Multiple equilibria for unlinked and weakly-linked cellular structural forms

Abstract

It is demonstrated that a structural form comprising n unlinked or weakly-linked separate identical cells can, by its nature, suffer an explosion of unstable post-buckling states, associated with an n-fold compound critical point. Examples of rigid-link models, and atomic matrix cellular models employing a Lennard-Jones potential, are included. Attention is paid to criteria for the appearance of homogeneous, localized but distributed, and thoroughly-localized solutions. For the atomic models, generalized coordinates that exploit local and global symmetries of unlinked cells are introduced in a block diagonalization context, to clarify the bifurcation structure. A discretized Lagrangian formulation is introduced to untangle the paths for weakly-linked cells.