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

## TL;DR

This paper develops strain incompatibility equations for nonlinear Kirchhoff-Love shells considering sources like dislocations, disclinations, and metric anomalies, applicable to various topological surfaces with or without boundaries.

## Contribution

It introduces a comprehensive framework for strain incompatibility in shells accounting for topological defects and metric anomalies, extending previous models to all embeddable surfaces.

## Key findings

- Derived general incompatibility equations for shells with defects.
- Applicable to all topologically embeddable surfaces.
- Provides a basis for analyzing defect-induced strains in 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.