Ole Sigmund's KTH Solid Mechanics KEYNOTE seminar "Third medium approaches for contact analysis with applications in topology optimization and meta-material design"

Ole_Sigmund_Oct_10_2024.pdf (pdf 149 kB)

Abstract. Topology optimization for problems with internal or external contact represents a seeming paradox: if the topology is initially unknown, how can one identify contact boundaries? And further: even if boundaries are known and well-described, it is complicated and logistically complex to administrate contact points or surfaces and their associated Lagrange Multipliers. Both challenges can be alleviated using so-called Third Medium Approaches (TMAs), where contact forces are transferred through “void” domains with tailored elastic properties that generate high stiffness when directionally compressed but zero stiffness in shearing. TMAs have obvious strong benefits for inverse design problems but also represent a viable alternative to traditional contact analysis in non-linear elasticity. In this talk, we discuss and demonstrate recent advances in applying TMAs: 1) improved computational stability through better finite element discretizations; 2) extensions to three dimensions, 3) extensions to multiphysics settings including thermoelectric contacts and 4) inclusion of friction effects by a crystal plasticity framework.