Post buckling behavior in Lead-rubber isolator

[Samyog]

Hello all,

My question is related to Lead-Rubber Isolator Example 1: Response to axial loading. 

The link to that example is:

https://mooseframework.inl.gov/mastodon/manuals/user/index.html#fig:axialresponse

I am looking at buckling behavior (negative forces in the figure). For this example, the deformation at the onset of buckling is around -10mm. It is mentioned in the "Theory manual" that a very small value of axial stiffness is assigned to the post-buckling region. 

I am trying to understand the force-deformation plot at deformations -10mm to -40mm (second input displacement cycle) and -10mm to -100mm (third input displacement cycle). Can anyone explain why such behavior is being observed or direct me towards literature related to it? I observe similar post-buckling behavior in the output even when the "vertical stiffness variation" is set to false in the input file.

When input shear displacement is removed in that example, the attached force-displacement plot is obtained which shows a very small value of axial stiffness at the post-buckling region.

Thank you,

Samyog

[Chandu Bolisetti]

Samyog, 

 

The parameter, `vertical_stiffness_variation`,  refers to the vertical stiffness variation with shear displacement. Since you don’t have a shear displacement in your model, that parameter wouldn’t change anything. The plot you attached looks like typical post-buckling behavior in compression and post cavitation behavior in tension. Critical buckling load in an absence of shear deformation is governed by equation 5 in the theory manual and after buckling the compression stiffness will be close to zero as indicated in the theory manual. The theory manual is not standalone, and for further information, you are encouraged to read the references cited in the text. The Kumar et al (2015) report referenced in the theory manual can be downloaded here. This report provides a detailed description of the material model. 

 

Chandu

[Samyog]

Hello Dr. Chandu,

My question is related to post-buckling behavior in the force-displacement plot of Example 1, not in the attached plot. Specifically I wanted to learn what the plot in the example was indicating in the compression region and why there is non-zero stiffness after buckling. I will try to clear my doubt from the document you shared as well.

When I set 'vertical_stiffness_variation' to false, there is still shear displacement in the model. Only when I remove shear displacement, I get near zero post-buckling stiffness.

Thank you for sharing the link.

Samyog

[Sai Sharath Parsi]

  Hello Samyog,

If I understand your question correctly, you are trying to understand why there is a negative stiffness in the compression part after buckling (I say negative because as displacement increases axial force decreases)

Please see the points below if they help answer your question:

1) The post-buckling behavior of LR bearing is not very well understood. The MASTODON model is based on Kumar et al (2015) and is the best approximation till date. 

2) Please refer to the attached Fig 1. The path A to B is essentially linear elastic. In addition to the axial displacement, there is a ramped shear displacement applied. So the vertical stiffness varies from point A to B at every time step. However, this change is small hence the effect is not clearly visible. The governing equation from A to B is identified by a red dashed line in Fig 1.

3) The bearings buckles at point B (Fcr, ucr). The buckling load is also a function of shear displacement and is updated every step. The current buckling load and displacement after updating are denoted by Fcrn and ucrn (see lines 167 to 183 in ComputeLRIsolatorElasticity.C). The screenshot is also attached for your reference (Fig 2). Once the bearing buckles at point B, the governing equation is identified by a green dashed line in fig 1. Here, fcrn decreases at every time step from B to C because there is a ramp shear displacement. Hence, the overall effect is seen as axial displacement increases, axial load decreases. Once you don't apply any shear displacement, Fcrn, ucrn will be constant values and will be equal to Fcr, and ucr respectively, and you only see an effect of small post-elastic stiffness as observed in the figures you attached. 

4) The same applies for path C to D (governed by green dashed line).

5) From D to A, it is again governed by red dashed line, but the axial stiffness of AB is different from DA, because of the difference in the shear displacement

6) From A to E, it is again linear elastic. But, buckling load at E is much smaller than at B because of the large shear displacement. The behavior after E is similar to what is explained above.

7) I would recommend you to refer to pages 97-99 of the link Chandu has posted earlier.  

Please let me know if this doesn't answer your question.

Thanks

Sharath

--
https://mooseframework.org/mastodon
https://github.com/idaholab/mastodon
---
You received this message because you are subscribed to the Google Groups "mastodon-users" group.
To unsubscribe from this group and stop receiving emails from it, send an email to mastodon-user...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/mastodon-users/59211f44-f319-465f-9567-097676962f64o%40googlegroups.com.

--

Sai Sharath Parsi

Doctoral Student

Department of Civil, Structural and Environmental Engineering

University of Buffalo

115 Ketter Hall, Buffalo, NY 14260

Ph: 1-716-380-9011

Alternate e-mail: parsisa...@gmail.com

[Samyog]

Hello Sharath,

Thank you for detailed reply.

I was expecting the line 'BC' in your attached figure to have a small (one-thousandth of vertical stiffness kvo) positive slope and the line 'CD' to coincide 'BC' and similar for the third cycle of displacement input (irrespective of any shear loading). I believe that would be the case only if  'Fcrn' is not updated in the post-buckling region. But, that's not how the code was written.

To summarize this discussion, I understand now that since 'Fcrn' is being updated every time-step even in the post-buckling region, the slope of lines 'BC' and 'CD' is different from each other and not actually one-thousand of 'kvo'.

Thank you

Samyog

To unsubscribe from this group and stop receiving emails from it, send an email to mastodo...@googlegroups.com.

To view this discussion on the web visit https://groups.google.com/d/msgid/mastodon-users/59211f44-f319-465f-9567-097676962f64o%40googlegroups.com.

[Sai Sharath Parsi]

Yes Samyog,

That's correct. Fcrn has to be updated in post buckling region, else tracking the difference in buckling load at point B and E was not possible. As said, post buckling behaviour is not well understood, but in my view "if it buckles, it is an issue irrespective of what happens after that".

In that example, we have a worst case scenario where axial load and shear displacement both are substantially large, and unlikely under an earthquake loading (for reference please look at the seismic load example)

Thank you

Sharath

To unsubscribe from this group and stop receiving emails from it, send an email to mastodon-user...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/mastodon-users/f65b41b8-6704-4abe-b164-54b189fab71co%40googlegroups.com.

[Samyog]

Makes sense, thank you.

I was also looking at that LR seismic load example and wanted to let you know that the vertical acceleration at top node is noisy, probably due to the convergence tolerance set in that input file. Also, the acceleration input in Y-direction as plotted in Fig 6 is of FP isolator example.

Samyog

To view this discussion on the web visit https://groups.google.com/d/msgid/mastodon-users/f65b41b8-6704-4abe-b164-54b189fab71co%40googlegroups.com.

[Chandu Bolisetti]

Samyog,

Thanks for pointing those out. The noise in the axial direction is because of the large stiffness, which results in high frequencies. We'll look into the input in Fig. 6. 

In the future, when you notice stuff like this can you please create an issue on GitHub? It would only take a minute and that would greatly help us out in logging bugs or requests.

Chandu

[Samyog]

Sure.

Thank you

Samyog