2019/08/02 by Alexei Cheviakov, Cheviakov, Alexei, Caylin Lee +3 · 1 citation
Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #physics.class-ph
paper · pdf · doi:10.48550/arxiv.1909.05627
arxiv created 2019/08/02 · arxiv updated 2019/09/13
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.