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...[ Read more ]

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 variable thickness triply periodic minimal surface (TPMS) shell lattices are proposed by a strain energy-based numerical homogenization and optimization procedure. The optimization results show that all the six selected types of TPMS lattices can be made to achieve elastic isotropy by varying the shell thickness accordingly, among which N14 can maintain over 90% of the HS upper bound of bulk modulus. All the optimized shell lattices exhibit superior stiffness properties and significantly outperform elastically-isotropic truss lattices of equal relative densities. Both uniform and optimized types of N14 shell lattices along [100], [110] and [111] directions are fabricated by the micro laser powder bed fusion techniques with stainless steel 316L and tested under quasi-static compression loads. Experimental results show that the elastic anisotropy of the optimized N14 lattices is reduced compared to that of the uniform ones. Large deformation compression results reveal different failure deformation behaviors along different directions. The [100] direction shows a layer-by-layer plastic buckling failure mode, while the failures along [110] and [111] directions are related to the shear deformation. The optimized N14 lattices possess a reduced anisotropy of plateau stresses and can even attain nearly isotropic energy absorption capacity.

Finally, two families of elastically-isotropic open-cell uniform thickness shell lattices are proposed via a strain energy-based numerical homogenization and shape optimization procedure, including the Primitive (P) and I-graph-wrapped package (IWP) families. A  B-spline parameterized Monge patch model is adopted to represent the shell mid-surfaces within the fundamental domain, thus naturally guaranteeing the cubic symmetry of the lattices, based on which a straightforward Galerkin residual based shape optimization algorithm is adopted to achieve the constant mean curvature (CMC) surfaces with targeted mean curvatures, including the TPMS as a special case. The homogenization and shape optimization procedure is then applied to the shell lattices of P and IWP families, with the initial designs adopted as the CMC surfaces with different mean curvatures, showing that both families of lattices can be made to achieve elastic isotropy by varying the shape of the shell mid-surface accordingly, among which the elastically-isotropic IWP-family lattices possess more superior stiffness properties than those of the elastically-isotropic P-family lattices. Furthermore, the introduction of Young’s/bulk modulus maximization into the shape optimization algorithm enables the highest achievable Young’s, shear and bulk moduli of elastically-isotropic IWP-family lattices to be improved to nearly 60%, 60% and 80% of the HS upper bounds in low relative densities, respectively.