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In the theory of composite materials, the representative elementary volume (REV) (also called the representative volume element (RVE) or the unit cell) is the smallest volume over which a measurement can be made that will yield a value representative of the whole.〔Hill (1963)〕 In the case of periodic materials, one simply chooses a periodic unit cell (which, however, may be non-unique), but in random media, the situation is much more complicated. For volumes smaller than the RVE, a representative property cannot be defined and the continuum description of the material involves Statistical Volume Element (SVE) and random fields. The property of interest can include mechanical properties such as elastic moduli, hydrogeological properties, electromagnetic properties, thermal properties, and other averaged quantities that are used to describe physical systems. == Definition == Rodney Hill defined the RVE as a sample of a heterogeneous material that:〔Hill (1963)〕 # "is entirely typical of the whole mixture on average”, and # "contains a sufficient number of inclusions for the apparent properties to be independent of the surface values of traction and displacement, so long as these values are macroscopically uniform.” 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. Both of these are issues of mesoscale (L) of the domain of random microstructure over which smoothing (or homogenization) is being done relative to the microscale (d).〔Huet (1990)〕〔Sab (1992)〕 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.〔Ostoja-Starzewski (2008)〕 In general, the stronger the mismatch in material properties, or the stronger the departure from elastic behavior, the larger is the RVE. The finite-size scaling of elastic material properties from SVE to RVE can be grasped in compact forms with the help of scaling functions universally based on stretched exponentials.〔Ranganathan and Ostoja-Starzewski (2008)〕 Considering that the SVE may be placed anywhere in the material domain, one arrives at a technique for characterization of continuum random fields.〔Sena, Ostoja-Starzewski and Costa (2013)〕 Another definition of the RVE was proposed by Drugan and Willis: * "It is the smallest material volume element of the composite for which the usual spatially constant (overall modulus) macroscopic constitutive representation is a sufficiently accurate model to represent mean constitutive response." 〔Drugan and Willis (1996).〕〔Kanit et al. (2003)〕〔Lydzba and Rozanski (2014)〕 The choice of RVE can be quite a complicated process. The existence of a RVE assumes that it is possible to replace a heterogeneous material with an equivalent homogeneous material. This assumption implies that the volume should be large enough to represent the microstructure without introducing non-existing macroscopic properties (such as anisotropy in a macroscopically isotropic material). On the other hand, the sample should be small enough to be analyzed analytically or numerically. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Representative elementary volume」の詳細全文を読む スポンサード リンク
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