Determination of the random spatial variation of the bending stiffness in composite materials

The macroscopic stiffness of a composite material is closely related to its microstructural configuration and multiscale simulation methods can establish this link through homogenization. In numerical homogenization, equivalent stiffness is usually described through stiffness tensor components, which are computed by applying specific boundary conditions (BCs) corresponding to characteristic deformation states, such as tension and shear. In this work, bending BCs are applied to compute the equivalent flexural stiffness in ABD matrix form according to classical laminate theory. In the case of random composites, the spatial variation of the volume fraction is known to significantly affect the apparent mechanical properties, which can be described by random fields. The case of a random short fiber-reinforced composite is investigated herein, and random fields of the equivalent stiffness are computed. Essentially, random fields of the ABD matrix are determined, whose components correspond to bending as well as extension/shear BCs, and their statistics are compared. The computed random stiffness components can be used in stochastic finite element analysis of composite shell structures.