Reduced-order computational homogenization for hyperelastic media using gradient based sensitivity analysis of microstructures

TL;DR

This paper introduces a gradient-based sensitivity analysis method for reduced-order homogenization of hyperelastic microstructures, significantly decreasing computational costs in large deformation simulations.

Contribution

It presents a novel model-order reduction algorithm that approximates homogenized coefficients via sensitivity analysis, reducing the number of microscopic problems needed.

Findings

Reduces computational time compared to full simulations.

Achieves controlled accuracy through a user-defined error tolerance.

Demonstrates effectiveness with 2D test examples.

Abstract

We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into subsets called "centroids", and, as a new ingredient, approximates the homogenized coefficients using sensitivity analysis of micro-configurations with respect to the macroscopic deformation. The novel "model-order reduction" approach significantly reduces the number of microscopic problems that must be solved in nonlinear simulations, thereby accelerating the overall computational process. The degree of reduction can be controlled by a user-defined error tolerance parameter. The algorithm is implemented in the finite element framework SfePy, and its performance effectiveness is demonstrated using two-dimensional test examples, when compared with solutions obtained by the proper orthogonal decomposition method, and by the full "FE-square" simulations. Extensions beyond the present implementations and the scope of tractable problems are discussed.