A robust and scalable unfitted adaptive finite element framework for nonlinear solid mechanics

In this work, we bridge standard Adaptive Mesh Refinement and coarsening (AMR) on scalable octree background meshes and robust unfitted Finite Element (FE) formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics problems posed on complex geometries, as an alter...

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Veröffentlicht in:Computer methods in applied mechanics and engineering Jg. 386; S. 114093
Hauptverfasser: Badia, Santiago, Caicedo, Manuel A., Martín, Alberto F., Principe, Javier
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 01.12.2021
Elsevier BV
Schlagworte:
Adaptive mesh refinement
Cantilever beams
Compressibility
Embedded boundary methods
Finite element method
Grid refinement (mathematics)
Materials selection
Mathematical analysis
Mechanics
Mesh generation
Nonlinear solid mechanics
Octrees
Parallel computers
Parallel computing
Robustness (mathematics)
Solid mechanics
Tree-based meshes
Unfitted finite elements
Nonlinear solid mechanics
Parallel computing
Adaptive mesh refinement
Tree-based meshes
Unfitted finite elements
Embedded boundary methods
ISSN:0045-7825, 1879-2138
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Zusammenfassung:In this work, we bridge standard Adaptive Mesh Refinement and coarsening (AMR) on scalable octree background meshes and robust unfitted Finite Element (FE) formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics problems posed on complex geometries, as an alternative to standard body-fitted formulations, unstructured mesh generation and graph partitioning strategies. We pay special attention to those aspects requiring a specialized treatment in the extension of the unfitted h-adaptive Aggregated Finite Element Method (h-AgFEM) on parallel tree-based adaptive meshes, recently developed for linear scalar elliptic problems, to handle nonlinear problems in solid mechanics. In order to accurately and efficiently capture localized phenomena that frequently occur in nonlinear solid mechanics problems, we perform pseudo time-stepping in combination with h-adaptive dynamic mesh refinement and re-balancing driven by a-posteriori error estimators. The method is implemented considering both irreducible and mixed (u/p) formulations and thus it is able to robustly face problems involving incompressible materials. In the numerical experiments, both formulations are used to model the inelastic behavior of a wide range of compressible and incompressible materials. First, a selected set of benchmarks is reproduced as a verification step. Second, a set of experiments is presented with problems involving complex geometries. Among them, we model a cantilever beam problem with spherical hollows distributed in a simple cubic (SC) array. This test involves a discrete domain with up to 11.7M Degrees Of Freedom (DOFs) solved in less than two hours on 3072 cores of a parallel supercomputer. •A robust adaptive unfitted finite element method for nonlinear solid mechanics.•Methodology to deal with history variables and aggregated finite elements.•Framework able to capture complex solid geometries without body-fitted meshes.•Parallel scalability via tree-based meshes and scalable nonlinear solvers.
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ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2021.114093