Tuesday, 12 October 2004 - 10:55 AM

This presentation is part of : Rajagopal Symposium

Superposition and coupling of plane strain and anti-plane shear deformations in hyperelastic materials

Cornelius O. Horgan, University of Virginia, P. O. Box 400742, Charlottesville, VA 22904 and Giuseppe Saccomandi, Universita degli Studi di Lecce, Dipartimento di Ingegneria dell'Innovazione, Lecce, 73100, Italy.

In this lecture, we discuss the basic issues that arise when generalized plane strain deformations are superimposed on anti-plane shear deformations in isotropic incompressible hyperelastic materials. Attention is confined to a subclass of such materials, namely generalized neo-Hookean materials, for which the strain-energy density depends only on the first invariant of the strain tensor. The governing equations of equilibrium are a coupled system of three nonlinear partial differential equations for three displacement fields. It is shown that, for general plane domains, this system decouples the plane and anti-plane displacements only for the case of a neo-Hookean material. Even in this case, the stress field involves coupling of both deformations. For generalized neo-Hookean materials, universal relations may be used in some situations to uncouple the governing equations.

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