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 functions of the deformation measure.
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Batra, R. Linear Constitutive Relations in Isotropic Finite Elasticity. Journal of Elasticity 51, 243–245 (1998). https://doi.org/10.1023/A:1007503716826
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DOI: https://doi.org/10.1023/A:1007503716826