Biomedical Engineering Reference
In-Depth Information
The Mathematical Model
of the Object
The Real Object
RVE
X
A Cartesian Reference
Coordinate System
THE REAL WORLD
EUCLIDEAN 3 SPACE
Fig. 4.1 The image of a representative volume element (RVE)
Fig. 4.2 The RVE for the representation of a domain of a porous medium by a continuum point,
modified from Cowin ( 1999 )
material microstructure is much less. For many applications the bounds on L RVE are
not seriously restrictive, although this is not generally the case with
nanomechanical and biological problems. Both in biology and in nanomechanics
there are structures that have a significant size range and the modeler must adjust
the value of L RVE to the size range of the objects modeled. For example, in
biomechanics, continuum models are often made of organs as well as of biological
membranes. In the case of the membrane, the L RVE may be less than 0.01 nm while
in the case of the organ, the L RVE may be of the order of 0.01 mm or larger.
The concept of stress is employed in both cases, with the modeler keeping in mind
that the two L RVE 0 s differ by a factor of 1,000,000. The concept of the L RVE may, in
this way, be used to justify the application of the concept of stress at different
structural levels. The modeler usually does not write down the value of the L RVE
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