Energy Minimization for Isotropic Nonlinear Elastic Bodies

  • M. Šilhavý
Part of the International Centre for Mechanical Sciences book series (CISM, volume 447)


The microstructures accompanying phase transitions in solids are governed by the minimum energy principle. Basic properties of the energy functional (the existence/nonexistence of minima, occurrence/absence of a microstructure) are reflected by the semiconvexity properties of the energy: convexity, rank 1 convexity, polyconvexity, and quasiconvexity. The occurrence of microstructures is connected with the incompatibility of individual solid phases and with the nonexistence of minimizers of energy. In their presence, one is concerned with effective properties. The procedure is the relaxation.


Energy Minimization Convex Function Deformation Gradient Invariant Function Macroscopic Deformation 
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.


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Copyright information

© Springer-Verlag Wien 2004

Authors and Affiliations

  • M. Šilhavý
    • 1
    • 2
  1. 1.Mathematical Institute AS CRPragueCzech Republic
  2. 2.Department of MathematicsUniversity of PisaPisaItaly

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