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In this paper we are concerned with the behavior of a certain class of hyperelastic materials with non-elliptic strain energy density functions that satisfy very weak growth conditions at infinity. It is shown, by means of an example, that solutions of boundary-value problems involving these materials do not exist within the usual admissible spaces in view of the severe discontinuities involved (displacement discontinuities).

On a certain class of elastic materials with nonelliptic energy densities