An effective model for Lipschitz wrinkled arches

Within the framework of the Koiter's linear elastic shell theory, we study the limit model of a Lipschitz curved arch whose mid-surface is periodically waved. The magnitude and the period of the wavings are of the same order. To achieve the asymptotic analysis, we consider a mixed formulation, for which we perform a two-scale homogenization technique. We prove the convergence of the displacements, the rotation of the normal, and the membrane strain. From the limit formulation, we derive an effective model for curved critically wrinkled arches. It introduces two membrane strain functions—instead of one in the classical case—and exhibits a corrector membrane term to the coupling between the rotation of the normal and the membrane strain.