Work Conditions and Energy Functions for Ideal Elastic-Plastic Materials

  • M. Šilhavý
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


The paper deals with the cyclic second law and Il’yushin’s condition for isothermal, ideal, isotropic, elastic-plastic materials at large deformations. The second law is equivalent to the existence of the elastic potential and the nonnegativity of plastic power. The material admits infinitely many free energies: The set of all energy functions is described in terms of a dissipation function. Its convexification provides the optimal lower bound for plastic work; it also figures in the maximal and minimal energies. Il’yushin’s condition is equivalent to the existence of the elastic potential and a new condition that is stronger than the normality of the plastic stretching and the convexity of the stress range. Il’yushin’s condition is also equivalent to the existence of a new kind of energy function called “the initial and final extended energy functions.” Materials of type C are introduced for which the initial extended energy function has additional convexity properties. It can be viewed as a stored energy of a Hencky hyperelastic material associated with the elastic-plastic material.


Energy Function Residual Energy Plastic Work Dissipation Function Elastic Range 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • M. Šilhavý
    • 1
    • 2
  1. 1.Mathematical Institute of the AV ČRCzech Republic
  2. 2.Department of MathematicsUniversity of PisaPisaItaly

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