Abstract
A body is composed of a homogeneous elastic material if there is a configuration of the body relative to which the Cauchy stress-response function does not depend upon position in that configuration. In this paper, necessary and sufficient conditions for the existence of such a configuration are deduced. These are expressed as restrictions on the stress-response function associated with a single reference configuration. In particular, it is shown that a body that possesses a stress-free reference configuration and has an associatedinvertible (but position-dependent) elasticity four tensor that governs the response of this material at infinitesimal deformations is comprised of anin homogeneous material.
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This paper is dedicated to the memory of Professor Eli Sternberg.
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Blume, J.A. Reference configurations for homogeneous and inhomogeneous nonlinearly elastic materials. J Elasticity 27, 247–266 (1992). https://doi.org/10.1007/BF00041689
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DOI: https://doi.org/10.1007/BF00041689