Interaction of a defect with the reference curvature of an elastic surface

Abstract

The morphological response of two-dimensional curved elastic sheets to an isolated defect (dislocation/disclination) is investigated within the framework of Foppl-von Karman shallow shell theory. The reference surface, obtained as a...

Singular Points and Singular Curves in von Kármán Elastic Surfaces

“…The following derivation of smooth von Kármán equations follows our recent work [20,21]. Let Ω ⊂ R 2…”

“…To begin with we assume that both the stress field and the moment field does not concentrate on S (this is less general than what was considered in writing the equilibrium equations); i.e., Σ ∈ B(Ω, Sym), with piecewise smooth bulk density σ, and M ∈ B(Ω, Sym), with piecewise smooth bulk density m. We also assume the elastic strain fields to not concentrate on S, i.e., E e ∈ B(Ω, Sym) and Λ e ∈ B(Ω, Sym), with bulk densities e e and λ e , respectively. We assume constitutive relations as given in (20), which can be equivalently written as…”

“…In order to elaborate on the contributions of this work, we begin by stating the inhomogeneous von Kármán equations for smooth fields with inhomogeneities given in terms of smooth plastic strain fields, an incompatibility field (which can be obtained in terms of smooth defect densities), and a smooth body force field. A brief derivation of these equations, following our recent work [20,21], has been given in Section 3.1.…”