In-plane effective shear modulus of generalized circular honeycomb structures and bundled tubes in a diamond array structure

• Effective transverse shear modulus of a generalized circular honeycomb/tube assemblies in a diamond array structure.
• Rigorous evaluation of the moduli of thick honeycombs/tube assemblies by employing theory of elasticity.
• Refined technical theories׳ analyses employing thin ring and curved beam theories.
• Compact formulae from thin ring theory for designers to tailor the arrays.

Use of circular hexagonal honeycomb structures and tube assemblies in energy absorption systems has attracted a large number of literature on their characterization under crushing and impact loads. Notwithstanding these, effective shear moduli (G⁎) required for complete transverse elastic characterization and in analyses of hierarchical structures have received scant attention. In an attempt to fill this void, the present study undertakes to evaluate G⁎ of a generalized circular honeycomb structures and tube assemblies in a diamond array structure (DAS) with no restriction on their thickness. These structures present a potential to realize a spectrum of moduli with minimal modifications, a point of relevance for manufactures and designers. To evaluate G⁎ in this paper, models based on technical theories – thin ring theory and curved beam theory – and rigorous theory of elasticity are investigated and corroborated with FEA employing contact elements. Technical theories which give a good match for thin HCS offer compact expressions for moduli which can be harvested to study sensitivity of moduli on topology. On the other hand, elasticity model offers a very good match over a large range of thickness along with exact analysis of stresses by employing computationally efficient expressions.