I am modelling 1D nonlinear elastic wave propagation using bar elements. A Gaussian pulse is applied at left end. The material used is nonlinear elastic material. Force vs time at various points along the member is plotted. There is very much noise in the image. I understand that the noise is due to high frequency oscillations.
I have also tried using GLL collocation points using higher order upto 12 nodes per element. That seems not solving the issue. Filtering is damping out the noise, but the results are not appropriate.
I am wondering, if anyone suggest what is best approach to model wave propagation in nonlinear elastic media?
Which time integration schema did you use? If your material is non-linear it is hard to determine the time step you need for an explicit time integration.
Hi Ravi
Take a look at ClawPack which is focused on the simulation of shock with various nonlinear mechanisms included. If you do not want to use ClawPack, I imagine that you should find ideas and experience to borrow for your own work. http://www.clawpack.org/
Sincerely
Claes
The following papers may be useful.
1. Olivier Bou Matar et.al.A nodal discontinuous Galerkin finite element method for nonlinear elastic wave propagation, The Journal of the Acoustical Society of America 131, 3650 (2012).
2. F.J.Seron et.al. Finite‐element method for elastic wave propagation. Int.J. for numerical methods in bio medical engineering, Volume6, Issue5
July 1990,Pages 359-368
3. N Rauter and R Lammering. Numerical simulation of elastic wave propagation in isotropic media considering material and geometrical nonlinearities. Smart Materials and Structures, 3 March 2015 .
Thank you all for the responses. I will go through the references and ClawPack.
Dr. Cristian,
I am using central difference scheme. Time step is always the concern for explicit integration (I used very small time step i.e. 1/100 of stable time step). However, i am observing very high frequencies developing in the nonlinear elastic wave propagation. Please refer the Force vs time plots, the right side slope is getting very much steep due to slow propagation speed at high strains. These high frequency content requires very tiny element size. Whatever may be the element size I am assigning, they are failing due to high frequency content generated as the wave propagates.
I used higher order elements and also using GLL collocation integration points up to 12 sub-elements per element seems failing to model this behavior.
Regards,
Ravi
You can build an approximate analytical solution based on the Ritz method
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