Modeling Material Symmetry - Continuum Mechanics of Anisotropic Materials - page 77

Fig. 4.3 An illustration of a
cross-section of trabecular
bone. The whiter regions are
the bone trabeculae and the
darker regions are the spaces
occupied by the marrow in the
bones of young animals.
The rectangular regions
represent various RVE's
discussed in the text. Adapted
from Cowin and Mehrabadi
( 1989 )
in a problem under consideration, hence it is a “hidden” parameter in many
applications of continuum models.
The selection of different size RVE's is illustrated in Fig. 4.2 .AsmallRVE
will just contain the solid matrix material while a much larger RVE will average
over both the pores and the solid matrix. As another illustration of these different
RVE sizes relative to a real material, consider a cross-section of trabecular bone
shown in Fig. 4.3 . The white regions are the bone trabeculae and the darker
regions are the pore spaces that are in vivo filled with marrow in the bone of
young animals. First consider the small rectangular white region in the lower right
quadrant as the first RVE for homogenization. This small rectangular white region
is entirely within the trabecular bone domain and thus the properties will be those
of trabecular bone. On the other hand, if the small RVE in the darker marrow
region is entirely within the bone marrow domain, the properties will be those of
the marrow. If the RVE or homogenization domain is taken to be one of the larger
rectangles in Fig. 4.3 , the properties of the RVE will reflect the properties of both
the bone and the marrow, and their values will lie in between these two limits and
be proportional to the ratio of the volume of marrow voids to the volume of bone
in each rectangle.