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

We present a code for modelling and topology optimization of hyperelastic structures, including contact modelled by the Third Medium Contact (TMC) approach. By using the so-called -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 scripts that replicate the results are included, and we discuss some possible extensions to more general problems.