Lagrangians for certain classes of inelastic solids (Q1082111)

The inverse problem of the calculus of variations is investigated in conjunction with two nonlinear models of inelastic solids, namely those of Kelvin-Voigt and of Zener. In both cases, on appealing to the general theory, the most general forms of the constitutive equations compatible with the existence of a variational formulation are determined. Next the pertinent (local-in-time) Lagrangian densities are established. The main features of the constitutive equations and the Lagrangian densities so obtained are also discussed.