This chapter contains the general integral or local balance law in Eulerian and Lagrangian form. Then, this general law is used to derive the mass conservation, the Cauchy stress-tensor, Piola–Kirchhoff tensor, the momentum equation, the angular momentum with the symmetry of Cauchy’s stress-tensor, the balance of energy, and the Clausius–Duhem entropy inequality. All the above laws are written in the presence of a moving singular surface across which the fields exhibit discontinuities. The balance laws considered in this chapter are fundamentals for all the developments of continuum mechanics, also in the presence of electromagnetic fields.
KeywordsJump Condition Entropy Inequality Singular Surface Heat Flux Vector Entropy Flux
- A. Marasco, A. Romano, Balance laws for charged continuous systems with an interface. Math. Models Methods Appl. Sci. (M3AS) 12(1), 77–88 (2002)Google Scholar
- I. Müller, The coldness, a universal function in thermoelastic bodies. Arch. Rat. Mech. Anal. 41, (1971)Google Scholar
- W. Noll, Lectures on the foundations of continuum mechanics and thermodynamics. Arch. Rat. Mech. Anal. 52, (1973)Google Scholar
- A. Romano, A macroscopic theory of thermoelastic dielectrics. Ric. Mat. Univ. Parma 5, (1979)Google Scholar
- A. Romano, A macroscopic non-linear theory of magnetothermoelastic continua. Arch. Rat. Mech. Anal. 65, (1977)Google Scholar