Numerical Approaches To Continuum Micromechanics
Finite Element Analysis (FEA) based methods - Most such micromechanical methods use periodic homogenization, which approximates composites by periodic phase arrangements, explicitly models a repeating unit cell, and applies appropriate boundary conditions to extract the composite's properties or response. The Method of Macroscopic Degrees of Freedom can be used with commercial FEA codes, whereas analysis based on asymptotic homogenization typically requires special-purpose codes.
In addition to studying periodic microstructures, embedding models and analysis using macro-homogeneous or mixed uniform boundary conditions can be carried out on the basis of Finite Element models. Due to its high flexibility and efficiency, the FEA at present is the most widely used numerical tool in continuum micromechanics.
Generalized Method of Cells (GMC) - Explicitly considers fiber and matrix subcells from periodic repeating unit cell. Assumes 1st-order displacement field in subcells and imposes traction and displacement continuity.
High-Fidelity GMC (HFGMC) - Like GMC, but considers a quadratic displacement field in the subcells.
A recent approach, Variational Asymptotic Method for Unit Cell Homogenization (VAMUCH), combines the merits of both asymptotic homogenization and FEA.
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