Contrasting bending energies from bulk elastic theories
arXiv:1808.01310 · doi:10.1039/C8SM02297F
Abstract
The choice of elastic energies for thin plates and shells is an unsettled issue with consequences for much recent modeling of soft matter. Through consideration of simple deformations of a thin body in the plane, we demonstrate that four bulk isotropic quadratic elastic theories have fundamentally different predictions with regard to bending behavior. At finite thickness, these qualitative effects persist near the limit of mid-surface isometry, and not all theories predict an isometric ground state. We discuss how certain kinematic measures that arose in early studies of rod mechanics lead to coherent definitions of stretching and bending, and promote the adoption of these quantities in the development of a covariant theory based on stretches rather than metrics.
arXiv commentSmall correction
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Cited by in corpus (8)
- Dilation-invariant bending of elastic plates, and broken symmetry in shells
- Stretch formulations and the Poynting effect in nonlinear elasticity
- Quadratic-stretch elasticity
- Some observations on variational elasticity and its application to plates and membranes
- Energies for elastic plates and shells from quadratic-stretch elasticity
- Anisotropic swelling of anisotropic elastic panels
- Shear stresses in fluid and solid membranes with bending elasticity
- Assorted remarks on bending measures and energies for plates and shells, and their invariance properties