In-plane loading of hexagonal honeycombs: Post- bifurcation and stability behavior (INVITED)

Abstract eng:
Buckling of honeycombs is an important problem. We identify three open questions: (i) How does the mechanical response depend on the applied loading device? (ii) What can the Bloch wave representation of all bounded perturbations contribute to our understanding of the stability of post-bifurcated equilibria? and (iii) How does material nonlinearity affect the critical bifurcation load? We model the honeycomb as a 2D infinite perfect periodic medium and use group theory (instead of the imperfection method) to study its bifurcation behavior under various far-field loadings. We evaluate stability using two criteria: rank-one convexity and Bloch wave stability. We find that the post-bifurcation behavior is extremely sensitive to the loading device, and confirm that the flower mode is unstable. Our (first ever) Bloch wave stability analysis of the post-bifurcated equilibria shows that the flower mode is stable for all sufficiently short wavelength perturbations, explaining its observation by Papka and Kyriakides (1999).

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