Thermomechanics of a Continuous System with Internal Structure

Summary

A motion of a three dimensional continuous body, admitting at each particle an internal structure of an unspecified nature, is represented in terms of a definite number of generalized co-ordinate fields which are given as functions of time and particle co-ordinates. With each generalized co-ordinate field is associated a generalized velocity, a generalized specific momentum, a generalized body force and a generalized contact force. Equations of motion are postulated in the form of balance equations for the generalized momenta. Balance of energy is postulated as an equation relating the rate of total energy change to the power of generalized contact and body forces and the supply of heat. The entropy principle is adopted in the form laid down by Truesdell and Toupin and a thermomechanical theory is developed in analogy to the scheme for simple materials given by Coleman and Noll. Only an outline of the general theory is given in the present report.