Stochastic higher-order three-scale strength prediction model for composite structures with micromechanical analysis

Abstract

Stochastic multiscale modeling and analysis for the strength prediction of composite structures with complex multiscale random configurations remain a challenging problem. This is mainly due to the high-dimensional physical properties, the non-linear and non-Gaussian features, and the fact that many repeated evaluations of the corresponding stochastic multiscale model are often required. In this paper, we develop a stochastic higher-order three-scale strength prediction (SHTSP) model for composite structures, which is designed to overcome the limitations of prohibitive computation involving the microscale, the mesoscale, and the macroscale. By virtue of asymptotic homogenization theory and micromechanical analysis, the SHTSP model is established from the detailed stochastic higher-order three-scale homogenization analysis implemented with analytic solutions of typical composite structures subjected to tension, bending, and twist loads. The SHTSP model represents strength anisotropy through different strength criteria for evaluating the yield state of the different component materials of composite structures, which are induced by material interface deboning or matrix cracking in multiple scales. Moreover, these are constructed and calibrated from the high-accuracy mechanical analysis with help of two classes of mesoscopic and microscopic auxiliary cell functions, respectively. The corresponding numerical algorithm of the SHTSP model and a preprocessing multilevel strategy is designed to improve the computational efficiency. Finally, the numerical experiments in 3D cases illustrate the outstanding performance of the proposed SHTSP model, and the proposed method can significantly reduce the computational time.