A nonlinear manifold model order reduction approach for thermo‐mechanically coupled plasticity

PAMM, vol. 24

Abstract

Abstract This study employs a nonlinear manifold mode order reduction (MOR) approach to address the high computational cost inherent in multi‐physical nonlinear models, which are discretized by the finite element method (FEM), with a particular focus on thermo‐mechanically coupled plasticity under finite strain conditions. Utilizing nodal snapshots obtained from a full‐order simulation, a projection matrix is constructed through singular value decomposition (SVD), facilitating the construction of a reduced system within a lower‐dimensional space. This reduction process entails the multiplication of the discretized residual vector and stiffness matrix by a linear projection matrix, complemented by the incorporation of a nonlinear projection component to ensure accurate reconstruction within the nonlinear part. Subsequently, a comprehensive three‐dimensional benchmark test is conducted to assess the accuracy and efficacy of the reduced‐order model.

Authors 3

1. Jian Zhang Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

   Institute of Applied Mechanics, RWTH Aachen University, Aachen, Germany

2. Stefanie Reese Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

   Institute of Applied Mechanics, RWTH Aachen University, Aachen, Germany

3. Tim Brepols Aachen Institute of Applied Mechanics

   RWTH Aachen University

   Affiliation as printed

   Institute of Applied Mechanics RWTH Aachen University Aachen Germany

   Institute of Applied Mechanics, RWTH Aachen University, Aachen, Germany