Papers by Author: Da Tian Niu

Abstract: The oscillation problem is examined for a rectangular sealing ring composed of a class of transversely isotropic incompressible vulcanized rubber materials about radial direction, where the sealing ring is subjected to a suddenly applied radial load at its inner surface. A nonlinear ordinary differential equation that describes the radial motion of the sealing ring is obtained. It is proved that if the applied load is lower than the critical load, the motion of the rubber ring with time will present a nonlinear periodic oscillation, while if it exceeds the critical load, the motion will increase infinitely with the increasing time and so the rubber ring will be destroyed ultimately.

Abstract: The problem of radially symmetric motion is examined for a pre-existing micro-void in the interior of a sphere under a suddenly applied outer surface tensile load, where the sphere is composed of a homogeneous incompressible hyper-elastic material. Through qualitatively analyzing the second-order ordinary differential equation that describes the motion of the pre-existing micro-void with time, some interesting conclusions are proposed. For any given values of surface tensile loads, it is proved that the motion of the pre-existing micro-void with time presents a nonlinear periodic oscillation, however, in certain cases, the oscillation amplitude increases discontinuously with the increasing values of surface tensile loads. Finally, based on the known transversely isotropic incompressible Gent-Thomas material model as an example, numerical simulations are carried out.

Abstract: The finite deformation about the radial direction is examined for a solid cylinder composed of a class of compressible hyper-elastic materials. Some interesting conclusions are proposed by using the theoretical solutions and the numerical simulations. There exists a critical stretch such that the cylinder would remain a solid one if the radial stretch does not exceed the critical value and that a cylindrical cavity would form at the axial line of the cylinder if the radial stretch exceeds the critical value. The phenomena of concentration and catastrophe of radial and circumferential stresses further show that cavitation in compressible hyper-elastic cylinder coincides with the actual physical grounds.

Abstract: In this paper, we investigate the radial compression and inflation of a spherical shell composed of two compressible hyperelastic materials. We first establish the mathematical model of this problem as a second order nonlinear differential equation with two boundary conditions, and then transform it into a system of first order nonlinear differential equations. By using dimensionless transformation, we obtain the parametrical analytic solution. Finally, the results of the numerical simulation are given. We analyze the influence of the material parameters and the structure parameters on radial deformation of the spherical shell. These results well fit the practical phenomena.