The Finite Elastic Plane Strain Deformation of a Mooney-Rivlin Body

Abstract

The problem of developing a general systematic method for obtaining solutions to boundary value problems in finite elasticity is still unsolved, although of paramount importance in many applications where geometrical nonlinearity cannot be neglected. This paper does not present such a method, but nevertheless, calls attention to the nature of the compatibility equation, for plane-strain deformation, which is cast in terms of a stress function. Some special solutions are recorded, at which time some interesting comments about the existence of singular stress fields are made. It is hoped that this paper may stimulate further investigations which might lead to more general solutions of the compatibility equation than are presented below.

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