Modeling curved interfaces without element‐partitioning in the extended finite element method

Chin, Eric B.; Sukumar, N.

doi:10.1002/nme.6150

Title: Modeling curved interfaces without element‐partitioning in the extended finite element method

Journal Article · 16 July 2019 · International Journal for Numerical Methods in Engineering

DOI: https://doi.org/10.1002/nme.6150 · OSTI ID:1543011

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Department of Civil and Environmental Engineering University of California, Davis Davis California

Summary In this paper, we model holes and material interfaces (weak discontinuities) in two‐dimensional linear elastic continua using the extended finite element method on higher‐order (spectral) finite element meshes. Arbitrary parametric curves such as rational Bézier curves and cubic Hermite curves are adopted in conjunction with the level set method to represent curved interfaces. Efficient computation of weak form integrals with polynomial integrands is realized via the homogeneous numerical integration scheme—a method that uses Euler's homogeneous function theorem and Stokes' theorem to reduce integration to the boundary of the domain. Numerical integration on cut elements requires the evaluation of a one‐dimensional integral over a parametric curve, and hence, the need to partition curved elements is eliminated. To improve stiffness matrix conditioning, ghost penalty stabilization and the Jacobi preconditioner are used. For material interface problems, we develop an enrichment function that captures weak discontinuities on spectral meshes. Taken together, we show through numerical experiments that these advances deliver optimal algebraic rates of convergence with h ‐refinement ( p =1,2,…,5) and exponential rates of convergence with p ‐refinement ( p =1,2,…,7) for elastostatic problems with holes and material inclusions on Cartesian p th‐order spectral finite element meshes.

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Sponsoring Organization:: USDOE

OSTI ID:: 1543011

Journal Information:: International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering Journal Issue: 5 Vol. 120; ISSN 0029-5981

Publisher:: Wiley Blackwell (John Wiley & Sons)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

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