Dear bigeyenemo
Your question is interesting and Drej's reply is very wise.
Apart from the negative elasticity, I'm afraid it's not possible to define but a single value for E & v for an element.
If the material properties vary spatially, why not refine your mesh and assign adjacent elements...
Dear flycloud
When you apply velocity, the cone will move with the specified velocity for the specified duration. It can apply whatever force is required to move, so you don't need to worry about the force at all.
Also the value of the velocity is not important in an elastic-platic response...
Dear flycloud
Further to your questions:
1.Since you have nonlinearity and contact, this problem is very much suited for an ABAQUS analysis, especially ABAQUS/Explicit.
2.The geometric model depends on yourself, but I'll go for the axisymmetric: you can save a lot of modelling effort and CPU...
