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

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.