Auxetic Properties of Chiral Hexagonal Cosserat Lattices Composed of Finite-Sized Particles

This article is devoted to the study of auxetic properties of Cosserat hexagonal lattices composed of finite-sized particles with complex connections. The description of complex connections is given; their mathematical model is elaborated and the properties are studied. The introduction of complex connections enables one varying their structure and component parameters. Due to that there arise possibilities for both simulation of nonchiral lattices with symmetrical bonds and with a chiral microstructure and construction of lattices with desired properties. The discrete and micropolar equations of the lattice are obtained. As a result, the macroparameters are expressed in terms of the lattice microparameters. The dependence of the Poisson's ratio on the lattice microparameters is obtained. It allows finding and analyzing parameters, for which the lattice possesses auxetic properties. The importance of rotational degrees of freedom of particles and chirality for the appearance of auxetic properties is shown. For verification, the results of the calculation of the Poisson's ratio obtained on the basis of theoretically obtained relations are compared with the results of numerical simulation of the stretching of the lattice.