Micromechanics 4649063 220239838 2008-06-18T22:31:32Z Mattisse 1386816 unreferenced article {{Copyedit|date=January 2008}}{{Unreferenced|date=June 2008}} '''Micromechanics''' is the analysis of [[Composite material|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 material|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 material|composite]], stresses volume-additive. Transversely: stresses constant in [[Composite material|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 material|Composite]] composed of cylindrical fibers surrounded by cylindrical matrix, cylindrical [[Elasticity (physics)|elasticity]] solution. Produces only bounds for transverse properties. '''Self-Consistent Scheme''' - Based on Eshelby (1957) inclusion in infinite medium [[Elasticity (physics)|elasticity]] solution. Infinite medium has properties of [[Composite material|composite]]. '''Mori-Tanaka Method''' - Also based on Eshelby (1957) inclusion in infinite medium [[Elasticity (physics)|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 (mechanics)|displacement field]] in subcells and imposes traction and [[displacement (vector)|displacement]] continuity. '''High-Fidelity GMC (HFGMC)''' - Like GMC, but considers a quadratic [[displacement field (mechanics)|displacement field]] in the subcells. '''[[Finite Element Analysis]] (FEA)''' - Explicitly models the [[Composite material|composite]] repeating unit cell and applies appropriate [[boundary conditions]] to extract the [[Composite material|composite]] properties or response. Many commercial FEA codes are available (e.g., ABAQUS, ANSYS, NASTRAN). For more information see: Herakovich, C.T. [http://www.amazon.com/gp/product/0471106364 Mechanics of Fibrous Composites], John Wiley & Sons, Inc., New York, 1998. A computer code called [http://www.grc.nasa.gov/WWW/LPB/mac/index.html MAC/GMC] including the GMC and HFGMC micromechanics models is available for free from [[NASA]] Glenn Research Center. [[Category:Composite materials]] [[ja:マイクロメカニクス]]