Class of Compressible Elastic Materials Capable of Sustaining Finite Anti-Plane Shear

摘要

This paper describes a simple class of homogeneous, isotropic, compressible hyperelastic materials capable of sustaining nontrivial states of finite anti-plane shear. One of the simplest classes of deformations of solids is that of anti-plane shear, in which each particle of a cylinder is displaced axially by an amount that depends on the position of the particle in its cross-section but not on the axial coordinate of the particle. In the linearized theory of infinitesimal deformations, every homogeneous, isotropic elastic material is capable of sustaining, in the absence of body force, anti-plane shears which are nontrivial in the sense that they are not simple shears. When finite deformations are considered, however, this is not the case. In the corresponding nonlinear theory, anti-plane shear is accompanied by normal stresses, and as a result the local equations of equilibrium may be violated unless suitably contrived body forces are present. (MJM)