Constitutive Equations

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


This chapter contains a wide discussion about the constitutive axioms. These axioms constitute general rules that any material must satisfy in answering to external agents. The first two of them state that the answer of a material at a point depends, in a certain way, on past history of a neighborhood of that point. The third one is the objectivity principle stating that the response of materials does not depend on the rigid frame of reference adopted to observe their behavior. The fourth is the equipresence principle postulating that, a priori, the fundamental variables of the thermokinetic process influence all the fields describing the answer of the body. Finally, the last one, the dissipation principle, requires that materials, in reacting to the external agents, satisfy the second principle of thermodynamics in any process. In such a way, the entropy inequality becomes a restriction on the constitutive equations rather than a restriction on the processes. The effects of these principles on the constitutive equations are analyzed for thermoviscoelastic materials.


Constitutive Equation Reference Configuration Entropy Inequality Kirchhoff Stress Tensor Heat Flux Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. [29]
    I-Shih Liu, Method of Lagrange multipliers for exploitation of the entropy principle. Arch. Rat. Mech. Anal. 46, (1972)Google Scholar
  2. [39]
    I. Müller, The coldness, a universal function in thermoelastic bodies. Arch. Rat. Mech. Anal. 41, (1971)Google Scholar

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

Personalised recommendations