(untitled) (Communications in Mathematical Research, 2022)
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 is 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 presents an important advance towards computationally efficient multiscale modeling frameworks considering microstructure uncertainties.