On a Class of Deformations of a Material with Nonconvex Stored Energy Function*

This paper considers the problem of finding the deformation of a nonlinear elastic layer contained between two infinite parallel rigid plates, each of which undergoes the same finite rotation, but about noncoincident axes. Each plane of the layer is assumed to rotate about a point whose position depends on its distance from the rigid bounding plates. The locus of these centers of rotation satisfies a differential equation which depends on the strain energy density of the material. In the case of a Mooney material, the locus is a straight line connecting the centers of rotation of the bounding plates, as is to be expected. It is shown that for a certain class of strain energy density functions, the solution is nonunique and consists of piecewise linear segments. 1984, Taylor & Francis Group, LLC. All rights reserved.

On a Class of Deformations of a Material with Nonconvex Stored Energy Function* Academic Article