Micromechanics (or, more precisely, micromechanics of materials) is the analysis of composite or heterogeneous materials on the level of the individual constituents that constitute these materials.
Aims of micromechanics of materials
Heterogeneous materials, such as composites, solid foams, polycrystals, or bone, consist of clearly distinguishable constituents (or phases) that show different mechanical and physical material properties. While the constituents can often be modeled as having isotropic behaviour, the microstructure characteristics (shape, orientation, varying volume fraction, ..) of heterogeneous materials often leads to an anisotropic behaviour.
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.
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.
Generality on micromechanics
A key point of micromechanics of materials is the localization, which aims at evaluating the local (stress and strain) fields in the phases for given macroscopic load states, phase properties, and phase geometries. Such knowledge is especially important in understanding and describing material damage and failure.
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 thermal 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".
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 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 isotropic inhomogeneous materials: Composite Sphere Assemblage (CSA)