2008-03-19
10:15 at HCI J 574

Variational formalism for the description of non-holonomic media models

Sergey Lurie

Institute of Applied Mechanics of Russian Academy of Sciences, Moscow, Russia

The variational formalism for description of the non-holonomic media models is offered. Formal generalization of continued mechanics models on the four-dimensional space of events with a four-dimensional vector of the generalized displacements is used. Time of process is included in the generalized four-dimensional system of coordinates and considered as one of independent coordinates. As kinematic connections it is proposed to use generalized Cauchy relations for the generalized deformations, which correspond to a four-dimensional vector of the generalized displacement media. The general form of the constitutive equations for non-holonomic media is given. Common properties of the symmetry for the tensor of the physical properties are established. Variational equation for the non-holonomic linear-medium model is obtained and the appropriate initial - boundary problem is formulated. It is shown that irreversible processes proceed with positive dissipation, and the second law of thermodynamics takes place. The possible types of the channels of dissipation are established for considered media model. Within the framework of specific model the generalized equation of heat conductivity is received. The relations between heat flow, temperature and different thermodynamic parameters are established which generalize the Fourier equation (for heat flow) and Duamel-Neumann equation. As a special case the combined model of the creep and relaxation is received.