Quadratic-stretch elasticity

Abstract

A nonlinear small-strain elastic theory is constructed from a systematic expansion in Biot strains, truncated at quadratic order. The primary motivation is the desire for a clean separation between stretching and bending energies for shells, which appears to arise only from reduction of a bulk energy of this type. An approximation of isotropic invariants, bypassing the solution of a quartic equation or computation of tensor square roots, allows stretches, rotations, stresses, and balance laws to be written in terms of derivatives of position. Two-field formulations are also presented. Extensions to anisotropic theories are briefly discussed.

arXiv commentMinor edits

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Cited by in corpus (5)

• Stretch formulations and the Poynting effect in nonlinear elasticity
• Dilation-invariant bending of elastic plates, and broken symmetry in shells
• Energies for elastic plates and shells from quadratic-stretch elasticity
• 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