Dislocations, disclinations, and metric anomalies as sources of global strain incompatibility in thin shells

Abstract

The strain incompatibility equations are discussed for nonlinear Kirchhoff-Love shells with sources of inhomogeneity arising due to a distribution of topological defects, such as dislocations and disclinations, and metric anomalies, such as point defects, thermal strains, and biological growth. The incompatibility equations are given for all topological surfaces, with or without boundary, which are isometrically embeddable in a 3-dimensional Euclidean space.