Cusp singularity-based bistability criterion for geometrically nonlinear structures

This letter introduces a method of analyzing multi-stable truss structures and unit cells of engineered materials using the third order derivative of the formulated system's potential energy function. The method can determine systematically all the cusp point singularities arising at the onset of bistability, and therefore identify the regions of hysteretic superelasticity and superplasticity from the usual geometrical nonlinearity in the solution space. The ability to design these behaviors is a great advantage that is highlighted with the example analysis of a bistable plane truss and a tetrahedral unit cell of a 3D lattice structure.