The Isotropic and Cubic Material Designs. Recovery of the Underlying Microstructures Appearing in the Least Compliant Continuum Bodies

Design Method of Lightweight Metamaterials with Arbitrary Poisson's Ratio

A heuristic approach to design lightweight metamaterials with novel configurations and arbitrary Poisson’s ratio is studied by using the functional element topology optimization (FETO) method. Mathematical model of the optimization problem is established, where the minimization of the mass is set as the objective, then a series of metamaterials with Poisson’s ratio ranging from −1.0 to +1.0 are designed by solving this model. The deformation resistance and vibration reduction performance of the novel metamaterials and conventional honeycomb are compared by numerical simulations. Specific stiffness analysis shows that the novel metamaterials are 5.6 to 21.0 times more resistant to deformation than that of the honeycomb, and frequency response shows about 60% improvement in vibration reduction performance. Finally, the lightweight effects of the novel metamaterials on deformation resistance and vibration reduction performance are analyzed, and further analysis reflects that the lightweight effects increase with the increase of the absolute value of the Poisson’s ratio.

Auxeticity of Concentric Auxetic-Conventional Foam Rods with High Modulus Interface Adhesive

While the rule of mixture is applicable for addressing the overall Poisson’s ratio of a concentrically aligned bi-layered rod under longitudinal loading, the same cannot be said for this rod under torsional loading due to the higher extent of deformation in the rod material further away from the torsional axis. In addition, the use of adhesives for attaching the solid inner rod to the hollow outer rod introduces an intermediate layer, thereby resulting in a tri-layered concentric rod if the adhesive layer is uniformly distributed. This paper investigates the effect of the adhesive properties on the overall auxeticity of a rod consisting of two concentrically aligned cylindrical isotropic foams with Poisson’s ratio of opposite signs under torsional loads. An indirect way for obtaining Poisson’s ratio of a concentrically tri-layered rod was obtained using a mechanics of materials approach. Results show that the auxeticity of such rods is influenced by the adhesive’s stiffness, Poisson’s ratio, thickness, and radius from the torsional axis.

Computational Modelling of Structures with Non-Intuitive Behaviour

This paper presents a finite-element analysis of honeycomb and re-entrant honeycomb structures made of a two-phase composite material which is optimized with respect to selected parameters. It is shown that some distributions of each phase in the composite material result in the counter-intuitive mechanical behaviour of the structures. In particular, negative values of effective Poisson's ratio, i.e., effective auxeticity, can be obtained for a hexagonal honeycomb, whereas re-entrant geometry can be characterized by positive values. Topology optimization by means of the method of moving asymptotes (MMA) and solid isotropic material with penalization (SIMP) was used to determine the materials' distributions.