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Micromechanics (or, more precisely, micromechanics of materials) is the analysis of heterogeneous materials including of composite, and Anisotropy and orthotropic materials on the level of the individual constituents that constitute them and their interactions.
Anisotropic material models are available for linear elasticity. In the nonlinear regime, the modeling is often restricted to orthotropic material models which do not capture the physics for all heterogeneous materials. An important goal of micromechanics is predicting the anisotropic response of the heterogeneous material on the basis of the geometries and properties of the individual phases, a task known as homogenization.S. Nemat-Nasser and M. Hori, Micromechanics: Overall Properties of Heterogeneous Materials, Second Edition, North-Holland, 1999, .
Micromechanics allows predicting multi-axial responses that are often difficult to measure experimentally. A typical example is the out-of-plane properties for unidirectional composites.
The main advantage of micromechanics is to perform virtual testing in order to reduce the cost of an experimental campaign. Indeed, an experimental campaign of heterogeneous material is often expensive and involves a larger number of permutations: constituent material combinations; fiber and particle volume fractions; fiber and particle arrangements; and processing histories). Once the constituents properties are known, all these permutations can be simulated through virtual testing using micromechanics.
There are several ways to obtain the material properties of each constituent: by identifying the behaviour based on molecular dynamics simulation results; by identifying the behaviour through an experimental campaign on each constituent; by reverse engineering the properties through a reduced experimental campaign on the heterogeneous material. The latter option is typically used since some constituents are difficult to test, there are always some uncertainties on the real microstructure and it allows to take into account the weakness of the micromechanics approach into the constituents material properties. The obtained material models need to be validated through comparison with a different set of experimental data than the one use for the reverse engineering.
Because most heterogeneous materials show a statistical rather than a deterministic arrangement of the constituents, the methods of micromechanics are typically based on the concept of the representative volume element (RVE). An RVE is understood to be a sub-volume of an inhomogeneous medium that is of sufficient size for providing all geometrical information necessary for obtaining an appropriate homogenized behavior.
Most methods in micromechanics of materials are based on continuum mechanics rather than on atomistic approaches such as nanomechanics or molecular dynamics. In addition to the mechanical responses of inhomogeneous materials, their Heat conduction behavior and related problems can be studied with analytical and numerical continuum methods. All these approaches may be subsumed under the name of "continuum micromechanics".
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 that can be visualized as each fiber having a vanishing diameter yet finite volume.
Composite Cylinder Assemblage (CCA) - Composite composed of cylindrical fibers surrounded by cylindrical matrix layer, cylindrical elasticity solution. Analogous method for macroscopically isotropy inhomogeneous materials: Composite Sphere Assemblage (CSA)
Zvi Hashin-Shtrikman Bounds - Provide bounds on the Elastic modulus and of transversally isotropic composites (reinforced, e.g., by aligned continuous ) and isotropic composites (reinforced, e.g., by randomly positioned particles).
Self-Consistent Schemes - Effective medium approximations based on Eshelby's elasticity solution for an inhomogeneity embedded in an infinite medium. Uses the material properties of the composite for the infinite medium.
Mori-Tanaka Method - Effective field approximation based on Eshelby's elasticity solution for inhomogeneity in infinite medium. As is typical for mean field micromechanics models, fourth-order concentration relate the average stress or average strain tensors in inhomogeneities and matrix to the average macroscopic stress or strain tensor, respectively; inhomogeneity "feels" effective matrix fields, accounting for phase interaction effects in a collective, approximate way.
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 FE models. Due to its high flexibility and efficiency, FEA at present is the most widely used numerical tool in continuum micromechanics, allowing, e.g., the handling of Viscoelasticity, elastoplastic and Damage mechanics behavior.
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