Cellular structures with hexagonal unit cells show a high degree of flexibility in design. Based on the geometry of the unit cells, highly orthotropic structures, structures with negative Poisson’s ratios, structures with high strain capability in a particular direction, or other desirable characteristics may be designed. Much of the prior work on cellular structures is based on hexagonal honeycomb-like unit cells, without any inclusions. The present paper envisages extending conventional cellular honeycomb-like structures to have inclusions or internal features within the unit cells. Various types of internal features such as contact elements, buckling beams, bi-stable/snap-through elements or viscous dashpots can result in unit cells which display stiffening, softening, negative stiffness, or dissipative behavior. A structure can be assembled using a specific element type, or different types of elements in specific arrangements, to provide desired system level behavior. The ability to so optimally and flexibly design cellular structures could potentially lead to their replacing conventional structures made from bulk materials.
As a first step, this paper presents work on hexagonal unit cells with linear springs as the simplest of inclusions. The hexagonal cell itself is comprised of rigid links and pin-joints. Since such a cell has no stiffness of its own, the behavior of any internal feature is emphasized. However, for kinematic stability purposes, three springs are required, and the significance of these constraints within the cell will be discussed. For different spring arrangements, closed-form analytical expressions are derived for the in-plane modulus and Poisson’s ratio. The analytical expressions are validated using NASTRAN finite element simulations, as well as against experimental tensile/compressive tests of fabricated unit cells with internal springs. When the spring stiffness exceeds certain values, the rigid cell wall assumption is no longer valid, and these bounds are established. The validated analysis is used to conduct design studies on how the cell modulus would vary with geometric parameters such as cell angle and cell wall length ratio.