Analysis and optimization of nonlinear structures and materials including internal contact

This thesis addresses the analysis and design optimization of structures and periodic materials with desired nonlinear mechanical responses. A special focus is given to the exploitation of internal contact modeling in topology optimization as a nonlinear effect. Firstly, a framework is introduced for evaluating the load carrying capacity of periodic materials under compression.

It relies on direct fully nonlinear continuum mechanics simulations and hence it is applicable for microstructures with moderate volume fraction and arbitrarily complex topologies. Failure can be predicted not only due to classical buckling but also progressive softening. Results are shown for common regular periodic lattice structures at different volume fractions and a hierarchical lattices with enhanced buckling resistance from the literature.

The superior buckling resistance of the hierarchical lattices is further investigated by an experimental study. For this purpose, physical specimens of the regular square and triangular lattices together with corresponding buckling resistance enhanced hierarchical microstructures are tested under uniaxial compression.

Secondly, a second order consistent framework for finite strain topology optimization is presented in weak form. It is based on the idea of a simultaneous solution of the involved coupled nonlinear equations. Combined with the methodology from the analysis of the periodic lattices, the optimization framework is utilized for the design optimization of periodic materials with desired nonlinear behavior.

Furthermore, a method for contact modeling in topology optimization is introduced by an adaption of the third medium approach. Is has proven to be an excellent fit, as both methods employ a void material phase surrounding solid parts within the design domain. The potential of the method is shown on optimization examples aiming for a desired load-displacement response.