Polyhedral finite elements for nonlinear solid mechanics using tetrahedral subdivisions and dual-cell aggregation

Bishop, Joseph E.; Sukumar, N.

doi:10.1016/j.cagd.2019.101812

Polyhedral finite elements for nonlinear solid mechanics using tetrahedral subdivisions and dual-cell aggregation

Journal Article · Tue Jan 07 00:00:00 EST 2020 · Computer Aided Geometric Design

DOI:https://doi.org/10.1016/j.cagd.2019.101812· OSTI ID:1601258

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Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Univ. of California, Davis, CA (United States)

General polyhedral discretizations offer several advantages over classical approaches consisting of standard tetrahedra and hexahedra. These include increased flexibility and robustness in the meshing of geometrically complex domains and higher-quality solutions for both finite element and finite volume schemes. Currently, the use of general polyhedra is hampered by the lack of general-purpose polyhedral meshing algorithms and software. One approach for generating polyhedral meshes is the use of tetrahedral subdivisions and dual-cell aggregation. In this approach, each tetrahedron of an existing tetrahedral mesh is subdivided using one of several subdivision schemes. Polyhedral-dual cells may then be formed and formulated as finite elements with shape functions obtained through the use of generalized barycentric coordinates. We explore the use of dual-cell discretizations for applications in nonlinear solid mechanics using a displacement-based finite element formulation. We present verification examples that yield optimal rates of convergence. Accuracy of the methodology is demonstrated via several nonlinear examples that include large deformation and plasticity.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1601258

Report Number(s):: SAND--2020-1024J; 683263

Journal Information:: Computer Aided Geometric Design, Journal Name: Computer Aided Geometric Design Journal Issue: C Vol. 77; ISSN 0167-8396

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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97 MATHEMATICS AND COMPUTING
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Polyhedral finite elements for nonlinear solid mechanics using tetrahedral subdivisions and dual-cell aggregation

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