Investigation of non-smooth solutions in finite elasticity using the phase-plane method


  • Adair R. Aguiar
  • Lucas A. Rocha



Phase-Plane Method, Phase Portrait, Finite Elasticity, Anisotropy


We use the phase-plane method to investigate a class of problems in finite elasticity for which the spatial derivative of a solution may have a finite jump at an interior point of the domain. In particular, we consider the equilibrium of a nonlinearly elastic annular disk fixed on its inner surface and subjected to a constant uniform pressure on its outer surface. We show that the solution of this problem is non-diferentiable at an interior point when the applied pressure exceeds a certain value. This value serves as an upper bound for the pressure that can be applied without violating the range of validity of the infinitesimal theory. On the other hand, non-smooth deformation fields are of interest in the study of crystalline materials that can exist in more than one crystal structure, such as the shape-memory alloys.


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Biografia do Autor

Adair R. Aguiar

EESC/USP, São Carlos, SP

Lucas A. Rocha

EESC/USP, São Carlos, SP


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