Large Elastic Deformations in Rubberlike Materials

Abstract

A complete description of the mechanical behaviour of an elastic material should enable the state of strain to be determined for any system of applied stresses. A convenient method of representation, which satisfies this requirement, is in terms of the energy stored elastically in the body as a function of the state of strain. Moreover, if the material is considered to be homogeneous, it is sufficient to determine this function for the case of a pure homogeneous strain. This follows from the considerations 1) that an inhomogeneously strained body may be divided up into a large number of small volume elements such that in any one element the strain is substantially homogeneous, and 2) that a strain which is not pure may be regarded as a pure strain, together with a rotation and translation. Of these, it is only the first which involves the performance of work on the material and which contributes, therefore, to the elastically stored energy.