Linear constitutive relations in isotropic finite viscoelasticity

Abstract. For simple shearing and simple extension deformations of a homogeneous and isotropic elastic body, it is shown that a linear relation between the second Piola–Kirchhoff stress tensor and the Green–St. Venant strain tensor does not predict a physically reasonable response of the body. This constitutive relation implies that the slope of the curve between an appropriate component of the first Piola–Kirchhoff stress tensor and a deformation measure is an increasing function of the deformation measure. Mathematics Subject Classification (1991): 73G05