Global Solution Branches of Forced Nonlinearly Elastic Single-Director Surfaces

We prove the existence of classical solutions for nonlinearly elastic, single-director surfaces or shells characterized by finite mid-plane strains and curvature. We employ topological methods, yielding solution continua far (in norm) from an unloaded, stress-free reference configuration, i.e., a global implicit function theorem of sorts. We first establish the existence of a local solution path, which is subsequently shown to be part of a global solution branch, viz., a maximal connected, locally compact set, emanating from the unloaded state.