For simple shearing and simple extension deformations of a homogeneous and
isotropic elastic body, it is shown that a Linear relation between the seco
nd Piola-Kirchhoff stress tensor and the Green-St. Venant strain tensor doe
s not predict a physically reasonable response of the body. This constituti
ve relation implies that the slope of the curve between an appropriate comp
onent of the first Piola-Kirchhoff stress tensor and a deformation measure
is an increasing function of the deformation measure.