Determination of homogenized viscoelastic properties of porous frame structures based on the microstructure geometry and solid constituent viscoelastic properties

Abstract: Polymer based porous materials largely exhibit viscoelastic properties which is a consequence of the viscoelastic nature of the constituent solid. If the constitutive relation for the constituent solid is known, then it is of interest to investigate how this constitutive relation of the solid at the microscale influences the macroscopic properties of the porous structure. In the present work porous structures are studied with the assumption that the constitutive solid is isotropic and that it also exhibits non-proportional damping characteristics. Non-proportional damping here refers to the dissimilarity in the frequency dependencies of the different complex elastic moduli of the constituent solid.Two different kinds of porous structures are investigated: pseudo random periodic microstructure and the other a pseudo random non-periodic microstructure. Both the structures are based on the implementation of Voronoi tessellations in 2D Euclidean space. A representative volume element(RVE) or a unit cell approach is adapted to analyse the properties of the porous structure. Periodic boundary conditions are implemented on the RVE in case of the periodic microstructure while a less elegant approach of using a large enough element size and measuring the stress strain fields at the interior boundaries is adapted for the non-periodic structure. A direct homogenisation technique based on the volume averaging of the micro stress and strain fields is used to estimate the macro level stress and strain fields. These macro fields are then used for determining the complex elastic moduli of the porous frame structures. Finally the results reveal that in spite of the assumption of non-proportional damping for the constituent solid, the porous frame structure exhibits proportional damping for structures of high porosity, thus possibly justifying the assumptions of proportional damping for a porous structure with sufficiently high porosity.