Optimal Design of Porous Materials

The focus of this thesis is topology optimization of material microstructures. That is, creating new materials, with attractive properties, by combining classic materials in periodic patterns. First, large-scale topology optimization is used to design complicated three-dimensional materials with exotic properties, such as isotropic negative Poisson’s ratio and negative thermal expansion. Furthermore, it is shown how topology optimization can be used to design materials with a good compromise between stiffness and damping. Both a simple quasi-static method suited for low frequency wave propagation, and a more general dynamic method (using Floquet-Bloch theory) applicable to arbitrary frequency ranges are presented. The quasi-static method is applied to the design of both two- and three-dimensional material microstructures. And it is shown, using two-dimensional examples, how the general method can be used to design materials with frequency dependent loss, which can be higher than depicted by the quasi-static bounds. The work is inspired by the increased availability of additive manufacturing facilities, and, thus, the possibility of manufacturing complicated structures. Therefore, throughout the thesis extra attention is given to obtain structures that can be manufactured. That is also the case in the final part, where a simple multiscale method for the optimization of structural damping is presented. The method can be used to obtain an optimized component with structural details on the same scale as the manufacturing precision, without being computationally exhaustive. Furthermore, the connectivity of the stiff phase is assured, making it possible to design components that can be manufactured, using additive manufacturing to print the stiff material phase, and, thereafter, infuse the component with the soft and lossy material phase.