Determination of the Strain Energy Density Function for Compressible Isotropic Nonlinear Elastic Solids by Torsion - Normal Force Experiments

Abstract

Penn and Kearsley derived expressions for the derivatives of the strain energy density function for an incompressible elastic material in terms of the measured torque - twist and axial force - twist relations obtained during experiments involving torsion of a circular cylinder. The present work is concerned with a method for determining the derivatives of the strain energy density function for a compressible isotropic elastic material by means of experiments involving torsion of a circular cylinder. The problem is made more difficult in the compressible case because cylindrical surfaces undergo deformation, which is then used to show why the Penn and Kearsley result cannot be extended to compressible materials. We then discuss the material identification method for determining the derivatives of the strain energy density function from the torque - twist, axial force - twist, and volume change - twist relations, which can be measured using the torsional dilatometer developed by Duran and McKenna. In this method, a polynomial representation for the strain energy density function is assumed and the constants are determined from the measured data.