An Informal Discussion on the Theory of Large Elastic Strains

In many papers on the mechanics of deformable materials, the manner in which strain is defined occupies a position of importance far greater than is justified. It will be seen that, on the basis of explicit physical assumptions defining what we mean by an “ideal isotropic highly-elastic material,” mathematical equations can be derived which are adequate for the calculation of the forces necessary to produce a specified deformation and for the solution of the inverse problem, as well as for the calculation of the stress at any point. All this can be done without the question of the definition of the term “strain” arising. It may, however, be convenient to describe by the single word “strain” certain quantities defined in terms of the displacements undergone in the deformation by the various points of the body.