Component-wise hyperreduction for nonlinear solid mechanics problems

arXiv (Cornell University)

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.

Authors 6

1. Stephan Ritzert Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics , RWTH Aachen University , Mies-van-der-Rohe-Str. 1 , 52074 Aachen , Germany

2. Jannick Kehls Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics , RWTH Aachen University , Mies-van-der-Rohe-Str. 1 , 52074 Aachen , Germany

3. Erik Faust Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics , RWTH Aachen University , Mies-van-der-Rohe-Str. 1 , 52074 Aachen , Germany

4. Hagen Holthusen

   Friedrich-Alexander-Universität Erlangen-Nürnberg

   Affiliation as printed

   Institute of Applied Mechanics , University of Erlangen-Nuremberg , Egerlandstraße 5 , 91058 Erlangen , Germany

5. Stefanie Reese Aachen Institute of Applied Mechanics

   University of Siegen · RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics , RWTH Aachen University , Mies-van-der-Rohe-Str. 1 , 52074 Aachen , Germany

   University of Siegen , 57076 Siegen , Germany

6. Tim Brepols Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics , RWTH Aachen University , Mies-van-der-Rohe-Str. 1 , 52074 Aachen , Germany