Evolution of a fibre-reinforced growing mixture

Grillo, Alfio and Federico, Salvatore and Wittum, G. and Imatani, S. and Giaquinta, G. and Mićunović, M. V. (2009) Evolution of a fibre-reinforced growing mixture. Il nuovo cimento C, 32 (1). pp. 97-119. ISSN 1826-9885

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We consider a biological tissue that can be macroscopically modelled as a biphasic mixture composed of a fluid and a solid phase. The former is a multi-constituent fluid, and the latter consists of a deformable porous medium comprising matrix and fibre-like inclusions. Both phases are assumed to be composed of several constituents, and are allowed to experience exchange interactions. In response to these interactions, the solid phase may either grow or be absorbed. We assume that each of these behaviours leads to the development of material inhomogeneities. Material inhomogeneities are treated by enforcing Kr¨oner’s multiplicative decomposition of the solid-phase deformation gradient tensor, and introducing an inhomogeneity velocity “gradient”. Through Onsager’s principle, it is proven that inhomogeneity velocity “gradient” is related to the Mandel stress tensor of the solid phase, and chemical potentials of fluid constituents. This relation is used in order to show that, in response to growth (or adsorption), development of material inhomogeneities may trigger fibre reorientation in the solid phase by inducing the evolution in time of its texture tensor.

Item Type: Article
Uncontrolled Keywords: Mechanical systems ; Microcirculation and flow through tissues
Subjects: 600 Tecnologia - Scienze applicate > 620 Ingegneria e attivita' affini > 621 Fisica applicata; Ingegneria meccanica
Depositing User: Marina Spanti
Date Deposited: 24 Mar 2020 16:20
Last Modified: 24 Mar 2020 16:20
URI: http://eprints.bice.rm.cnr.it/id/eprint/16446

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