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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

[1] Baker, M. and Ericksen, J. L. Inequalities restricting the form of the stress deformation relations for isotropic elastic solids and Reiner-Rivlin fluids. Journal of the Washington Academy of Sciences, 44, 33-35 (1958).

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[3] Trusdell, C. and Noll, W. The non-linear field theories of mechanics, in Encyclopedia of Physics, Vol. III/3, ed. S. Flügge , Springer, Berlin, 1965.

[4] Truesdell, C. and Noll, W. The non-linear field theories of mechanics, in Encyclopedia of Physics, Vol. III/3, ed. S. Flügge , Springer, Berlin, 1992.

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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.

Restrictions on the Strain-Energy Function for an Elastic Material

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