Negative Poisson's ratio in hollow sphere materials

This paper presents a study on the auxetic behaviour of the materials composed of hollow spheres. Although, as a newly developed material, the hollow sphere structures have gained a great deal of scientific attention, few studies have acknowledged its auxetic performance. Auxetic materials or materials with a negative Poisson's ratio have been a subject of intensive research due to their unusual and, in many extents, superior mechanical properties. A number of different auxetic systems that have been developed commonly based on designing special geometry of the material microstructure. However, in the hollow sphere structures, this mechanism is essentially different and the auxetic effect is attributed to the peculiarities of deformation of a thin-wall hollow sphere and to the interaction between the spheres in the assembly. In this study it is shown that the negative Poisson's ratio in this material is due to the high ratio between tangential to normal stiffnesses of a thin-wall hollow sphere. To evaluate the mechanical properties of these materials a homogenisation procedure based on the Cosserat 3D continuum theory is adopted. In this procedure, an assembly of the flexible thin-wall spheres is modelled as a stack of rigid spheres connected by a set of linear springs. The developed continuum model is validated against the direct finite element analysis of a regular assembly of the hollow spheres. Influence of the various design parameters on the macroscopic mechanical behaviour of the hollow sphere materials is investigated. The numerical study is focused on the auxetic behaviour of various kinds of packing arrangements of the hollow spheres.