Quantum mechanics

Anisotropy

Mathematics education

Composite number

Engineering

Materials science

Computer science

Constitutive equation

Statistical physics

Micromechanics

Representative elementary volume

Multiscale modeling

Mechanical engineering

Physics

Finite element method

Nanotechnology

Mathematics

Macro

Characterization (materials science)

Computational chemistry

Composite material

Microscale chemistry

Structural engineering

Chemistry

Programming language

Multiscale and Multidisciplinary Modeling Experiments and Design

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. FE2 is an increasingly popular class of multiscale methods because of its versatility to model heterogeneous material behaviour across multiple scales. In classical FE2 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, FE2 analysis is computationally expensive and the generally more complex classical nested implementation of FE2 is disadvantageous. This paper presents a review of the FE2 method to model various phenomena in the mechanics of composite materials and discusses various implementations. Recently, the Direct FE2 method, a variant of the FE2 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 FE2.

A review of the FE2 method for composites