The Yield-Stress evolution is shown in red while the normal stress, velocity, and plastic deformation are shown from top to bottom in Lagrangian coordinates. In this example we show the same problem above but now in 2d Eulerian coordinates . Two elastic expansion waves propagate inwards from the edges of the material. When the waves constructively interfere in the center the stress exceeds yield and causes plastic deformation. Note that this problem is 1d in nature and any horizontal slice is identical.
Color represents the amount of plastic deformation in each cell.
Here we show the 2d extension of the problem above. One can see that after the waves have passed the material is left with a permanent plastic deformation. As in the previous case, after the waves have passed there is a permanent plastic deformation left over. Here we show the same case as above but with no difference in elastic properties of the elastic center layer.