A Matlab code for analysis and topology optimization with Third Medium Contact

TL;DR

This paper introduces a MATLAB code for modeling and optimizing hyperelastic structures with contact, utilizing the Third Medium Contact approach and HuHu-regularization to improve solver convergence.

Contribution

The paper provides a compact MATLAB implementation for contact modeling and topology optimization of hyperelastic structures, including contact scenarios and extensions.

Findings

Successful simulation of contact and force transfer in hyperelastic structures.

Effective topology optimization for structures with boundary and self-contact.

Inclusion of MATLAB scripts for reproducibility.

Abstract

We present a Matlab code for modelling and topology optimization of hyperelastic structures, including contact modelled by the Third Medium Contact (TMC) approach. By using the so-called HuHu-regularization we penalize the skew distortion of the bilinear finite elements discretizing void regions, thus promoting convergence of the nonlinear solver. First, we show how this method is implemented in a compact code, allowing to simulate contact and force transfer in hyperelastic structures. We then solve two topology optimization problems for minimum end-compliance of structures exhibiting contact. In the first example, contact happens at the supported boundary, while the second features self-contact. The Matlab scripts that replicate the results are included, and we discuss some possible extensions to more general problems.