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.
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.
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.
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.
Mori-Tanaka Method[13][14] - Effective field approximation based on Eshelby's[12] elasticity solution for inhomogeneity in infinite medium.
A single repeating volume element is studied, appropriate boundary conditions being applied to extract the composite's macroscopic properties or responses.
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 viscoelastic, elastoplastic and damage behavior.
[20] Using MSG, it is possible to directly compute structural properties of a beam, plate, shell or 3D solid in terms of its microstructural details.
A further group of periodic homogenization models make use of Fast Fourier Transforms (FFT), e.g., for solving an equivalent to the Lippmann–Schwinger equation.