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In this paper, a stochastic second-order two-scale (SSOTS) method is proposed for predicting the non-deterministic mechanical properties of composites with random interpenetrating phase. Firstly, based on random morphology description functions (RMDF), the randomness of the material properties of the constituents as well as the correlation among these random properties are fully characterized through the topologies of the constituents. Then, by virtue of multiscale asymptotic analysis, the random effective quantities such as stiffness parameters and strength parameters along with their numerical computation formulae are derived by a SSOTS strategy combined with the Monte-Carlo method. Finally, the SSOTS method developed in this paper shows an excellent computational accuracy, and therefore present an important advance towards computationally efficient multiscale modeling frameworks considering microstructure uncertainties. AMS subject classifications: 65M60, 35Q74 ∗Corresponding author. Email addresses: guanxf@tongji.edu.cn (X. Guan), yangzhiqiang@ hit.edu.cn (Z. Yang) 194 D. Hao, Z. Yang, X. Guan and Z. Yang / Commun. Math. Res., 36 (2020), pp. 193-210

Stochastic Second-Order Two-Scale Method for Predicting the Mechanical Properties of Composite Materials with Random Interpenetrating Phase