Post-buckling and dynamic response of angled struts in elastic lattices

This paper presents analytical and reduced-order numerical solutions describing the non-linear response of slender, elastic struts (or plates) inclined relative to the loading direction. The solutions provide a highly efficient framework to predict post-buckling behaviors in cellular structures, including: stability regimes, peak strains during and after buckling, the work dissipated via cyclic loading, the impact of biaxial loading, and the role of geometric imperfections in the struts. Regime maps are presented that illustrate configurations that lead to snap-through, permanent deformation after unloading, strut failure, and enhanced hysteresis during cyclic loading. The maps illustrate that reversible snap-through events only occur within a very specific range of relative density (e.g. ̴0.25-0.4 for rhombic lattices). A highly efficient non-linear single degree-of-freedom dynamics model is derived from the statics solution, and is shown to be in excellent agreement with fully explicit, non-linear, dynamic finite element simulations for inclined struts. This simplified dynamics model is used to quantify the relationships between quasi-static responses, loading frequencies and energy dissipation during cycling loading. A key finding is that effective damping during cyclic loading is dramatically increased by non-linear behavior, even when the corresponding quasi-static result exhibits zero hysteresis. The implications for structured foams and the design of lightweight structural dampers is briefly discussed.