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arXiv · 2608.18868

Component-wise hyperreduction for nonlinear solid mechanics problems

Stephan Ritzert·Jannick Kehls·Erik Faust·Hagen Holthusen·Stefanie Reese·Tim Brepols
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Abstract

Hyperreduced nonlinear solid-mechanics components can be generated offline and reused as transferable building blocks across different assemblies, boundary conditions, meshes, material parameters, and constitutive models. We use proper orthogonal decomposition (POD) and energy conserving sampling and weighting (ECSW) on the component level and connect the substructures by mortar mesh tying. The POD modes and the ECSW weights and elements are computed offline from simulations of single components and the finite rigid body motions are treated by 12 additional rigid body modes per substructure. The numerical examples demonstrate errors below 1 \% for large quasi-static assemblies while evaluating less than 10 \% of the elements. The same component bases and ECSW elements are successfully reused for finite-strain viscoelastic dynamics, although they were trained only on elastic Neo-Hookean component simulations. These results indicate that component-wise hyperreduction can provide reusable reduced building blocks for modular nonlinear solid-mechanics simulations.

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Stephan Ritzert, Jannick Kehls, Erik Faust, Hagen Holthusen, Stefanie Reese, Tim Brepols. 2026-08-19. Component-wise hyperreduction for nonlinear solid mechanics problems. https://arxiv.org/abs/2608.18868

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