A stochastic micromechanical model for multiphase composites containing spherical inhomogeneities

A stochastic micromechanical framework for multiphase composites is proposed to characterize the probabilistic behaviors of effective properties of composite materials. Based on our previous work, the deterministic micromechanical model of the multiphase composites is derived by introducing the strain concentration tensors. By modeling the volume fractions and properties of constituents as stochastic, we extend the deterministic framework to stochastic to incorporate the inherent randomness of effective properties among different specimens. A new simulation framework, consisting of univariate approximation for multivariate function, Newton interpolations, and Monte Carlo simulation, is developed to quantitatively evaluate the stochastic characteristics of the effective properties of composites. Numerical examples including limited experimental validations, comparisons with existing micromechanical models, and the Monte Carlo simulations indicate that the proposed models provide an accurate and computationally efficient framework in characterizing the effective properties of multiphase composites. Finally, the effects of the correlation between the constituents’ material parameters are discussed based on our proposed stochastic micromechanical model, which shows that the negative correlation between Young’s modulus and Poisson’s ratio of the constituents can enhance the effective properties of the composites.