Variational-Lagrangian Thermodynamics of Non-Linear Thermorheology.
Scientific interim rept.,
BIOT (MAURICE A) BRUSSELS (BELGIUM)
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A principle of virtual dissipation generalizing dAlemberts principle to non-linear irreversible thermodynamics provides a unifying foundation which leads to an extremely general variational - Lagrangian analysis of dissipative phenomena. Thus a synthesis is achieved between thermodynamics and classical mechanics. The present paper applies this principle to the non-linear thermomechanics of continua with dissipation and heat conduction. Field equations, constitutive equations and Lagrangian equations with generalized coordinates are derived for non-linear thermoviscoelasticity, non-linear thermoelasticity and heat conduction, plasticity, and compressible heat conducting fluids with Newtonian and non-Newtonian viscosity. The thermodynamics of instability is also analyzed from the same fundamental viewpoint.