Deformation behavior of fluid-filled porous elastomers: Analytical estimates and validation

Abstract

Fluid-filled elastomers are used in soft body wearable electronics devices, optics, soft pressure transducers, vibration damping and impact protection. Deformation behavior of these materials is complex and would depend on elastomer properties, fluid properties, loading rate, porosity, pore size, pore shape, and pore end conditions. In this work, closed form analytical estimates are derived for effective behavior of a special class of fluid-filled elastomers composed of incompressible, hyperelastic matrix with mono-disperse circular pores, distributed in a square grid, filled with an incompressible, Newtonian fluid. The analytical estimates are validated using three dimensional numerical simulations modeled in COMSOL multiphysics software. The analytical estimates for pressure and velocity fields in the fluid, deformation of the matrix, viscous dissipation in fluid, and stored energy in the solid are seen to match well with that from numerical simulations. For small deformations and small porosities, while storage modulus is seen to be linearly proportional to shear modulus of elastomer and inversely proportional to the porosity, the loss modulus is seen to be linearly proportional to the product of loading frequency and fluid viscosity and inversely proportional to the product of porosity and square of ratio of pore radius to pore length. The analytical estimates presented here can be used to design fluid-filled elastomers with desired stiffness and damping by selecting appropriate elastomer stiffness, fluid viscosity, porosity, pore size and pore aspect ratio.