Biomedical Engineering Reference
In-Depth Information
7.9 Relevant Literature
Good discussions of the RVE concept appear in the topics by Christensen ( 1979 )
and Nemat Nasser and Hori (1999). The inaugural quote of the next Chapter, Chap.
8 , describes a very early application of the RVE concept by Maurice Biot ( 1941 )to
poroelasticity.
The topics on composite materials by Jones ( 1975 ), Tsai and Hahn ( 1980 ), Hull
( 1981 ) and Halpin ( 1984 ) tend to specialize in laminated composites, that is to
composites constructed in the manner illustrated in Fig. 7.7 . The early topic of
Spencer ( 1972 ), which develops the theory of fiber reinforced materials, has been
used in developing mathematical models for several biological tissues. Early
rigorous summaries of composite material modeling were given by Sendeckyj
( 1974 ) and Christensen ( 1979 ); a contemporary rigorous and exhaustive develop-
ment of elastic composite theory is contained in Nemat Nasser and Hori (1999).
Torquato ( 2002 ) presents a general, contemporary, rigorous and exhaustive devel-
opment of the quantification and modeling of microstructure.
Wainwright et al. ( 1976 ) and Neville ( 1993 ) are two interesting topics on
biological composites, both plant and animal natural composites. Neville's topic
explores nature's wide use of the helicoidal structure as a composite building
geometry. The topic of Vincent ( 1982 ) is of more restricted scope. Wood is the
most widely analyzed natural composite material and its mechanics and micro-
structure are described in an abundant literature, for example Kollmann and Cote
( 1968 ) and Bodig and Jayne ( 1982 ). The topic by Niklas ( 1992 ) on plant biome-
chanics covers a wider range of the plant world, but it also deals with mechanism
and microstructure.
The quantification and measurement of material microstructure is not addressed
in the present topic, but it is addressed in topics on histology, metallurgy, and
materials science. The topic of Underwood ( 1969 ) on quantitative stereology, that
of Bunge ( 1982 ) on texture analysis in material science and any standard textbook
on histology are examples of this literature.
References
Biot MA (1941) General theory of three-dimensional consolidation. J Appl Phys 12:155-164
Bodig J, Jayne BA (1982) Mechanics of wood and wood composites. Van Nostrand, New York
Bunge HJ (1982) Texture analysis in materials science. Butterworths, London
Burridge R, Keller JB (1981) Poroelasticity equations derived from microstructure. J Acoust Soc
Am 70:1140-1146
Christensen RM (1979) Mechanics of composite materials. Wiley, New York
Chiang MYM, Wang X, Landis FA, Dunkers J, Snyder CR (2006) Quantifying the directional
parameter of structural anisotropy in porous media. Tissue Eng 12(6):1597-1606
Cowin SC, Mehrabadi MM (1989) Identification of the elastic symmetry of bone and other
materials. J Biomech 22:503-515
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