Micromechanics
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Micromechanics is the analysis of composite or heterogeneous materials on the level of the individual phases that constitute these materials. Given the properties (or nonlinear response) of the constituent phases, the goal of micromechanics is to predict the properties (or nonlinear response) of the composite material. The benefit is that the behavior of the composite can be determined without resorting to testing the composite, which can be expensive given the large number of permutations (e.g., constituent material combinations, fiber/inclusion volume fractions, fiber/inclusion arrangements, processing histories) represented by composites. Further, micromechanics can predict the full multi-axial properties and response of composites, which are usually anisotropic. Such properties are often difficult to measure experimentally, but they are required for structural analysis. Of course, to rely on micromechanics, the particular micromechanics theory must be validated through comparison to experimental data.
Examples of micromechanics theories include:
Voigt (1889) - Strains constant in composite, Rule of Mixtures for stiffness components.
Reuss (1929) - Stresses constant in composite, Rule of Mixtures for compliance components.
Strength of Materials (SOM) - Longitudinally: strains constant in composite, stresses volume-additive. Transversely: stresses constant in composite, strains volume-additive.
Vanishing Fiber Diameter (VFD) - Combination of average stress and strain assumptions visualized as each fiber having a vanishing diameter yet finite volume.
Composite Cylinder Assemblage (CCA) - Composite composed of cylindrical fibers surrounded by cylindrical matrix, cylindrical elasticity solution. Produces only bounds for transverse properties.
Self-Consistent Scheme - Based on Eshelby (1957) inclusion in infinite medium elasticity solution. Infinite medium has properties of composite.
Mori-Tanaka Method - Also based on Eshelby (1957) inclusion in infinite medium elasticity solution. Fourth-order tensor relates avg. inclusion strain to average matrix strain and approximately accounts for fiber interaction effects.
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.
Finite Element Analysis (FEA) - Explicitly models the composite repeating unit cell and applies appropriate boundary conditions to extract the composite properties or response. Many commercial FEA codes are available (e.g., ABAQUS, ANSYS, NASTRAN).
For more information see: Herakovich, C.T. Mechanics of Fibrous Composites, John Wiley & Sons, Inc., New York, 1998.
A computer code called MAC/GMC including the GMC and HFGMC micromechanics models is available for free from NASA Glenn Research Center.
