A highly efficient explicit constitutive model for linear viscoelastic closed-cell porous materials

In this paper, a highly efficient explicit constitutive model for linear viscoelastic closed-cell porous materials is proposed based on micromechanics and homogenization method in the time domain. The deformation first is additively divided into volumetric and deviatoric parts and then the viscoelastic behaviors are decomposed into the time-dependent and time-independent parts. Finite element simulations based on representative volume element models are utilized to numerically verify the constitutive model. The effects of the void-shape, porosity, elastic and viscous parameters of the matrix, strain rate, and angular frequency on the effective linear viscoelastic responses are studied. The results demonstrate that the constitutive model can provide accurate estimation of the effective linear viscoelastic properties for the closed-cell porous materials in both time and frequency domains. The 3D printed nylon porous materials with various porosities are employed to experimentally validate the constitutive model through simple uniaxial compression tests, stress relaxation uniaxial compression tests, and uniaxial compression tests with different strain rates. The results reveal that the constitutive model can also predict well the behaviors of linear viscoelastic closed-cell porous materials with different porosities in the time domain under various loading conditions.