Dilation-Invariant Bending of Elastic Plates, and Broken Symmetry in Shells

@article{Vitral2022DilationInvariantBO,
  title={Dilation-Invariant Bending of Elastic Plates, and Broken Symmetry in Shells},
  author={Eduardo Vitral and J A Hanna},
  journal={Journal of Elasticity},
  year={2022}
}
We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is invariant under spatial dilations. This kinematic measure and its corresponding isotropic quadratic energy resolve outstanding issues in thin structure elasticity, including the natural extension of primitive bending strains for straight rods to plates, the… 
Energies for Elastic Plates and Shells from Quadratic-Stretch Elasticity
We derive stretching and bending energies for isotropic elastic plates and shells. Through the dimensional reduction of a bulk elastic energy quadratic in Biot strains, we obtain two-dimensional
Remarks on stretch formulations and the Poynting effect in nonlinear elasticity
The second invariant of the left Cauchy-Green deformation tensor B (or right C ) has been argued to play a fundamental role in nonlinear elasticity. Generalized neo-Hookean materials, which depend

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