A higher-order three-scale reduced homogenization approach for nonlinear mechanical properties of 3D braided composites

A more effective higher-order three-scale reduced homogenization (HTRH) approach is developed for predicting the nonlinear mechanical properties of three-dimensional (3D) 4-directional braided composite. In this work, the 3D braided composites are considered by periodic distributions of different unit cells on microscale and mesoscale configurations. First, the various high-order unit cell functions based on the microscopic and mesoscopic domain are obtained by multiscale expansion methods. Then, two kinds of homogenization coefficients are given, and relative nonlinear homogenized equations are derived on the macroscopic domains. Further, the reduced order systems for the nonlinear multiscale problem are constructed. The significant features of the reduced-order multiscale method are: (i) an asymptotic higher-order homogenized solution evaluated by post-processing that does not need high-order continuities for the homogenization solutions, (ii) an effective model reduction format for investigating the higher-order nonlinear multiscale problems with less computational cost and (iii) an novel three-scale formulas established for analyzing the 3D braided composites. Finally, the validity of the proposed approach in comparison to the direct numerical simulations and classical multiphase method is computed on some damage and elasto-plastic problems. These numerical examples show that the HTRH method is effective to study the nonlinear problems of the 3D braided composites, and provides a potential application for practical engineering calculation.