An efficient physics-based model order reduction for geometrically nonlinear solid mechanics

Model order reduction simplifies detailed and complex Finite Element (FE) models by solving a reduced set of equations, typically through projection methods. This work proposes a physics-based model order reduction technique that circumvents the need for training data to solve quasi-static geometrically non-linear solid mechanics utilizing the concept of modal derivatives. This method comprises two key components. Firstly, the modified Gram–Schmidt process is incorporated to ensure an orthogonal projection in the reduction procedure. Secondly, a greedy selection algorithm that constructs the projection function with the most significant modal derivatives. This proposed method is applied to various test cases, showcasing its validity and efficacy in diverse scenarios. • Physics-based Model Order Reduction for geometrically nonlinear solid mechanics. • Modified Gram–Schmidt orthogonalization for an orthogonal Galerkin projection. • Greedy selection to limit the projection size while maintaining accuracy.