7. Determine the approximate order of magnitude (in 10\" m) for an appropriate r

Question

7. Determine the approximate order of magnitude (in 10" m) for an appropriate representative volume element in the follow materials, given the system or problem to be modeled. First, identify the largest microstructural dimension. Then, explain how you came about each length scale for the RVE. With the exception of part (d), cite the appropriate reference(s) used to determine these length scales. (a) Neoprene rubber foam (b) Liver (tissue-level, excluding blood vessels and support structures) (c) White adipose tissue (tissue-level, excluding blood vessels and basement membranes) (d) Loaf of bread (excluding the crust)

Explanation / Answer

Answer-

Representative elementary volume (REV):

In the theory of composite materials, the representative elementary volume (REV) (also called therepresentative 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.

a) Neoprene or polychloroprene is a family of synthetic rubbers that are produced by polymerization of chloroprene. Neoprene exhibits good chemical stability and maintains flexibility over a wide temperature range. Neoprene is sold either as solid rubber or in latex form, and is used in a wide variety of applications. Analytical or numerical micromechanical analysis of fiber reinforced compositesinvolves the study of a representative volume element (RVE). Although fibers are distributed randomly in real composites, many micromechanical models assume periodic arrangement of fibers from which RVE can be isolated in a straightforward manner. The RVE has the same elastic constants and fiber volume fraction as the composite.

b)

Liver consists of a matrix of hepatocytes (liver cells) and spaces filled with fluids e.g. blood and can be treated as a porous medium. In porous media when a solid matrix cannot be described within pore size, a representative elementary volume (REV) with a characteristic length of l and volume of Vl is defined to represent the structure of the matrix. Since a lobule is functionally considered as a representative processing.

c) White adipose tissue (WAT) is a dynamic and modifiable tissue that develops late during gestation in humans and through early postnatal development in rodents. It is specially a homogenous material. Accoring to Drugan and Willis (1996): “ REV of WAT 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”

d)

Loaf of bread - a shaped mass of baked bread that is usually sliced before eating. loaf. bread, breadstuff, staff of life - food made from dough of flour or meal and usually raised with yeast or baking powder and then baked.

In order to measure REV of porous material , one has to have to measure samples of the porous medium. If the sample is too small, the readings tend to oscillate. As we increase the sample size, the oscillations begin to dampen out. Eventually the sample size will become large enough that we begin to get consistent readings. This sample size is referred to as the representative elementary volume. If we continue to increase our sample size, measurement will remain stable until the sample size gets large enough that we begin to include other hydrostratigraphic layers. This is referred to as the maximum elementary volume (MEV)

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