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Multiple Natural States for an Elastic Isotropic Material with Polyconvex Stored Energy

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Abstract

We show a necessary and sufficient condition for the undistorted reference configuration y(x)=x, with ∇y=F=1, to be a minimizer of the total stored energy for an isotropic elastic body. Polyconvexity of the stored energy function is not sufficient, and we give an example which possesses two distinct natural (i.e., unstressed) states to illustrate this point.

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Authors and Affiliations

  1. Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN, 55455, U.S.A.

    Roger Fosdick & Gianni Royer-Carfagni

  2. Department of Civil Engineering, University of Parma, Parco Area delle Scienze 181/A, I 43100, Parma, Italy

    Roger Fosdick & Gianni Royer-Carfagni

Authors
  1. Roger Fosdick
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  2. Gianni Royer-Carfagni
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Fosdick, R., Royer-Carfagni, G. Multiple Natural States for an Elastic Isotropic Material with Polyconvex Stored Energy. Journal of Elasticity 60, 223–231 (2000). https://doi.org/10.1023/A:1010960902320

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  • DOI: https://doi.org/10.1023/A:1010960902320

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