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 first-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 first-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. (C) 2000 Elsevier Science Ltd. All rights reserved.