Theory of Large Elastic Deformations

WHEN rubber is subjected to a large elastic deformation, which may be assumed to take place without change of volume, it ceases to be isotropic, and the attempt to relate the stresses and strains in different directions may be a matter of some difficulty. However, if the assumption is made that Hooke's law is obeyed in simple shear in any isotropic plane, it is possible, as Mooney has shown1, to deduce certain relations which represent the elastic behaviour under the most general type of homogeneous deformation. If such a deformation is defined by the three principal strains, λ1, λ2 and λ3 (where λi is the ratio of final to initial length along the i-strain axis), the expression for the work of deformation W is