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arXiv · 1909.05627

Radial waves in fiber-reinforced axially symmetric hyperelastic media

Alexei Cheviakov·Caylin Lee·Rehana Naz
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Abstract

Complex elastic media such as biological membranes, in particular, blood vessels, may be described as fiber-reinforced solids in the framework of nonlinear hyperelasticity. Finite axially symmetric anti-plane shear displacements in such solids are considered. A general nonlinear wave equation governing such motions is derived. It is shown that in the case of Mooney-Rivlin materials with standard quadratic fiber energy term, the displacements are governed by a linear cylindrical wave equation. Extensions of the model onto the case when fibers have a radial projection, as well as onto a viscoelastic case taking into account dissipative effects, are considered; wave equations governing shear displacements in those cases are derived and analyzed.

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Alexei Cheviakov, Caylin Lee, Rehana Naz. 2019-08-02. Radial waves in fiber-reinforced axially symmetric hyperelastic media. https://arxiv.org/abs/1909.05627

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