Generalized variational principle in dissipative hydrodynamics and continuum mechanics

Generalized Variational Principle for Dissipative Hydrodynamics: Shear Viscosity from Angular Momentum Relaxation in the Hydrodynamical Description of Continuum Mechanics

Gyarmati's Variational Principle of Dissipative Processes

Like mechanics and electrodynamics, the fundamental laws of the thermodynamics of dissipative processes can be compressed into a variational principle. This variational principle both in its differential (local) and in integral (global) forms was formulated by Gyarmati helped by the present author in 1965. This principle was applied to several fields of irreversible processes: first of all, his...

Variational Methods, Multisymplectic Geometry and Continuum Mechanics

This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order multisymplectic field theories with constraints, such as the incompressibility constraint. The results obtained in this paper set the stage for multisymplectic re...

Variational Theory of Mixtures in Continuum Mechanics

In continuum mechanics, the equations of motion for mixtures were derived through the use of a variational principle by Bedford and Drumheller in [1978]. Only immiscible mixtures were investigated. We have chosen a different approach. In this paper, we first write the equations of motion for each constituent of an inviscid miscible mixture of fluids without chemical reactions or diffusion. The ...

Variational Multisymplectic Formulations of Nonsmooth Continuum Mechanics

This paper develops the foundations of the multisymplectic formulation of nonsmooth continuum mechanics. It may be regarded as a PDE generalization of previous techniques that developed a variational approach to collision problems. These methods have already proved of value in computational mechanics, particularly in the development of asynchronous integrators and efficient collision methods. T...