Linear thermodynamics and the mechanics of solids

Abstract

The Thermodynamics of linear irreversible processes is presented from a unified viewpoint. This provides a new and synthetic approach to the linear mechanics of deformation of solids, which includes as particular cases the classical theory of Elasticity, Thermoelasticity and Viscoelasticity. The first two sections constitute an introduction to the general concepts and principles of linear Thermodynamics as developed in the writer’s earlier work and presented in somewhat more detail. This is followed by the application of the general thermodynamic theory to Thermoelasticity which combines the theories of Elasticity, Heat Transfer, and their coupled effects into a single treatment. Some immediate consequences are derived such as the property of diffusion of entropy and certain fundamental relations with reference to thermal stresses. The introduction of inertia forces leads to a general formulation of thermoelastic dissipation of dynamical systems by Lagrangian methods. The second order heat produced by the dissipation is evaluated. Linear Viscoelasticity and Relaxation Phenomena are also a particular case of the thermodynamic theory. The resulting stress-strain relations with heredity properties are discussed. The operational formulation of these relations leads naturally to a formal correspondence with the theory of Elasticity and to an operational-variational principle. The latter provides a generalization of Lagrange’s equations in integro-differential form to the dynamics and stress analysis of viscoelastic structures. Some specific applications of these principles are presented.