Prediction of mechanical properties in statistically inhomogeneous core–shell materials by second-order two-scale method

Abstract

This paper develops a novel second-order two-scale (SOTS) method to predict the mechanical performance of statistically inhomogeneous core–shell materials. As for these kinds of materials, the sophisticated microscopic information of inclusions, including their shape, size, orientation, spatial distribution, volume fraction, and so on, leads to changes of the macroscopic mechanical properties. Firstly, the microscopic configuration for the core–shell structure with random distribution is briefly characterized. Secondly, the SOTS formulae for solving the mechanical problems are proposed, and the importance of the two-scale approximate solutions in pointwise sense is given. Then, the associated prediction algorithm based on the two-scale model is brought forward in detail. Finally, some numerical results for the effective properties of the materials with varying probability distribution models are calculated and compared with the data by analytical and experimental results. The comparison shows that the statistical second-order two-scale model is validated for determination of the mechanical properties of inhomogeneous core–shell materials and demonstrates its potential applications in actual engineering applications.