THE DYNAMIC EXPANSION OF A SPHERICAL CAVITY IN AN ELASTIC-PERFECTLY- PLASTIC MATERIAL
ARMY BALLISTIC RESEARCH LAB ABERDEEN PROVING GROUND MD
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It was shown that a finite-difference numerical technique can be used to solve mixed initial- and boundary-value problems involving high-speed elastic-plastic flow with spherical symmetry. Numerical solutions for the dynamic expansion of a spherical cavity under a constant pressure are presented to demonstrate the nature and capability of the numerical scheme. The solution for an elastic material agrees closely with the exact solution. The solution for an elastic-perfectly-plastic material confirmed Greens prediction concerning the motion of the elastic-plastic boundary. At large times, the asymptotic solution of the dynamic problem is different from the quasi-static solution. This result indicates that the quasi-static approximation may not hold in dynamic plasticity. A non-linear dependence of the plastic solution on the boundary condition is also observed in the results.
- Fluid Mechanics