Abstract
Static and dynamic responses of a circular cylindrical shell made of hyperelastic arterial material are studied. The material is modeled as a combination of Neo-Hookean and Fung materials. Two types of pressure loads are studied—distributed radial forces and deformation-dependent pressure. The static responses of the shell under these two loads differ essentially at moderate strains, while the behavior is similar for small loads. The principal difference is that the axial displacements are much larger for the shell under distributed radial forces, while for actual pressure the shell is stretched both in circumferential and axial directions. Free and forced vibrations around preloaded configurations are analyzed. In both cases, the nonlinearity of the single-mode (driven mode) response of the preloaded shell is quite weak, but a resonant regime with both driven and companion modes active has been found with more complicated nonlinear dynamics.
Highlights
IntroductionThe study of pressurized circular cylindrical shells has long history. Firstly, the problem was formulated for the case of infinitely small deformations and linear elasticity by Lamé [21], whose name the problem carries now
In the present study we extend the method for the case of a thick shell made of special type of hyperelastic material that is able to reproduce the actual behavior of an arterial tissue [17]
Legrand — Static and dynamic behaviors of circular cylindrical shells made of hyperelastic arterial materials pressure loads – dead distributed radial force and deformation-dependent pressure, which are similar for small deflections but differ significantly for large strains
Summary
The study of pressurized circular cylindrical shells has long history. Firstly, the problem was formulated for the case of infinitely small deformations and linear elasticity by Lamé [21], whose name the problem carries now. Most of the modern computational works on the problem [16, 1, 12, 30, 31, 32, 20] employ finite elements This allows taking into account pressure as the follower load, which is crucial in the case of soft materials, since they usually experience large deformations. Legrand — Static and dynamic behaviors of circular cylindrical shells made of hyperelastic arterial materials pressure loads – dead distributed radial force and deformation-dependent pressure, which are similar for small deflections but differ significantly for large strains. Legrand — Static and dynamic behaviors of circular cylindrical shells made of hyperelastic arterial materials kx.1Â/ D . The potential and kinetic energies are given by [7]: T
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