On speeding up an asymptotic-analysis-based homogenisation scheme for designing gradient porous structured materials using a zoning strategy

Gradient porous structured materials possess significant potential of being applied in many engineering fields. To accelerate the design process of infill graded microstructures of uniform local density, a novel asymptotic homogenisation topology optimisation method was proposed by Zhu et al. (J Mech Phys Solids 124:612–633, 2019), aiming for (1) significantly enriching the pool of representable graded microstructures; and (2) deriving an homogenised formulation for stress analysis in consistency with fine-scale results. But the work is severely confined from being widely applied, mainly due to the following two reasons. Firstly, to circumvent macroscopically pointwise computation for solving various microscopic cell problems, linearisation had to be adopted for its numerical implementation, and this significantly reduces the design freedom. Secondly, lacking of sensitive analysis, genetic algorithm was chosen for optimisation, inevitably decreasing the computational efficiency. To address these bottleneck challenging issues, a zoning scheme empowered by computational parallelism is introduced, and the sensitivity analysis associated with the new asymptotic framework is conducted. Through comparisons with fine-scale simulation results, the proposed algorithm is shown to be an effective tool for evaluating the mechanical behaviour of graded microstructures. As an optimisation tool, the mapping function takes a concise and explicit form. But its parameterisation still needs further investigation, so as to improve the solution optimality of the present approach, especially in comparison with another recently proposed method (Groen and Sigmund, Internat J Numer Methods Engrg 113(8):1148–1163, 2018). Optimisation results for three-dimensional graded microstructures are also shown, which are not frequently discussed in literature, possibly because of the high computational cost generated.