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 Föppl–von Kármán shallow shell theory. The reference surface, obtained as a shell configuration in the absence of defect and external forces, accordingly has a finite non-zero curvature. The interaction of the defect with the curvature of the reference surface is emphasized through the problem of defect driven buckling of an elastic sheet. Detailed bifurcation diagrams, including the post-buckling deformation behaviour, are plotted for several combinations of defect types, reference curvatures, and boundary conditions. A pitchfork bifurcation is obtained when the reference surface is flat irrespective of the defect type and boundary condition. For curved reference surfaces there are some cases where the pitchfork bifurcation persists and others where it does not. The varied response demonstrates the rich interaction of the defects with the curvature of the reference surface.