Dear all,
I am currently dealing with a problem of spurious oscillations in wave propagation in elastoplastic bodies.
The problem in question is a 1D column subjected to a 10Hz sine wave acceleration input motion at the bottom of the mesh. Abaqus/Standard is used for the dynamic analysis.
Generally, the stress strain behavior looks fine, the same with displacements and velocities. The oscillations are most pronouncedly experienced in the calculated accelerations. They appear in time when the element/Gauss point is subjected to a sharp change in stiffness, e.g. from elastic branch into plastic one when no smooth hyperbolic relationship is used. The oscillations are of much higher frequency than the input motion [say around 100Hz].
I am wondering where these oscillations come from. I have tried to include numerical damping in the HHT direct time integration scheme however this did not influence the observed oscillations. I am wondering if further “play” with alpha, beta, gamma parameters in the HHT method could result in damping out the oscillation I experience. So far I have only used set of parameters as suggested in Abaqus Manual for “application=moderate dissipation” option.
I have also tried the effects of time and space discretization, non of the two was effective [for space discretization going for much finer solution than the minimum of 10 nodes per wave length as typically advised]. The problem remains and is insensitive to mesh or time step refinement. The only way of removing the oscillations is applying the Rayleigh damping, however this seems to be artificial way of removing the problem since the constitutive model is elastoplastic and deemed to be capable of accounting for material damping.
Generally, Abaqus manual says “The principal advantage of these operators is that they are unconditionally stable for linear systems; there is no mathematical limit on the size of the time increment that can be used to integrate a linear system” so I understand that maybe this scheme is not stable or inaccurate for the nonlinear dynamic problems or a family of nonlinear dynamic problems. Would some another commonly used direct time integration scheme, such as lets say Bathe be more accurate here?
Anyone has experienced maybe a similar problem? Where is it I can look for the reason of the oscillations?
Thanks in advance for any help and advice on that.
Hey Fabian,
Thanks for your answer and ideas!
Regarding the element type, I have not mentioned that, is it a 1D column but the one built of continuum elements. I use quadratic full integration elements but I also tried quadratic reduced integration and linear elements. No change in the observed oscillations.
Regarding the input, I have also tried various options here, such as a sin function in a tabular form, sin/cos function by defining *Amplitude, definition=periodic. Indeed, the insufficient sampling, for example for tabular definition of sin function will cause introduction of higher frequencies in the input motion. However, I did ensure this is not a problem in my analysis.
If I run my model with elastic material, no oscillations occur. Thus, I would assume both, the input motion definition and the element type [here not sure, maybe there is some coupling between element type and elastoplasticity?] should be fine. The problem of the spurious oscillations appears when "non-linearity" is material behavior is introduced.
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