Nonlinear Model Order Reduction on Polynomial Manifolds for Computational Homogenisation Problems

Model order reduction (MOR) techniques utilising nonlinear approximation spaces can search for solutions to computational homogenisation problems on low‐dimensional approximation spaces. In combination with hyperreduction techniques, this allows for computations on representative volume elements (RVEs) to be accelerated by multiple orders of magnitude. In this work, we apply a polynomial manifold approach to efficiently compute solutions to a hyperelastic quasi‐static RVE problem.