Pure measures of bending for soft plates

Abstract

This paper, originally motivated by a question raised by Wood and Hanna [Soft Matter, 2019, 15, 2411], shows that pure measures of bending for soft plates can be defined by introducing the class of bending-neutral deformations, which represent finite incremental changes in the plate's shape that do not induce any additional bending. This class of deformations is subject to a geometric compatibility condition, which is fully characterized. A tensorial pure measure of bending, which is invariant under bending-neutral deformations, is described in detail. As shown by an illustrative class of examples, the general notion of a pure measure of bending could be useful in formulating direct theories for soft plates, where stretching and bending energies are treated separately.