Modeling time and frequency domain viscoelastic behavior of architectured foams

The time-dependent behavior of architected lightweight cellular solids or foams is important to investigate for various structural applications. In this paper, the authors studied the linear viscoelastic properties of a novel architectured foam based on the mathematically known Schwarz primitive (P) triply periodic minimal surface (TPMS), referred to here as P-foam, in both time and frequency domains. Here, three dimensional (3D) representative volume elements (RVEs) at different relative densities (i.e., the ratio of the foam's density to the density of its solid counterpart) were generated and studied using the finite-element method. The effective time-dependent response of P-foams as a function of relative density and frequencies is investigated. For the first time, an approach similar to the time-temperature superposition principle (TTSP) was adopted to create the master curve of the observed relative density-dependent mechanical responses in both time and frequency domains. Reduced uniaxial, bulk, and shear stiffness-loss map results suggested that the P-foam possesses the highest bulk response whereas the highest damping can be achieved under uniaxial responses. Depending on the applications and loading conditions, variable-stiffness P-foam dampers can be designed with unique and optimized dynamic mechanical properties. Comparison of the relaxation responses of various generic cellular architectures with P-foam showed that the uniaxial response of P-foam is similar to that of Kelvin foam. However, shear relaxation and bulk responses are higher than simple cubic, body centered cubic, reinforced body centered cubic, and Gibson- Ashby foams. Based on RVE micromechanical simulations, a macroscopic constitutive model is proposed for modeling the viscoelastic behavior of structural systems made of the P-foam.