Superelasticity and stability of a shape memory alloy hexagonal honeycomb under in-plane compression

Nitinol (NiTi) shape memory alloy honeycombs, fabricated in low densities using a new brazing method [Grummon, D., Shaw, J., Foltz, J., 2006. Fabrication of cellular shape memory alloy materials by reactive eutectic brazing using niobium. Materials Science and Engineering A 438–440, 1113–1118], recently demonstrated enhanced shape memory and superelastic properties [Shaw, J. A., Grummon, D. S., Foltz, J., 2007b. Superelastic NiTi honeycombs: Fabrication and experiments. Smart Materials and Structures 16, S170–S178] by exploiting kinematic amplification of thin-walled deformations. The realization of such adaptive, light-weight cellular structures opens interesting possibilities for design and novel applications. This paper addresses the consequent need for design and simulation tools for engineers to make effective use of such structures by, as a first step, analyzing the multi-scale stability aspects of the superelastic behavior of a particular hexagonal, thin-walled, SMA honeycomb under in-plane compression. An in-depth parameter study is performed of the influence of different material laws on the behavior of honeycombs of finite and infinite extent with perfect and imperfect initial geometries. A finite element-based simulation is presented that credibly captures the behavior seen in experiments.