Stiffness and yield strength of architectured foams based on the Schwarz Primitive triply periodic minimal surface

Architectured foams based on the mathematically-known non-self-intersecting Schwarz Primitive triply periodic minimal surfaces (TPMS) might have superior mechanical properties as compared to stochastic or lattice foams. In this paper, the elastic properties (uniaxial, shear and bulk moduli, Zener anisotropy index, and Poisson's ratio) and yield strengths under several different stress states of the Schwarz Primitive TPMS sheet-based foam (referred to as P-foam) is investigated by finite element analyses of unit cells under periodic boundary conditions. The P-foam has a cubic symmetry with three independent elastic constants and yield strengths and is interconnected and intertwined in the three-dimensional space. The relative density (i.e., the density of the foam with respect to the density of the base solid material) of the P-foam can be varied by changing the thickness of the Schwarz Primitive TPMS-based sheet solid. It is found that the shear modulus and shear yield strength as well as the bulk modulus and hydrostatic yield strength scale linearly with the P-foam relative density indicating a stretching-dominated behavior. On the other hand, the uniaxial modulus and yield strength scale with a power law indicating a coupled stretching- and bending-dominated deformation. The macroscopic yield surface of the P-foam for various stress states is adequately and equally described by the extension of Hill's anisotropic yield function.