In-plane mechanical behaviors of 2D repetitive frameworks with four-coordinate flexible joints and elbowed beam members

The mechanical properties of an open-framework structure constructed of joints and beam members are strongly influenced by both its geometrical configuration and joint flexibility. This paper clarifies the relationship between joint flexibility and Poissonʹs ratio, which is a mechanical criterion for solid deformation, and discusses two types of in-plane anisotropic structures made up of four-coordinate flexible joints and elbowed beam members. Uniaxial tensile analyses estimate the linear and nonlinear elastic properties of these frameworks by applying straightforward joint modeling with multi-rotational degrees of freedom. The numerical results show that these proposed frameworks produce a variety of deformability dependent on the joint flexibility in auxetic deformation with a negative Poissonʹs ratio, the folding mechanics under kinematic indeterminacy, and the transition of Poissonʹs ratio between the positive and negative values. The geometrical and topological aspects of the obtained mechanical behaviors are discussed.