The isothermal reversible work of deformation w per unit volume of an elastomer is given by the statistical theory of elastomer deformation as w = 1/2 G(1^2_1 + 1^2_2 + 1^2_3 - 3) where lambda_2, lambda_2 and lambda_3 are the principal extension ratios. Using this equation, deduce the stress-strain relations for the general two-dimensional strain of a sheet of material and hence show that the stress-strain relation for an equal two-dimensional extension of lambda is S_t = G(1^2 - 1/1^4) where sigma_t is the true stress acting on planes normal to the plane of stretch.
