Abstract
Incremental stability criteria appropriate for compressible and incompressible, general isotropic elastic solids are used to study the stability of all undistorted states of an arbitrary body subject to dead loads corresponding to a uniform hydrostatic stress. General conditions sufficient for stability of all such hydrostatic stress states are derived. The results indicate a geometrical dependence for the apparent shear and bulk moduli. The relation of the main results (4.10) and (4.21) to uniqueness theorems in the theory of small deformations superimposed on large, to broad plausibility restrictions imposed on the elasticities so as to assure physically reasonable material behavior, and to the propagation of elastic waves is also outlined; these relations constitute only specific application of certain general theorems already in the literature. Finally, it is shown that the principal results coincide with estimates that may be gotten by aid of Holden's inequality.
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