Pure measure of bending for soft plates

TL;DR

This paper introduces a new tensorial measure of bending for soft plates based on bending-neutral deformations, enabling the separation of bending and stretching energies in theoretical models.

Contribution

It defines and characterizes a class of bending-neutral deformations and develops a pure measure of bending invariant under these deformations.

Findings

Tensorial measure of bending is fully characterized.

Bending-neutral deformations are identified and described.

Potential for formulating direct theories with separate bending and stretching energies.

Abstract

This paper, originally motivated by a question raised by Wood and Hanna [Soft Matter, 15, 2411 (2019)], shows that pure measures of bending for soft plates can be defined by introducing the class of bending-neutral deformations, finite incremental changes of the plate's shape bearing no further bending. This class of deformations is subject to a geometric compatibility condition, which is fully characterized. A tensorial pure measure of bending, which is accordingly invariant under bending-neutral deformations, is described in details. As shown by an illustrative class of examples, the general notion of pure measure of bending could be of use to formulate direct theories for soft plates, where stretching and bending energies are kept separate.