Propagation of Elastic Plastic Stress Waves simulated with FEM
This page has opened to public since 16 June 2006.
Japanese 
All Rights Reserved by Dr. Shinozuka, Jun.

When a bar collides with a bar, stress wave propagates like a wave in these bars.
There are two kinds of stresses, an elastic stress and a plastic stress. A impact stress increment depends on density, stresses wave speeds and the change in a particle velocity of the bar. Of course, the change in a particle velocity depends on the impact speed. An elastic wave speed (sonic speed of bulk material ) depends on density, the Young's modulus and Poisson's ratio. While, plastic wave speeds depend on density, Poisson's ratio and the material hardening rate ( tangent of strainstress curve). The speed of an elastic wave is one because it depends on Young's modulus. In contrast, there are many speeds of plastic waves because the stressstrain characteristic is nonlinear. The plastic wave speed becomes slow with the plastic strain, if the stressstrain curve is concave down.
Assuming that the impact speed is fast and an impact stress, which is obtained integrating the stress increment with respect to time, exceeds the yield stress of the bar, the plasttic waves and also an elastic stress wave propagates from the impacted surface into these bars. In this case,an the elasticplastic deformation occurs.
The following animation shows one of results simulated. The results were simulated by using of a dynamic and thermo elastic plastic FEM software (RDynFem) that I have developed.
An elastic plastic projectile collides with an elastic target. The projectile is deformed plastically, so that the shape of the imapcted surface becomes cone.
This animation shows the effective stress distribution.
This animation shows the temperature distribution.
These results were simulated with FEM software "RDynFem" that has been developed by Dr. Shinozuka, Jun.