On the Correlation of Theory and Experiment for Transversely Isotropic Nonlinear Incompressible Solids

Abstract

A novel strain energy function for finite strain deformations of transversely isotropic elastic solids which is a function five invariants that have immediate physical interpretation has recently been developed. Three of the five invariants are the principal stretch ratios and the other two are squares of the dot product between the preferred direction and two principal directions of the right stretch tensor. A strain energy function, ex- pressed in terms of these invariants, has a symmetrical property almost similar to that of an isotropic elastic solid written in terms of principal stretches. This constitutive equation is attractive if principal axes techniques are used in solving boundary value problems and experimental advantage is demonstrated by showing a simple triaxial test can vary a single invariant while keeping the remaining invariants fixed. Explicit expressions for the weighted Cauchy response functions are easily obtained since the response function basis is almost mutually orthogonal. In this paper a specific form of the strain energy function for incompressible materials which is linear with respect to its physical parameters is developed. When a curve fitting method is (sensibly) applied on an experimental data, the values of the parameters are obtained uniquely via a linear positive definite system of equations. The theory compares well with experimental data and the performance of the proposed specific form is discussed. A constitutive inequality, which may reasonably be imposed upon the material parameters, is discussed.