Cattaneo's relative formulation of relativistic mechanics is based on the covariant transverse derivative of an arbitrary totally spatial tensor field. On the other hand, Bressan bases relativistic elasticity, possibly with couple stresses, on the Lagrangian spatial derivative of an arbitrary double tensor. I give a chronotopic expression of the spatial projection of the Lagrangian derivative in the case that the reference configuration coincides with the one of the body on a locally time-orthogonal...
We state a criterion for existence of a stored-energy function from which we will derive the stress in the case of microstructures with finite deformations. The problem was examined by Truesdell in the case of classical continuous media and is connected to the possibility of an extension of the classical Betti theorem to the case of finite deformations. Unlike what happens in the case of classical continuous media, we realise that the existence condition for a stored-energy function in the case...
In the present work an extension of a classical Menabrea’s theorem on a variational principle of the second potential energy is considered. Such extension deals with hyperelastic micropolar media without constraints.
In the present work an extension of a classical Menabrea’s theorem on a variational principle of the second potential energy is considered. Such extension deals with hyperelastic micropolar media without constraints.
In a previous paper I have proved that in a subclass of viscous fluids with structure some longitudinal acceleration waves are possible. In this Note I state their law of decay when the fluid is at rest in its unperturbed region. Waves carrying discontinuities in the third derivatives of the velocity are induced, whereas in some particular cases also waves carrying discontinuities in the second derivatives of the velocity are induced.
Propagation of acceleration waves is impossible in classical viscous fluids. One could suppose that the same could occur in case of viscous fluids with structure. Speaking of adiabatic or isothermal cases I have found that propagation of acceleration waves is actually possible in a subclass of such continua. Only longitudinal waves carrying discontinuities in the first derivatives of the velocity are possible but not waves carrying discontinuities in the first derivatives of the angular velocity....
A. Bressan fonda la sua teoria relativistica dei materiali di ordine n su una relativizzazione del gradiente n-simo della posizione ottenuta mediante derivazione su una superficie totalmente geodetica e tempo ortogonale. D'altra parte Lianis, nella sua teoria di elasticità relativistica, introduce una relativizzazione del gradiente primo di posizione, differente almeno concettualmente da quello di Bressan, espresso in coordinate ottiche mediante derivazione della posizione sulla ipersuperfice ...
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