This study develops a new multi-material topology optimisation framework for design of periodic micro-composites with optimal functional performance and reduced stress concentration. First, multi-material topology optimisation is developed based on the alternating active phase algorithm and inverse homogenisation method with the sensitivity analysis derived for specific property objective i.e., negative Poisson's ratio (NPR) or maximum effective bulk modulus (EBM) and (p-norm macroscopic) stress objective. Then, the effects of initial material distribution and weight ratio (w₁, w₂ assigned to the property and stress objectives, respectively) are investigated, and the evaluation indices are also developed to obtain the optimal solution. Further, two cases related to the design of micro-composites for maximised either NPR or EBM with reduced maximum stress are performed. The results show that when designing the multi-material NPR micro-composites, the decrease of w₁/w₂ contributes to a general decease of both NPR and maximum stress. While in designing the maximum EBM, decreasing w₁/w₂ leads to the reduced maximum stress and simultaneously reduced EBM; hereby, a decision-making method as well as the proposed evaluation index are both applied and compared for acquiring the optimal result. This study provides new methods and solutions to multi-material micro-composites design for future industrial applications.

本研究开发了一种新的多材料拓扑优化框架，用于设计具有最佳功能性能和减少应力集中的周期性微复合材料。首先，基于交替活性相位算法和逆均质化方法开发多材料拓扑优化，并针对特定属性目标，即负泊松比 (NPR) 或最大有效体积模量 (EBM) 和 ( p -norm宏观）应力目标。那么，初始材料分布和重量比的影响 ( w ₁ , w ₂分别分配给属性和应力目标）进行研究，并且还开发了评估指标以获得最佳解决方案。此外，还进行了两个与微复合材料设计相关的案例，以最大限度地降低 NPR 或 EBM，并降低最大应力。结果表明，在设计多材料NPR微复合材料时，w ₁ / w ₂的减小导致NPR和最大应力普遍减小。在设计最大 EBM 时，减小w ₁ / w ₂导致最大应力降低，同时 EBM 降低；因此，决策方法和建议的评价指标都被应用和比较以获得最佳结果。这项研究为未来工业应用的多材料微复合材料设计提供了新的方法和解决方案。