In-plane elastic properties of auxetic multilattices

摘要

Numerous studies proposed the possible use of auxetic periodic structures in engineering applications. The regular cellular structures with several nodes in a unit cell of the lattice are referred to as multilattices. In this work, a homogenization procedure was applied to three types of plane multilattices: conventional and re-entrant honeycombs (REH), double arrowheads, and semi REH constructed from elastic ribs. It was shown, that for all considered lattices the components of effective tensors of elasticity can be obtained in an explicit way in the frames of the same approach taking stretching, bending and shear of the ribs into account. As a result, equivalent elastic in-plane properties were found analytically as the functions of geometrical parameters of the lattices and the elastic parameters of the ribs. The estimation of the limits for the elastic properties was also performed. It was investigated how the condition of constant density changes the dependence of the elastic constants on the angles between the nodes. Also, different lattices were investigated at the same reference density taken equal to the density of the honeycomb lattice. The most typical cases from the practical point of view were considered and the corresponding elastic parameters were calculated for them.