Onde di discontinuità ed equazioni costitutive nei corpi elastici isotropi sottoposti a deformazioni finite

Summary We consider an elastic isotropic material with finite deformations. The existence of a double wave (therefore exceptional because the field equations are in the conservative form) for all the deformations and the discontinuity propagation direction is required. This because in the linear theory there exists a double wave, furthermore, because in many non-linear theories of Mathematical physics there exists at least one exceptional wave (this wave doesn’t produce shocks). This request implies conditions for the response function in the constitutive equations. Furthermore, under these assumptions, we can determine explicitly all the possible propagation speeds. Therefore we can find theorems generalizing (in the case of the imposed conditions) those ones obtained by Truesdell and Green for the principal waves (whose unit normal has the direction of the eigenvectors of the deformation matrix). In the last part of this work we examine the case of a hyperelastic material and we determine some classes of possible thermodynamic potentials.

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Entrata in Redazione il 18 febbraio 1976.

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Lavoro eseguito nell’ambito dei contratti del C.N.R. - Gruppo Nazionale per la Fisica Matematica.