasticity
journal, January 2015

  • Martin, A.; Esnault, J. -B.; Massin, P.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 283
  • DOI: 10.1016/j.cma.2014.09.028

An XFEM method for modeling geometrically elaborate crack propagation in brittle materials
journal, June 2011

  • Richardson, Casey L.; Hegemann, Jan; Sifakis, Eftychios
  • International Journal for Numerical Methods in Engineering, Vol. 88, Issue 10
  • DOI: 10.1002/nme.3211

Formulation of implicit finite element methods for multiplicative finite deformation plasticity
journal, March 1990

  • Moran, B.; Ortiz, M.; Shih, C. F.
  • International Journal for Numerical Methods in Engineering, Vol. 29, Issue 3
  • DOI: 10.1002/nme.1620290304

Quadrature schemes for arbitrary convex/concave volumes and integration of weak form in enriched partition of unity methods
journal, May 2013

  • Sudhakar, Y.; Wall, Wolfgang A.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 258
  • DOI: 10.1016/j.cma.2013.01.007

Partially Symmetric Cubature Formulas for Even Degrees of Exactness
journal, June 1986

  • Wissmann, Johannes W.; Becker, Thomas
  • SIAM Journal on Numerical Analysis, Vol. 23, Issue 3
  • DOI: 10.1137/0723043

Extended finite element method in computational fracture mechanics: a retrospective examination
journal, November 2015

  • Sukumar, N.; Dolbow, J. E.; Moës, N.
  • International Journal of Fracture, Vol. 196, Issue 1-2
  • DOI: 10.1007/s10704-015-0064-8

Finite element analysis on implicitly defined domains: An accurate representation based on arbitrary parametric surfaces
journal, January 2011

  • Moumnassi, Mohammed; Belouettar, Salim; Béchet, Éric
  • Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 5-8
  • DOI: 10.1016/j.cma.2010.10.002

Generalization of selective integration procedures to anisotropic and nonlinear media
journal, September 1980

  • Hughes, Thomas J. R.
  • International Journal for Numerical Methods in Engineering, Vol. 15, Issue 9
  • DOI: 10.1002/nme.1620150914

The partition of unity finite element method: Basic theory and applications
journal, December 1996


Elastic crack growth in finite elements with minimal remeshing
journal, June 1999


MOOSE: A parallel computational framework for coupled systems of nonlinear equations
journal, October 2009


Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework: XFEM/GFEM FRAMEWORK
journal, January 2010

  • Natarajan, Sundararajan; Mahapatra, D. Roy; Bordas, Stéphane P. A.
  • International Journal for Numerical Methods in Engineering, Vol. 83, Issue 3
  • DOI: 10.1002/nme.2798

    Works referencing / citing this record:

    A general mass lumping scheme for the variants of the extended finite element method
    journal, May 2020

    • Asareh, Iman; Song, Jeong‐Hoon; Mullen, Robert L.
    • International Journal for Numerical Methods in Engineering, Vol. 121, Issue 10
    • DOI: 10.1002/nme.6308