Representative elementary volume

Rodney Hill defined the RVE as a sample of a heterogeneous material that:[3] In essence, statement (1) is about the material's statistics (i.e. spatially homogeneous and ergodic), while statement (2) is a pronouncement on the independence of effective constitutive response with respect to the applied boundary conditions.

[4][5] As L/d goes to infinity, the RVE is obtained, while any finite mesoscale involves statistical scatter and, therefore, describes an SVE.

With these considerations one obtains bounds on effective (macroscopic) response of elastic (non)linear and inelastic random microstructures.

[7] Considering that the SVE may be placed anywhere in the material domain, one arrives at a technique for characterization of continuum random fields.

Several types of boundary conditions can be prescribed on V to impose a given mean strain or mean stress to the material element.

[15] Analytical or numerical micromechanical analysis of fiber reinforced composites involves the study of a representative volume element (RVE).

In the adjacent figure, the RVE consists of a split-ring resonator and its surrounding backing material.

[18][19] Uncorrelated volume element (UVE) is an extension of SVE which also considers the co-variance of adjacent microstructure to present an accurate length scale for stochastic modelling.