β Scribed by Jerzy Kijowski; Giulio Magli
No coin nor oath required. For personal study only.
A new formulation of relativistic elastomechanics is presented. It is free of any assumption about the existence of a global relaxation state of the material. The strain, the stress and the energy-momentum tensors are expressed in terms of the first-order derivatives of a field describing the configuration of the material. Its elastic properties are completely determined by a scalar function describing the dependence of the mechanical energy accumulated in the deformed material upon the three invariants of the deformation. The stress-strain relations are generated in a canonical way by this function. Dynamical equations of the theory are derived from the variational principle. They form a hyperbolic system of second-order partial differential equations for the unknown field. Energy-momentum conservation laws are consequences of the Noether theorem. The hamiltonian formulation of the dynamics and the linear version of the theory are also discussed.
π SIMILAR VOLUMES