We propose a theory of remodelling in fibre-reinforced biological tissues, in which the fibre orientation follows a given probability density. The latter is characterised by variance and mean angle. We claim that the fibres may change their orientation in time, thereby triggering a remodelling process that can be described by the spatiotemporal evolution of the mean angle. This is determined by solving a balance of external and internal generalised forces. We assign the latter ones by establishing a constitutive theory capable of resolving the spatial variability of the fibre mean angle and featuring a free energy density of the Allen–Cahn type. Through numerical simulations, we compare the predictions of our model with the results of another model available in the literature. Finally, we interpret the evolution of the mean angle as the consequence of a symmetry breaking that occurs in the tissue both spontaneously and due to the coupling between remodelling and deformation

An Allen–Cahn approach to the remodelling of fibre-reinforced anisotropic materials / Grillo, Alfio; Carfanga, Melania; Federico, Salvatore. - In: JOURNAL OF ENGINEERING MATHEMATICS. - ISSN 0022-0833. - STAMPA. - 109:1(2018), pp. 139-172. [10.1007/s10665-017-9940-8]

An Allen–Cahn approach to the remodelling of fibre-reinforced anisotropic materials

GRILLO, ALFIO;FEDERICO, SALVATORE
2018

Abstract

We propose a theory of remodelling in fibre-reinforced biological tissues, in which the fibre orientation follows a given probability density. The latter is characterised by variance and mean angle. We claim that the fibres may change their orientation in time, thereby triggering a remodelling process that can be described by the spatiotemporal evolution of the mean angle. This is determined by solving a balance of external and internal generalised forces. We assign the latter ones by establishing a constitutive theory capable of resolving the spatial variability of the fibre mean angle and featuring a free energy density of the Allen–Cahn type. Through numerical simulations, we compare the predictions of our model with the results of another model available in the literature. Finally, we interpret the evolution of the mean angle as the consequence of a symmetry breaking that occurs in the tissue both spontaneously and due to the coupling between remodelling and deformation
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2683512