Design optimization of structures with path-dependent and non-linear material behavior

Topology optimization is a mathematical tool for the computational design of structures,particularly valuable in the early stages of the design process. Gradient-basedoptimization methods, combined with finite element analysis, form the foundation ofan iterative procedure where the design is continuously updated and evaluated. To expandthe applicability of topology optimization, this thesis explores a range of designproblems involving path-dependent and non-linear material behavior, including hyperelasticity,transient thermo-elasticity, and elasto-plasticity.The thesis begins with an introduction to topology optimization, followed by formulations,models, and numerical procedures for handling non-linear and path-dependentresponses. Thermodynamical principles are presented and linked to constitutive modeling,followed by the balance laws and non-linear solution strategies employed inthe optimization frameworks. Topology optimization procedures for both single- andmulti-material structures are developed, along with material interpolation schemestailored to each class of materials. Finally, path-dependent sensitivity analysis is derivedand discussed in the context of transient and elasto-plastic problems.Five appended papers provide detailed studies of specific applications. Paper A introducesa framework for stress-constrained topology optimization of finite strain hyperelasticstructures under non-proportional loading, showing that different load trajectoriesleading to the same terminal state can result in distinct optimal designs. PaperB investigates non-linear transient thermo-elasticity in the design of multi-materialthermal actuators, where the material distribution is influenced by the operating time.Papers C–E address the design of 3D elasto-plastic structures for tailored mechanical response,plastic work maximization, self-locking behavior, and stiffness optimization.