The statistical second-order two-scale method for thermomechanical properties of statistically inhomogeneous materials

A statistical second-order two-scale (SSOTS) method is established in a constructive way for predicting the thermomechanical properties of statistically inhomogeneous materials. For this kind of composite materials, the complicated micro-characteristics of inclusions, including their shape, size, orientation, spatial distribution, volume fraction and/or material properties and so on, lead to changes of the macroscopic thermomechanical properties, such as stiffness, coefficient of thermal expansion and strength of material. In this paper, a statistical model at an arbitrary position of the composite material is defined to represent the microstructure of the statistically inhomogeneous media at first. And then, the statistical second-order two-scale analysis formulation is derived. Finally, the numerical results for some statistically inhomogeneous composites are calculated by SSOTS algorithm, and compared with the data by experimental and theoretical methods.