caa a22 4500 463247345 CHVBK 20180405153329.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s10086-007-0897-5 doi (NATIONALLICENCE)springer-10.1007/s10086-007-0897-5 A mathematical verification of the reinforced-matrix hypothesis using the Mori-Tanaka theory [Elektronische Daten] [Hiroyuki Yamamoto, Tancréd Almèras] 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. The Japan Wood Research Society, 2007 Wood cell wall nationallicence Composite material nationallicence Micromechanics nationallicence Inhomogeneities nationallicence Biomaterial nationallicence Yamamoto Hiroyuki School of Bioagricultural Sciences, Nagoya University, 464-8601, Furo-cho, Chikusa-ku, Nagoya, Japan aut Almèras Tancréd Unite Mixte de Recherche INRA-CNRS-CIRAD-ENGREF Ecologie des Forets de Guyane, Campus Agronomique, BP 709, Kourou cedex, 97387, Guyane Francaise, France aut Journal of Wood Science Springer-Verlag 53/6(2007-12-01), 505-509 1435-0211 53:6<505 2007 53 10086 https://doi.org/10.1007/s10086-007-0897-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10086-007-0897-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Yamamoto Hiroyuki School of Bioagricultural Sciences, Nagoya University, 464-8601, Furo-cho, Chikusa-ku, Nagoya, Japan aut NATIONALLICENCE 700 1- Almèras Tancréd Unite Mixte de Recherche INRA-CNRS-CIRAD-ENGREF Ecologie des Forets de Guyane, Campus Agronomique, BP 709, Kourou cedex, 97387, Guyane Francaise, France aut NATIONALLICENCE 773 0- Journal of Wood Science Springer-Verlag 53/6(2007-12-01), 505-509 1435-0211 53:6<505 2007 53 10086 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer