A virtual scale approach to multi-scale calculations and its application in fiber-reinforced composites

With the development of materials science and technology into the nano-/micro-world, multi-scale problems have become a research focus. Multi-scale calculations usually select a periodic structure as a representative unit with a certain physical meaning and can represent the material properties at a given scale. However, due to the large number of representative elements with complex shape and boundary conditions, the workload of multi-scale calculations is normally huge. In the present effort, a novel virtual scale method is proposed for multi-scale calculations. To demonstrate the validity and significance of the new algorithm, multi-scale calculations have been carried out for the prediction of properties of the ever-popular fiber reinforced composite materials. The equivalent elastic modulus, Poisson`s ratio and coefficient of thermal expansion (CTEs) of fiber reinforced plastic in different scales predicted by the new method have been compared with those predicted by the well-established finite element method (FEM) and checked against the experimental results. The good agreements offer solid proof in terms of the validity of the newly developed virtual scale method. In principle, the method can be extended to tackle all multi-scale problems.