  This paper presents a class of 3D single-scale isotropic materials with
tunable stiffness and buckling strength obtained via topology optimization and
subsequent shape optimization. Compared to stiffness-optimal closed-cell plate
material, the material class reduces the Young's modulus to a range from 79% to
58%, but improves the uniaxial buckling strength to a range from 180% to 767%.
Based on small deformation theory, material stiffness is evaluated using the
homogenization method. Buckling strength under a given macroscopic stress state
is estimated using linear buckling analysis with Block-Floquet boundary
conditions to capture both short and long wavelength buckling modes. The 3D
isotropic single-scale materials with tunable properties are designed using
topology optimization, and are then further simplified using shape
optimization. Both topology and shape optimized results demonstrate that
material buckling strength can be significantly enhanced by hybrids between
truss and variable thickness plate structures.
