Tuesday, 12 October 2004 - 1:50 PM

This presentation is part of : Rajagopal Symposium

On Strong Ellipticity for a Non-Linear Elastic Material with Strain Energy Function of Certain Orthogonal Invariants

Jay R. Walton and Tsvetanka Sendova. Texas A&M University, Department of Mathematics, Texas A&M University, College Station, TX 77845-3368

In an important paper (An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity, {\it J. Mech. Phys. Solids}, {\bf 48}, pp. 2445-2465), J.~C.~Criscione, J.~D.~Humphrey, A.~S.~Douglas and W.~C.~Hunter proposed a model for the strain energy function of a hyperelastic material body that was in terms of certain isotropic invariants of the {\it natural} or Hencky strain. These invariants, which specify the {\it amount of dilatation}, the {\it magnitude of distortion} and the {\it mode of distortion}, offer many attractive features that aid the characterization of the constitutive response of hyperelastic material. Presented herein is a discussion of the stability of models utilizing these invariants. In particular, we discuss various classes of both necessary conditions and sufficient conditions for such models to be strongly elliptic. We illustrate the use of these conditions by applying them to some models used by Criscione et al to fit data on the mechanical response of rubber.

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