A review of the FE2 method for composites - Raju, Karthikayen; Tay, Tong-Earn; Tan, Vincent Beng Chye (Multiscale and Multidisciplinary Modeling, Experiments and Design, 2021)
Composite materials and structures are inherently inhomogeneous and anisotropic across multiple scales. Multiscale modelling offers opportunities to understand the coupling of material behaviour and characteristics from the micro- to meso- and macro-scales, critical to the optimal design of composite structures for lightweighting and mechanical performance. FE 2 is an increasingly popular class of multiscale methods because of its versatility to model heterogeneous material behaviour across multiple scales. In classical FE 2 analysis, two finite elements (FE) calculations are carried out in a nested manner, one at the macroscale and the other at the microscale. Unlike conventional analysis, the macroscale FE analysis does not require homogenized constitutive properties because these are derived from the microscale FE simulations at the representative volume element (RVE) level. This has exciting significance for composite mechanics because properties characterized and defined at the microscale can be directly transferable to higher scales and validated with experiments. For example, failure criteria for composites need only be formulated at the microscale level of fibers and matrix. However, FE 2 analysis is computationally expensive and the generally more complex classical nested implementation of FE 2 is disadvantageous. This paper presents a review of the FE 2 method to model various phenomena in the mechanics of composite materials and discusses various implementations. Recently, the Direct FE 2 method, a variant of the FE 2 method, has been shown to be particularly easy to implement in commercial FE codes, which also means that it has the additional advantage of ready access to inbuilt constitutive models library and other advanced features of the commercial code. We conclude with future directions for multiscale modelling of composites using FE 2 .