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Rank 1 Convexity for a Class of Incompressible Elastic Materials

  • J. Ernest Dunn
  • Roger Fosdick
  • Ying Zhang

Abstract

We consider the class of incompressible elastic solids for which the stored energy function W(・) depends on the deformation gradient F through |F|2, W( F )=φ(κ), \( \kappa=\sqrt {{{{\left|F \right|}^2}-3}} \). We show that W(・) is rank 1 convex at a given Fφ(・) is non-decreasing at \( \sqrt {{{{\left|F \right|}^2}-3}} \) and has \( \sqrt {{{{\left|F \right|}^2}-3}} \) as a point of convexity.

Keywords

Tangent Space Deformation Gradient Order Tensor Lagrange Multiplier Method Deformation Gradient Tensor 
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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Reference

  1. [1]
    Dunn, J.E., Fosdick, R. (1994): The Weierstrass condition for a special class of elastic materials. J. Elasticity 34, 167–184MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Italia, Milano 2003

Authors and Affiliations

  • J. Ernest Dunn
  • Roger Fosdick
  • Ying Zhang

There are no affiliations available

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