# Component based model order reduction with mortar tied contact for nonlinear quasi-static mechanical problems

arXiv: https://arxiv.org/abs/2407.02072 · HTML: https://mlsanity.com/paper/2407.02072/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2024.

## Built on by (most cited first, 1 of 1)

- [Autoencoder-based non-intrusive model order reduction in continuum mechanics](https://mlsanity.com/paper/2509.02237/) (2025)

## Abstract (arXiv)

In this work, we present a model order reduction technique for nonlinear structures assembled from components.The reduced order model is constructed by reducing the substructures with proper orthogonal decomposition and connecting them by a mortar-tied contact formulation. The snapshots for the substructure projection matrices are computed on the substructure level by the proper orthogonal decomposition (POD) method. The snapshots are computed using a random sampling procedure based on a parametrization of boundary conditions. To reduce the computational effort of the snapshot computation full-order simulations of the substructures are only computed when the error of the reduced solution is above a threshold. In numerical examples, we show the accuracy and efficiency of the method for nonlinear problems involving material and geometric nonlinearity as well as non-matching meshes. We are able to predict solutions of systems that we did not compute in our snapshots.