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Radial waves in fiber-reinforced axially symmetric hyperelastic media. (English) Zbl 1455.74050

Summary: 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.

MSC:

74J30 Nonlinear waves in solid mechanics
74B20 Nonlinear elasticity
74E30 Composite and mixture properties
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