A mathematical verification of the reinforced-matrix hypothesis using the Mori-Tanaka theory |
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| Authors: | Hiroyuki Yamamoto Tancréd Almèras |
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| Institution: | (1) School of Bioagricultural Sciences, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan;(2) Unite Mixte de Recherche INRA-CNRS-CIRAD-ENGREF Ecologie des Forets de Guyane, Campus Agronomique, BP 709, Kourou cedex, 97387 Guyane Francaise, France |
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| Abstract: | This article presents a theoretical verification of the reinforced-matrix hypothesis derived from tensor equations, σ
W = σ
f + σ
m and ε
W = ε
f = ε
m (Wood Sci Technol 32:171–182, 1998; Wood Sci Technol 33:311–325, 1999; J Biomech Eng 124:432–440, 2002), using classical
Mori-Tanaka theory on the micromechanics of fiber-reinforced materials (Acta Metall 21:571–574, 1973; Micromechanics — dislcation
and inclusions (in Japanese), pp 141–147, 1976). The Mori-Tanaka theory was applied to a small fragment of the cell wall undergoing
changes in its physical state, such as those arising from sorption of moisture, maturation of wall components, or action of
an external force, to obtain 〈σ
A〉D = ϕ·〈σ
F〉I + (1−ϕ)·〈σ
M〉D−I. When the constitutive equation of each constituent material was applied to the equation 〈σ
A〉D = ϕ·〈σ
F〉I + (1−ϕ)·〈σ
M〉D−I, the equations σ
W = σ
f + σ
m and ε
W = ε
f = ε
m were derived to lend support to the concept that two main phases, the reinforcing cellulose microfibril and the lignin-hemicellulose
matrix, coexist in the same domain. The constitutive equations for the cell wall fragment were obtained without recourse to
additional parameters such as Eshelby’s tensor S and Hill’s averaged concentration tensors AF and AM. In our previous articles, the coexistence of two main phases and σ
W = σ
f + σ
m and ε
W = ε
f =ε
m had been taken as our starting point to formulate the behavior of wood fiber with multilayered cell walls. The present article
provides a rational explanation for both concepts. |
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| Keywords: | Wood cell wall Composite material Micromechanics Inhomogeneities Biomaterial |
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