A multiscale topology optimisation framework for hollow spheres as cellular materials

Cellular materials can be designed to achieve mechanical properties with low weight. Among them, hollow spheres have been investigated since modern manufacturing methods can accurately produce them. This work aims to develop an optimisation procedure to distribute hollow spheres to minimise the compliance of a structure through a multiscale approach. The model has two geometrical parameters: internal and external diameters, in which the asymptotic homogenisation method (AHM) is employed to predict the effective properties of the material. Equations relating the effective properties to geometrical parameters are obtained through the least square method. Then, topology optimisation is employed to minimise compliance constrained by an admissible relative density. The optimised structures are compared to homogeneous distributions of hollow spheres, and compliance reductions up to 79% are reached. The optimum distributions of hollow spheres are validated against the classical solid isotropic with material penalisation (SIMP) approach. Moreover, some structures are 3D-printed to show the feasibility and capabilities of the proposed approach. Experimental tests are conducted on the structures through additive manufacturing. It is shown that optimised structures outperform the ones with homogeneous distributions of hollow spheres with the same relative density.