Principle of Virtual Power for thermomechanics of fluids and solids with dissipation

A fundamental variational principle, called the Principle of Virtual Power, is proposed in this paper to govern the irreversible thermomechanical processes for a material body. The principle and the corresponding variational equation of virtual velocity are formulated by integrating the classical field theories of continuum mechanics and thermodynamics. From the variational equation, we establish simultaneously the balance equations of linear momentum, of angular momentum, and of virtual internal power by applying the procedure of relaxation in Lagrangian mechanics. By assuming different types of system functions for internal power consisting of internal energy and newly introduced working dissipation, we are able to derive the constitutive equations for gas, liquid, or solid and the Fourier equation of heat conduction from the balance of virtual internal power. The combination of the law of conservation of mass, the first law of thermodynamics, and the proposed principle forms a complete set of fundamental principles for the thermomechanics of deformable bodies.

► We propose a Principle of Virtual Power to govern the irreversible thermomechanical processes for a material body.
► We establish the balance equations of momenta and of virtual internal power with the relaxation procedure.
► We derive constitutive and heat equations from the Principle of Virtual Power.