Editing Continuum mechanics (section)

==Validity==

The validity of the continuum assumption may be verified by a theoretical analysis, in which either some clear periodicity is identified or statistical [[Homogeneity (physics)|homogeneity]] and [[ergodicity]] of the [[microstructure]] exist. More specifically, the continuum hypothesis hinges on the concepts of a representative elementary volume and separation of scales based on the Hill–Mandel condition. This condition provides a link between an experimentalist's and a theoretician's viewpoint on [[constitutive equation]]s (linear and nonlinear elastic/inelastic or coupled fields) as well as a way of spatial and statistical averaging of the microstructure. 
When the separation of scales does not hold, or when one wants to establish a continuum of a finer resolution than the size of the representative volume element (RVE), a statistical volume element (SVE) is employed, which results in random continuum fields. The latter then provide a micromechanics basis for stochastic finite elements (SFE). The levels of SVE and RVE link continuum mechanics to [[Statistical physics#Statistical mechanics|statistical mechanics]]. Experimentally, the RVE can only be evaluated when the constitutive response is spatially homogenous.