A nonlinear generalization of the Koiter–Sanders–Budiansky bending strain measure

A physically motivated kinematical property to be demanded of a bending strain measure, beyond the ones that are conventionally agreed upon, is proposed. Guided by the criterion, a bending strain measure is proposed for a ®rst-order, nonlinear, elastic shell theory that has the property of vanishing in rigid and pure-stretch deformations of the shell. The measure is motivated by the Koiter±Sanders±Budiansky (KSB) bending measure of the ®rst-order, linear shell theory, and is shown to linearize to the KSB measure about the undeformed shell. On retaining the standard measure for membrane straining, work-conjugate stress and stress-couple resultants to the membrane and bending strains are derived, as is the expression for the internal virtual work in terms of the proposed strains, stress and stress-couple resultants. The bending strain is calculated for some simple deformations and compared with other generalizations of the KSB measure of the linear theory