Abstract
We investigate certain issues pertaining to plane deformations with discontinuous gradients sustained by compressible, isotropic, hyperelastic materials. Conditions on the elastic potential which are necessary and sufficient for the existence of such deformations are derived. An alternative, explicit set of criteria is deduced from these, which involves jump conditions restricting the deformation invariants on either side of the discontinuity. This result, which is expressed in terms of the local amounts of shear and dilatation, characterizes all possible two-phase states sustained by a given elastic potential. Some implications of ellipticity loss on the existence of such states are considered.
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Rosakis, P., Jiang, Q. Deformations with discontinuous gradients in plane elastostatics of compressible solids. J Elasticity 33, 233–257 (1993). https://doi.org/10.1007/BF00043250
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DOI: https://doi.org/10.1007/BF00043250