Elastically-isotropic open-cell mechanical metamaterials : design, analysis, fabrication and experiments

Mechanical metamaterials are artificial structures whose mechanical properties are determined by the downscale micro-architectures and can be made to achieve unconventional mechanical properties through appropriate design of the architectures. The elastically-isotropic open-cell mechanical metamaterials are attracting increasingly attention for the identical stiffness properties along all directions and the open-cell topology to facilitate the additive manufacturing through easier removal of resins or metal powders, thus making them ideal candidates in a variety of fields where the primary loading direction is unknown and a considerable mass and heat transfer is required. In this thesis, two classes of elastically-isotropic open-cell mechanical metamaterials are proposed, including the elastically-isotropic truss lattices and shell lattices, which are all shown to possess superior mechanical properties and therefore have a wide range of application prospects. First, a family of elastically-isotropic truss lattices are proposed via compositions of elementary cubic symmetric truss lattices with contrary elastic anisotropy, which are all shown to undergo stretching-dominated deformations under arbitrary loading conditions through matrix analysis of the static and kinematic determinacies. The stiffness properties of the combined lattices are first analytically shown to reach the upper bounds for elastically-isotropic truss lattices, which are nearly 1/3 of the Hashin-Shtrikman (HS) upper bounds in low relative densities, and then further validated by the strain energy-based numerical homogenization procedure. Further comparisons between the stiffness properties of the combined lattices with the relative densities of 10% and 1% reveal that those with lower relative densities possess closer stiffness properties to the theoretical values due to their lower bending effects and higher stretching to bending stiffness ratio. Then, a family of elastically-isotropic open-cell va