Balance Equations

  • Antonio Romano
  • Addolorata Marasco
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


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.


Jump Condition Entropy Inequality Singular Surface Heat Flux Vector Entropy Flux 
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Antonio Romano
    • 1
  • Addolorata Marasco
    • 1
  1. 1.Department of Mathematics and Applications “R. Caccioppoli”University of Naples Federico IINaplesItaly

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