Third Medium Contact for Topology Optimization

This thesis provides a comprehensive introduction to third medium contact (TMC) for topology optimization, offering a unified framework for understanding the published papers included at the end of this thesis. The work begins by establishing foundational concepts through one-dimensional spring models, followed by a general continuum formulation. Notably, the thesis introduces the HuHu-LuLu regularization, an improvement upon the existing HuHu regularization, which overcomes stability challenges in TMC models experiencing sliding or bending.

The chapters in this thesis provide a structured introduction to the TMC frameworks and extensions developed during the PhD project. By presenting the underlying theories and methods, these chapters make it easier to understand the published papers included in the thesis. The research covers the first friction model for TMC, integrating concepts from crystal plasticity with Coulomb-friction yield criteria, and presents a complete TMC topology optimization framework that enables the design of complex structures with internal contact. The thesis also introduces improved discretization methods, objective functions supporting transverse stiffness, and an extension to thermal contact problems. The practical efficacy of these approaches, TMC and topology optimization, is demonstrated through benchmark examples.

By addressing the limitations of traditional contact methods in topology optimization, this work establishes TMC as a viable approach for designing structures where contact mechanics play a crucial role. The frameworks and models presented provide a foundation for further research and applications across various engineering disciplines requiring integrated contact handling in structural optimization