Internal contact modeling for finite strain topology optimization

TL;DR

This paper extends the third medium contact method for finite strain topology optimization, enabling accurate modeling of self-contact in large deformation scenarios within a second order framework.

Contribution

It introduces a new regularization for the void region as contact medium and integrates it into a coupled second order topology optimization method.

Findings

Successfully models self-contact in large deformation topology optimization.

Demonstrates accurate control of non-linear force-displacement paths.

Validates the method's effectiveness through numerical examples.

Abstract

The present work proposes an extension of the third medium contact method for solving structural topology optimization problems that involve and exploit self-contact. A new regularization of the void region, which acts as the contact medium, makes the method suitable for cases with very large deformations. The proposed contact method is implemented in a second order topology optimization framework, which employs a coupled simultaneous solution of the mechanical, design update, and adjoint problems. All three problems are derived and presented in weak form, and discretized with finite elements of suitable order. The capabilities and accuracy of the developed method are demonstrated in a topology optimization problem for achieving a desired non-linear force-displacement path.