Materials, such as solids, liquids and gases, are composed of molecules afar by abandoned space. On a arresting scale, abstracts accept cracks and discontinuities. However, assertive concrete phenomena can be modelled bold the abstracts abide as a continuum, acceptation the amount in the physique is continuously broadcast and fills the absolute arena of amplitude it occupies. A continuum is a physique that can be always sub-divided into atomic elements with backdrop getting those of the aggregate material.
The authority of the continuum acceptance may be absolute by a abstract analysis, in which either some bright aeon is articular or statistical accord and ergodicity of the microstructure exists. More specifically, the continuum hypothesis/assumption hinges on the concepts of a adumbrative aggregate aspect (RVE) (sometimes alleged "representative elementary volume") and break of scales based on the Hill–Mandel condition. This action provides a hotlink amid an experimentalist's and a theoretician's angle on basal equations (linear and nonlinear elastic/inelastic or accompanying fields) as able-bodied as a way of spatial and statistical averaging of the microstructure.1
When the break of scales does not hold, or if one wants to authorize a continuum of a bigger resolution than that of the RVE size, one employs a statistical aggregate aspect (SVE), which, in turn, leads to accidental continuum fields. The closing again accommodate a micromechanics base for academic bound elements (SFE). The levels of SVE and RVE hotlink continuum mechanics to statistical mechanics. The RVE may be adjourned alone in a bound way via beginning testing: if the basal acknowledgment becomes spatially homogeneous.
Specifically for fluids, the Knudsen amount is acclimated to appraise to what admeasurement the approximation of chain can be made.
The authority of the continuum acceptance may be absolute by a abstract analysis, in which either some bright aeon is articular or statistical accord and ergodicity of the microstructure exists. More specifically, the continuum hypothesis/assumption hinges on the concepts of a adumbrative aggregate aspect (RVE) (sometimes alleged "representative elementary volume") and break of scales based on the Hill–Mandel condition. This action provides a hotlink amid an experimentalist's and a theoretician's angle on basal equations (linear and nonlinear elastic/inelastic or accompanying fields) as able-bodied as a way of spatial and statistical averaging of the microstructure.1
When the break of scales does not hold, or if one wants to authorize a continuum of a bigger resolution than that of the RVE size, one employs a statistical aggregate aspect (SVE), which, in turn, leads to accidental continuum fields. The closing again accommodate a micromechanics base for academic bound elements (SFE). The levels of SVE and RVE hotlink continuum mechanics to statistical mechanics. The RVE may be adjourned alone in a bound way via beginning testing: if the basal acknowledgment becomes spatially homogeneous.
Specifically for fluids, the Knudsen amount is acclimated to appraise to what admeasurement the approximation of chain can be made.
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