A nonlinear stress-strain relation

Abstract

A new nonlinear stress-strain relation for an isotropic, homogeneous material is presented. It provides a realistic nonlinear uniaxial stress-strain curve and accounts for the apparent variation of Poisson's ratio found experimentally when classical linear theory is assumed. It also accounts for the Poynting effect, for the nonlinear effect of hydrostatic stress superimposed upon simple tension and upon simple shear. The conditions set forth by Truesdell for the acceptability of a constitutive equation are met, and the nonlinear stress-strain relation reduces to the classical linear stress-strain relation for sufficiently small stresses.