This thesis is dedicated to the development and analysis of methods for computer-aided design of materials with tailored mechanical properties. The mechanical metamaterials were studied through two different approaches: modelling periodic structures through a parameterized growth model and procedural noise functions. To tackle the challenge of obtaining near-regular microstructures with progressively varying properties, I proposed and studied a cellular material spawned by a growth process. The growth is parameterized by a 3D star-shaped set at each lattice point, defining the geometry that will appear around it. Individual tiles may be computed and used in a periodic lattice, or a global structure may be produced under spatial gradations, changing the parametric star-shaped set at each lattice location. Beyond free spatial gradation, an important advantage of this approach is that elastic symmetries can be intrinsically enforced. It is shown in this work how shared symmetries between the lattice and the star-shaped set directly translate into symmetries of the periodic structures’ elastic response. Thus, the approach enables restricting the symmetry of the elastic responses – monoclinic, orthorhombic, trigonal, and so on – while freely exploring a wide space of possible geometries and topologies. I provide a comprehensive study of the space of symmetries and broad combinations of growth process parameters. Furthermore, I demonstrate through numerical and experimental results the expected responses triggered by the obtained structures.

The second contribution of this thesis is a novel procedural pattern synthesis technique. This approach exhibits desirable properties for modeling highly contrasted patterns, that are well suited to produce surface and microstructure details. This approach defines a stochastic smooth phase field — a phasor noise — that is then fed into a periodic function (e.g. a sine wave), producing an oscillating field with prescribed main frequencies and preserved contrast oscillations. I present in this thesis a mathematical model, that builds upon a reformulation of Gabor noise in terms of a phasor field that affords for a clear separation between local intensity and phase. In particular, I study the behavior of phasor noise in terms of its power spectrum. Hence, a comparative theoretical study of phasor noise was performed in order to gain understanding of links between its properties and parameters.”