Topology Optimization and Analysis of Thermal and Mechanical Metamaterials

To take advantage of multi-material additive manufacturing technology using mixtures of metal alloys, a topology optimization framework is developed to synthesize high-strength spatially periodic metamaterials possessing unique thermoelastic properties. A thermal and mechanical stress analysis formulation based on homogenization theory is developed and is used in a regional scaled aggregation stress constraint method, and a method of worst-case stress minimization is also included to efficiently address load uncertainty. It is shown that the two stress-based techniques lead to thermal expansion properties that are highly sensitive to small changes in material distribution and composition. To resolve this issue, a uniform manufacturing uncertainty method is utilized which considers variations in both geometry and material mixture. Test cases of high stiffness, zero thermal expansion, and negative thermal expansion microstructures are generated, and the stress-based and manufacturing uncertainty methods are applied to demonstrate how the techniques alter the optimal designs. Large reductions in stress are achieved while maintaining robust strength and thermal expansion properties. An extensive analysis is also performed on structures made from two-dimensional lattice materials. Numerical homogenization, finite element analysis, analytical methods, and experiments are used to investigate properties such as stiffness, yield strength, and buckling strength, leading to insights on the number of cells that must be included for optimal mechanical properties and for homogenization theory to be valid, how failure modes are influenced by relative density, and how the lattice unit cell can be used to build macrostructures with performance superior to structures generated by conventional topology optimization