On the Bending Energy of Buckled Edge-Dislocations

Abstract

The study of elastic membranes carrying topological defects has a longstanding history, going back at least to the 1950s. When allowed to buckle in three-dimensional space, membranes with defects can totally relieve their in-plane strain, remaining with a bending energy, whose rigidity modulus is small compared to the stretching modulus. In this paper, we study membranes with a single edge-dislocation. We prove that the minimum bending energy associated with strain-free configurations diverges logarithmically with the size of the system.

References in corpus (2)

• Elastic theory of unconstrained non-Euclidean plates
• Scaling laws for non-Euclidean plates and the $W^{2,2}$ isometric immersions of Riemannian metrics

Cited by in corpus (1)

• From Volterra dislocations to strain-gradient plasticity