Embedded symmetric positive semi-definite machine-learned elements for reduced-order modeling in finite-element simulations with application to threaded fasteners

Journal Article · Mon May 06 00:00:00 EDT 2024 · Computational Mechanics

DOI:https://doi.org/10.1007/s00466-024-02481-5· OSTI ID:2530858

Parish, Eric ^[1]; Lindsay, Payton ^[2]; Shelton, Timothy Ryan ^[2]; Mersch, John Philip ^[2]

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1. Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
2. Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Here, we present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain into an “outer” coarse-scale domain that we resolve using a finite element method (FEM) and an “inner” fine-scale domain. We then develop a machine-learned (ML) model for the impact of the inner domain on the outer domain. In essence, for solid mechanics, our machine-learned surrogate performs static condensation of the inner domain degrees of freedom. This is achieved by learning the map from displacements on the inner-outer domain interface boundary to forces contributed by the inner domain to the outer domain on the same interface boundary. We consider two such mappings, one that directly maps from displacements to forces without constraints, and one that maps from displacements to forces by virtue of learning a symmetric positive semi-definite (SPSD) stiffness matrix. We demonstrate, in a simplified setting, that learning an SPSD stiffness matrix results in a coarse-scale problem that is well-posed with a unique solution. We present numerical experiments on several exemplars, ranging from finite deformations of a cube to finite deformations with contact of a fastener-bushing geometry. We demonstrate that enforcing an SPSD stiffness matrix drastically improves the robustness and accuracy of FEM–ML coupled simulations, and that the resulting methods can accurately characterize out-of-sample loading configurations with significant speedups over the standard FEM simulations.

• Research Organization: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: NA0003525
• OSTI ID: 2530858
• Report Number(s): SAND--2024-10125J
• Journal Information: Computational Mechanics, Journal Name: Computational Mechanics Journal Issue: 6 Vol. 74; ISSN 0178-7675
• Publisher: Springer
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Contact
Machine learning
Neural network
Reduced-order modeling
Solid mechanics
Symmetric positive definite