Multi-material topology optimisation of micro-composites with reduced stress concentration for optimal functional performance

Highlights: • A new multi-material topology optimisation framework for design of periodic micro-composites is developed. • The effects of weight ratios assigned to the property and stress objectives are investigated. • Evaluation indices are proposed with decision-making approaches to obtain the optimal solution for competing objectives. 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.