A Matlab code for analysis and topology optimization with Third Medium Contact
This work addresses the challenge of efficiently simulating contact in hyperelastic topology optimization for researchers in computational mechanics, but it is incremental as it builds on existing methods with specific regularization.
The authors tackled the problem of modeling and topology optimization for hyperelastic structures with contact by developing a Matlab code using the Third Medium Contact approach and HuHu-regularization to improve solver convergence. They demonstrated the method by solving two minimum end-compliance optimization problems, including cases with boundary and self-contact, and provided scripts for replication.
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.