I am looking to find a code to compute the viscoelastic deformation of a beam over a fluid, in order to compute the time dependant flexure of the lithosphere under a load.
Can anyone suggest an easy way to do this? Is it possible to do it for a broken and an infinite beam (like in regional isostasy)? Is it posible to do it with variable Te?
I think the best strategy is to look for books (educational) treating this problem. Out of my mind I think of Watt's books and Turcotte and Schubert (Geodynamics). They contain what you need and you will be able to elaborate a modelling strategy.
I am not a specialist but I have tried what you are intending.
Broken beam is relatively easy but generally not realistic. Infinite beam is also relatively easy. Variable Te you go into troubles. There is a massive amount of literature to dig out.
Good luck in your developments!
Jon Pelletier's book, 'Quantitative Modeling of Earth Surface Processes' has a chapter on flexure which describes displacement under line loading. The book also has some code related to the problem in the appendix. And I agree with Julien, Turcotte and Schubert is always a good place to start.
I kindly suggest you to examine my notes on Theoretical Geomechanics
http://www.geotechlinks.com/download.php?id=GL0226
There is an algorithm explained in detail there.
Hello everyone. I have gone over Turcotte and Schubert's book several times and I think it covers elasticity but not viscoelasticity. I will look into Jon Pelletier's book to see. I have read several times Profesor Watt's book and is a great text, but it treats the viscoelasticity problem in a simpler way than I want. By the way, Ivan thanks for the link to the notes. Kind regards to everyone
If you are looking to compute the viscoelastic response for a simple load and a 1D homogeneous Earth structure, you can find analytical solutions; cf. section 6.10 Potsglacial Rebound in Turcotte & Schubert textbook: e.g. equation 6.103 will give you time-dependent surface displacement for a given viscosity and maximum flexure related to a given elastic thickness.
For more complex loads, you will probably need to look into numerical codes. SELEN is a good one that allows you to solve for nearly all Earth response variables, but it is limited to 1D uniform rheology (elastic thickness and viscosity structure). Cf. the SELEN web page: http://www.fis.uniurb.it/spada/SELEN_minipage.html
If you are dealing with spatially variable elastic thickness, then you will need to go to finite-element modelling to include spatial variations in rheology. There are several FEM codes out there that can do simple regional calculations for any kind of load of complex Earth visco-elastic structures.
Good luck!
Hello Stephane. Thanks for the comment. I was thinking on using FEM but I've had some problems finding literature that clearly defines the stiffness matrix, the connectivity approach and the global stiffness matrix for a simple geometry (triangles or boxes). Can you suggest any literature that describes these based on the Galernik approach? That would be very helpful.
Hi Mariano,
I don't have references for this particular problem (stiffness matrices for GIA modelling). Unless you are set on writing your own code, I would suggest looking into existing FEM codes used in Earth Sciences that can do visco-elastic models. One example is ADELI: https://code.google.com/p/adeli/. My colleagues and I have used for simple GIA problems; it's fast and simple enough to implement spatially varying rheology.
Cheers.
Hello again Stephane. Thank you for the suggested code. I will try download and try it to see if I can use it!.
Regards!
Hi Mariano,
You can also try Pylith. I've been working with this FEM code for a while now and it's very straight forward and easy to set up. You can generate complex geometries and it will handle viscoelastic materials. I don't know if it is the best option for GIA (if that's what you are trying to do), but you may want to take a look at it: http://geodynamics.org/cig/software/pylith/ The documentation is fairly good, but I don't know if you'll find the stiffness matrix definitions.
You'll also need to develop your FEM model. There are several ways. You can use a trial version of Trelis: http://www.csimsoft.com/trelis-fea.jsp. This program will let you generate pretty complex models, but it's not free. Look into Pylith's manual to find other free options to develop simpler FEM models.
Good luck, y saludos.
Demián
Hello Demian. Thank you for the recommendations. I will look up into Pylith to see if I can get it running and use it with some simple geometries first.
Thanks again!
Mariano
Mariano S. Arnaiz-Rodríguez ...Good question.. Please share me the best answer might you trust...
Regards…
Dear Hussam. The best answer so far is to use the TEKTON distribution my Jay Melosh
Mariano S. Arnaiz-Rodríguez Dear Mariano, do you know where i can download the Tekton distribution? or do i should contact H. J. Melosh to request this software?
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