Benchmark Solutions in Solid Mechanics and Implicit-Explicit Schemes in Radiation Hydrodynamics
Abstract not provided.
97 MATHEMATICS AND COMPUTING↗
Engineering topics
Chabaud, Brandon M.
Publications and source records attributed to Chabaud, Brandon M..
The dynamic sphere test problem
In this manuscript we define the dynamic sphere problem as a spherical shell composed of a homogeneous, linearly elastic material. The material exhibits either isotropic or transverse isotropic symmetry. When the problem is formulated in material coordinates, the balance of mass equation is satisfied automatically. Also, the material is assumed to be kept at constant temperature, so the only relevant equation is the equation of motion. The shell has inner radius r i and outer radius r o . Initially, the shell is at rest. We assume that the interior of the shell is a void and we apply a time-varying radial stress on the outer surface.
97 MATHEMATICS AND COMPUTING↗
The Jump-Off Velocity of an Impulsively Loaded Spherical Shell
We consider a constant temperature spherical shell of isotropic, homogeneous, linearly elastic material with density ρ and Lamé coefficients λ and μ. The inner and outer radii of the shell are r i and r o , respectively. We assume that the inside of the shell is a void. On the outside of the shell, we apply a uniform, time-varying pressure p(t). We also assume that the shell is initially at rest. We want to compute the jump-off time and velocity of the pressure wave, which are the first time after t = 0 at which the pressure wave from the outer surface reaches the inner surface. This analysis computes the jump-off velocity and time for both compressible and incompressible materials. This differs substantially from [3], where only incompressible materials are considered. We will consider the behavior of an impulsively loaded, exponentially decaying pressure wave p(t) = P 0 e -αt , where α ≥ 0. We notice that a constant pressure wave P(t) = P 0 is a special case (α = 0) of a decaying pressure wave. Both of these boundary conditions are considered in [3].
36 MATERIALS SCIENCE↗