# Rayleigh damping and numerical damping. (Ls-Dyna vs Msc.MARC)

Hi to all of you!

I have used Msc.MARC to simulate a Hopkinson bar experiment. We usually use a
"numerical damping" in these analysis.
As you know, MARC is a implicit FEM and it takes a lot of time to complete each
simulation.
So, I want to use Ls-Dyna, but I have the problem of damping. In Ls-dyna, we use
the Raylegh damping: there are 2 coefficients that multiply the matrix of
stifness and mass.
Is there any relation between these two kinds of dampings?
It could be very useful for me.

Thank you.

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### Re: Numerical vs. Rayleigh damping

The term "numerical damping" usually refers to damping introduced by errors introduced by a numerical algorithm. I prefer the term "artificial viscosity" instead.  The most commonly used form of artificial viscosity is that developed by von Neumann and Richtmeyer for use in hydrocodes (see, e.g., equation (12) in www.csafe.utah.edu/pdf/papers/2004_Banerjee_(Energy_Balance).pdf ).

Rayleigh damping is explained in Akumar's link and typically involves eigenvalue analyses.

-- Biswajit

### First of all, thanks for

First of all, thanks for replies.

I meant that we have always used Msc.MARC for simulation of the experiments to Hopkinson Bar. In these simulations, we use a "numerical damping" for the material of the bars. From the Vol.A of Marc, the numerical damping is explained is this way:

Numerical damping is used to damp out unwanted high-frequency chatter in the structure. If the time step is decreased (stiffness damping might cause too much damping), use the numerical damping option to make the damping (stiffness) coefficient proportional to the time step. Thus, if the timestep decreases, high-frequency response can still be accurately represented. This type of damping is particularlyuseful in problems where the characteristics of the model and/or the response change strongly during analysis (forexample, problems involving opening or closing gaps).

Now, I am doing simulations with Ls-Dyna, where there isn't the numerical damping but only the Rayleigh damping. I have to give to the code the costants alpha (actually alpha, in the code, isn't a costant, it wants a curve) and beta (which are the multipliers of the mass matrix and stiffness matrix, respectively).

I tried various values of beta, and I got strange results. These are the images of the strain on the bars. It's simple, you don't have to know the theory of the Hopkinson apparatus, I have just to eliminate the oscillations and getting a square wave: This is the magnification on the first peak, you can see the difference between Marc and many values of beta for Dyna simulation: I would like to know, just how get the same results that I have got on Marc, for the Dyna simulations.

Thank you all and sorry for my bad english.

### Re: LS Dyna and artificial viscosity

The LS-DYNA Theory Manual discusses the concept of artificial bulk viscosity in some detail.  I think Rayleigh damping is only used in implicit computations.

Look for cards of the form  *CONTROL_BULK_VISCOSITY in the keyowrd manual to set the artificial viscosity parameters. A blog post in the context of shells can be found at http://blog2.d3view.com/bulk-viscosity-for-shells-and-solids-in-ls-dyna/.

-- Biswajit

### Thank you for reply.  I

I tried with that, but I have not noticed changes. I don't know.

Thank you all.

### MSC Marc

A bit late, but you should read A Finite Element Dynamics Primer from Nafems. There is a chapter that describes the use of Rayleigh damping, the way to evaluate the coefficients and the sort of limitations that are associated

All the best

Andy 