Quadratic-stretch elasticity

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