Restrictions on the Strain-Energy Function for an Elastic Material

Abstract

Conditions are obtained for the incremental shear modulus to be positive for small simple shear superposed on a pure homogeneous deformation of an elastic material, the direction and plane of shear being parallel to a principal direction and principal plane respectively. Results are obtained for an isotropic elastic material and for a transversely isotropic elastic material in which the axis of rotational symmetry is in a principal direction of the pure homogeneous deformation. For an isotropic material, it is shown that the Baker-Ericksen condition on the strain-energy function follows from the assumption that the incremental shear modulus is positive. A number of further conditions that have been proposed are shown to be unacceptable.

Keywords

elastic material isotropic transversely isotropic Baker-Ericksen

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References

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Reprinted in Collected Papers of R. S. Rivlin, Vol. 1, pp. 55-72, eds. G. I. Barenblatt and D. D. Joseph , Springer, New York, 1997.