Dynamic fiber reorientation in a fiber-reinforced hyperelastic material

Melnik, A. V. and Goriely, A. (2013) Dynamic fiber reorientation in a fiber-reinforced hyperelastic material. Mathematics and Mechanics of Solids, 18(6), pp. 634-648. (doi: 10.1177/1081286513485773)

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Abstract

Fiber alignment in biological tissues is created and maintained by the cells, which respond to mechanical stimuli arising from properties of the surrounding material. This coupling between mechanical anisotropy and tissue remodeling can be modeled in nonlinear elasticity by a fiber-reinforced hyperelastic material where remodeling is represented as the change in fiber orientation. Here, we study analytically a simple model of fiber reorientation in a rectangular elastic tissue reinforced by two symmetrically arranged families of fibers subject to constant external loads. In this model, the fiber direction tends to align with the maximum principal stretch. We characterize the global behaviour of the system for all material parameters and applied loads, and show that provided the fibers are tensile initially, the system converges to a stable equilibrium, which corresponds to either complete or intermediate fiber alignment.

Item Type:Articles
Additional Information:This publication is based on work supported by King Abdullah University of Science and Technology (award number KUK-C1-013-04). AG is a Wolfson Royal Society Merit Holder and acknowledges support from a Reintegration Grant under EC Framework VII.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Melnik, Dr Andrey
Authors: Melnik, A. V., and Goriely, A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematics and Mechanics of Solids
Publisher:SAGE Publications
ISSN:1081-2865
ISSN (Online):1741-3028
Published Online:13 June 2013

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