Initial displacement for explicit dynamic

[luc]

Hi,
I have implemented a thermo-mechanical in explicit dynamic using the user time integration.
I set things so that the integration scheme for the displacement is a Newmark method with gamma=1/2 and beta=0.
For the thermal field I use an simple forward Euler scheme.

I have a time dependent displacement boundary condition applied to my solid (basically a velocity or strain rate is applied).

Finally due to the particular constitutive relation that I use, I need to know the strain rate in the solid.
This information is not provided correctly at the boundary. No strain rate is passed to my constitutive model ul(1:2,:,4)=0 instead of ul(1:2,:,4)=velocity.

How can I fix this? My Newmark implementation is the same as the one provided in dyna04.f
Do I have to retrieve the boundary condition information myself? Do I need to store in ud(1,n) or will it cause some problems with the time integration if I do so?

Any help is appreciated.

Best,
Luc

[Prof. R.L. Taylor]

You are correct, feap does not compute the velocity and acceleration for specified boundary motions.  In an explicit solution the solution increments are in terms of accelerations and these can be used to update the displacements and velocities directly.  But if you have boundary motions the reverse is not always possible in a convenient manner.

In general, what we have done in the past is integrate rate dependent models independently from the time integration method.  Stability is one reason, the other is due to the above difficulty.  For example, visco-plastic models have been integrated using a simple backward Euler implicit method.  This requires saving strain type data in history variables within the element.

One other comment.  In general, using an explicit solution for the thermal problem may require very small time steps compared to what could be used for the solid problem since time steps depend on the square of element size whereas solids depend only on the size.  If you have fairly coarse meshing this may not be a problem, but if you go to fine meshes then you may have performance issues.

[luc]

Pr. Taylor,
thanks for confirming this, I decided to switch to a velocity based element which is integrated using first a FIRST order Euler scheme. I think this allow me to get the results I want, I might post process the displacements using a finite difference formula.

I will make some comment on the implicit vs explicit in a few weeks when my research on this topic gives hopefully conclusive answers on which one makes more sense here.

Best,
Luc