Analytical Methods of Continuum Micromechanics
Voigt (1887) - 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. Analogous method for composite reinforced by spherical particles: Composite Sphere Assemblage (CSA)
Hashin-Shtrikman Bounds - Provide bounds on the elastic moduli and tensors of transversally isotropic composites (reinforced,e.g., by aligned continuous fibers) and isotropic composites (reinforced, e.g., by randomly positioned particles).
Self-Consistent Scheme - Effective medium theory based on Eshelby elasticity solution for inhomogeneity in infinite medium. Uses material properties of composite for infinite medium.
Mori-Tanaka Method - Effective field theory based on Eshelby's elasticity solution for inhomogeneity in infinite medium. Fourth-order tensor relates average inclusion strain to average matrix strain and approximately accounts for fiber interaction effects.
The Bridging Model - A mircomechanical approach based on Mori-Tanaka method for simulating properties of fibrous composites material. Fourth-order tensor relates average fiber stress to average matrix stress and thermal residual constituent stresses can be predicted.
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