Topology optimisation of composites containing base materials of distinct poisson's ratios

From recent studies on natural composites such as nacre and bone, it has shown that the mechanical properties of the composite are significantly affected by the Poisson's ratio of each constituent phase. In some cases it is found that when the Poisson's ratio approaches the incompressibility limit, the stiffness of the composite in one or more directions can increase dramatically, in some cases by two or more orders of magnitude than the softer phase. In this paper we investigate designing the composite of maximum stiffness by a topology optimisation approach. The method used is based on the bi-directional evolutionary structural optimisation (BESO). The Optimisation problem is formulated and it is solved by a searching algorithm based on the sensitivity analysis. The effect of interpolation function in the sensitivity analysis is studied. Examples of different combinations of Poisson's ratios are presented. The stiffness is found to increase from its base value. In the case of one phase having negative Poisson's ratio, the increase is very significant. It is concluded that the proposed method is effective in optimising the stiffness of this class of composite.