Extended isogeometric analysis of multi-material and multi-physics problems using hierarchical B-splines

Schmidt, Mathias; Noël, Lise; Doble, Keenan; Evans, John A.; Maute, Kurt

doi:10.1007/s00466-023-02306-x

Extended isogeometric analysis of multi-material and multi-physics problems using hierarchical B-splines

Journal Article · Mon Mar 20 00:00:00 EDT 2023 · Computational Mechanics

DOI:https://doi.org/10.1007/s00466-023-02306-x· OSTI ID:2371782

Schmidt, Mathias ^[1]; Noël, Lise ^[2]; Doble, Keenan ^[3]; Evans, John A. ^[3]; Maute, Kurt ^[3]

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Delft Univ. of Technology (Netherlands)
Univ. of Colorado, Boulder, CO (United States)

Here, this paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate conformal meshes, this work uses an extended finite element method (XFEM) to discretize the governing equations on non-conforming, embedding meshes. A flexible approach to create truncated hierarchical B-splines discretizations is presented. This approach enables the refinement of each state variable field individually to meet field-specific accuracy requirements. To obtain an immersed geometry representation that is consistent across all hierarchically refined B-spline discretizations, the geometry is immersed into a single mesh, the XFEM background mesh, which is constructed from the union of all hierarchical B-spline meshes. An extraction operator is introduced to represent the truncated hierarchical B-spline bases in terms of Lagrange shape functions on the XFEM background mesh without loss of accuracy. The truncated hierarchical B-spline bases are enriched using a generalized Heaviside enrichment strategy to accommodate small geometric features and multi-material problems. The governing equations are augmented by a formulation of the face-oriented ghost stabilization enhanced for locally refined B-spline bases. We present examples for two- and three-dimensional linear elastic and thermo-elastic problems. The numerical results validate the accuracy of our framework. The results also demonstrate the applicability of the proposed framework to large, geometrically complex problems.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

Sponsoring Organization:: Defense Advanced Research Projects Agency (DARPA); National Science Foundation (NSF); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2371782

Report Number(s):: LLNL--JRNL-842737; 1064591

Journal Information:: Computational Mechanics, Journal Name: Computational Mechanics Journal Issue: 6 Vol. 71; ISSN 0178-7675

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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Extended isogeometric analysis of multi-material and multi-physics problems using hierarchical B-splines

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