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.

From Volterra dislocations to strain-gradient plasticity

“…This extends the uniqueness result [KMS15, Theorem 3] in the dislocation-free case v = 0; the method of proof here is quite different and requires new ideas. The importance of this result is that in different contexts, it is useful to describe the geometry of a dislocation in different ways-compare, for example, the different metrics used in [KMS15], in [Kup17] and in the current work. Theorem 3.3 establishes that they all describe the same object.…”

“…This framework has other potential payoffs: for example, it can be used for analyzing the bending energy of thin bodies with dislocations[Kup17], whereas it is not obvious how to treat bending within the admissible strain model. It also relates to other recent work describing the dynamics of dislocations using a multiplicative strain decomposition rather an additive one[HR22].…”