Poynting effect in fluid-saturated poroelastic soft materials in torsion

Abstract

This work studies the Poynting effect in fluid-saturated poroelastic soft materials in torsion. The Poynting effect is a nonlinear mechanical phenomenon commonly observed in soft solids such as biological soft tissues, gels and rubber. When sheared or twisted, such materials tend to either expand or contract in the direction perpendicular to the plane of shearing or twisting. Thus, to maintain a constant height, a compressive (positive Poynting effect) or tensile (negative Poynting effect) normal force must be applied to the material’s sheared face or twisted end. The mechanical response of fluid-saturated poroelastic soft materials can be described using mixture theory. Although both of its constituents are intrinsically incompressible, the biphasic material as a whole is compressible since it may gain or lose fluid through its pores. Our model—an extension of the single-constituent, incompressible solid models found in anterior studies—allows one to quantify the effect of the fluid and the solid on the normal force and torque required to maintain the torsion deformation and shows that the anomalous negative Poynting effect cannot be attributed to the poroelastic nature of the material alone. We use finite element simulations to predict the normal force and torque for biphasic materials with weakly-compressible and fully-compressible Mooney–Rivlin skeletons and Holmes–Mow-type hydraulic permeability. We also approximate analytical expressions for the normal force and torque for a weakly-compressible Mooney–Rivlin solid, which set a benchmark for the numerical simulations.