Compatibility Conditions for Singular Strain Fields on Linear Shells

Abstract

Strain compatibility conditions are derived for orientable linear shells with strain fields which are piecewise smooth and develop concentrations along curves and junctions on the shell surface. The concentrations in strain fields appear due to folds, fold dipoles, and tears in the shell. The compatibility equations include local conditions in the bulk of the shell surface, local equations at the singular curves in terms of jump in strain fields (and their gradients) and strain concentrations, local equations at the junction of singular curves, and global conditions for every family of irreducible curves on the shell surface. These equations couple shell kinematics with the geometry and topology of the shell surface. The applicability of the framework is illustrated assuming the bulk strains to be elastic and the strain concentrations to be plastic. The compatibility equations then lead to a boundary value problem for the determination of stresses and moments in an elastic surface in response to the incompatibility induced by the plastic strains.