Elastically-isotropic mechanical metamaterials : theory and experiments

Abstract

Lightweight engineering requires the development of low-density materials featuring high mechanical properties with an emphasis on high-specific stiffness and strength. Besides improvement in the composition of bulk materials, high specific mechanical properties are obtained by carefully architecting materials through the controlled introduction of porosities. The recent rise of additive manufacturing allows for the manufacturing of complex structures at the material length scale, opening an unprecedented design space of metamaterials. Amongst this design space, this thesis is concerned with the conception of three-dimensional isotropic metamaterials, a particularly important class of mechanical metamaterials exhibiting direction-independent behavior at the macroscopic level.

The mechanical behavior of the anisotropic Face-Centered-Cubic (FCC) and Body-Centered-Cubic (BCC) lattices is investigated at small and large strains, through a combined analytical, numerical and experimental study including an extensive characterization of stainless steel micro-lattices. Based on this investigation, elastically-isotropic truss lattices are designed via topological constraints obtained from analytical homogenization. The precise composition of anisotropic lattices including the Simple Cubic (SC), BCC and FCC lattices allows achieving elastic isotropy. The introduction of elastically-isotropic hollow-truss lattices eliminates the need of combining anisotropic lattices, as the anisotropy in hollow-truss lattices is dictated by the ratio of the inner to outer radii of each beams. Finally, a new class of plate-lattice is proposed which reaches optimal isotropic elastic properties. They are conceived by placing plates along the close-packed planes of crystal structures.

Based on theoretical analysis, a design map is developed for elastically isotropic plate-lattices of cubic symmetry. The newly-proposed designs are validated through extensive unit cell simulations and experiments carried on polymeric specimens. Furthermore, the initial yield surface of the elastically-isotropic lattices is investigated numerically and the direction-dependency of the initial strength is reported using pole figures. A plate-lattice is found to exhibit an almost isotropic initial yield with its strength close to theoretical upper bound for porous solids. The main outcomes of this thesis are (i) the design strategies used to create elastically-isotropic three-dimensional lattices based on truss, shell and plates assemblies and (ii) the discovery of an optimal elastically-isotropic lattice family with almost optimal initial yield response.