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updated Lagrangian formulation
Posted Jan 13, 2016, 4:01 p.m. EST Version 5.2 2 Replies
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Hi, all,
I am curious how to activate the updated Lagrangian for the calculation of the internal stress of a compressed body.
I attached my comsol model. Because of the file size, I just attached the model file without the results. When you 'compute' the model, you can see the measured stress at the center of the body; the model requires several minutes.
The body is 1 m by 1 m (plane strain). The right wall has a velocity boundary (-1e-5 m/s) to compress the body. The displacement of 0.1 m yields ~3.0781e7 Pa at the center of the body. However, I found that the internal stress is lower than the analytic solution, 3.2376e7 Pa. I heard that the stress difference happens because I do not use the 'updated Lagrangian formulation' for calculating the strain used for the model. Under the updated Lagrangian formulation, the strain is recalculated at each time step using the deformed (shortened) body, that means that the strain at each step is slightly increased at each time step.
I am not sure but, it seems that the COMSOL calculate the strain by using the initial state, here 1 m. If right, the strain at each time step is increased as a same value, not consistent with the updated Lagrangian formulation.
Please let me know how to deal with this issue. I can convert the calculated stress to the stress under the updated Lagrangian formulation but, I am wondering whether the COMSOL can calculate the stress under the updated Lagrangian formuation.
Thank you in advance.
Changyeol
I am curious how to activate the updated Lagrangian for the calculation of the internal stress of a compressed body.
I attached my comsol model. Because of the file size, I just attached the model file without the results. When you 'compute' the model, you can see the measured stress at the center of the body; the model requires several minutes.
The body is 1 m by 1 m (plane strain). The right wall has a velocity boundary (-1e-5 m/s) to compress the body. The displacement of 0.1 m yields ~3.0781e7 Pa at the center of the body. However, I found that the internal stress is lower than the analytic solution, 3.2376e7 Pa. I heard that the stress difference happens because I do not use the 'updated Lagrangian formulation' for calculating the strain used for the model. Under the updated Lagrangian formulation, the strain is recalculated at each time step using the deformed (shortened) body, that means that the strain at each step is slightly increased at each time step.
I am not sure but, it seems that the COMSOL calculate the strain by using the initial state, here 1 m. If right, the strain at each time step is increased as a same value, not consistent with the updated Lagrangian formulation.
Please let me know how to deal with this issue. I can convert the calculated stress to the stress under the updated Lagrangian formulation but, I am wondering whether the COMSOL can calculate the stress under the updated Lagrangian formuation.
Thank you in advance.
Changyeol
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2 Replies Last Post Jan 14, 2016, 10:28 a.m. EST
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Posted:
9 years ago
Hi,
To account for geometrically nonlinear effect, you must check 'Include geometric nonlinearity' in the settings for the study step.
The formulation used in COMSOL Multiphysics is however 'Total Lagrangian' and not 'Updated Lagrangian'. This affects for example the strain and stress definitions. So if you have an analytically computed strain assuming 'Updated Lagrangian' theory, the value is not the same as you would get in COMSOL. It is different strain measures. None is more correct than the other.
See also the following blog posts:
www.comsol.com/blogs/what-is-geometric-nonlinearity/
www.comsol.com/blogs/why-all-these-stresses-and-strains/
www.comsol.com/blogs/modeling-linear-elastic-materials-how-difficult-can-it-be/ (the section about Geometric Nonlinearity)
Regards,
Henrik
To account for geometrically nonlinear effect, you must check 'Include geometric nonlinearity' in the settings for the study step.
The formulation used in COMSOL Multiphysics is however 'Total Lagrangian' and not 'Updated Lagrangian'. This affects for example the strain and stress definitions. So if you have an analytically computed strain assuming 'Updated Lagrangian' theory, the value is not the same as you would get in COMSOL. It is different strain measures. None is more correct than the other.
See also the following blog posts:
www.comsol.com/blogs/what-is-geometric-nonlinearity/
www.comsol.com/blogs/why-all-these-stresses-and-strains/
www.comsol.com/blogs/modeling-linear-elastic-materials-how-difficult-can-it-be/ (the section about Geometric Nonlinearity)
Regards,
Henrik
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Posted:
9 years ago
Dear Henrik,
Thank you for your kind response which help me a lot!
Sincerely,
Changyeol
Thank you for your kind response which help me a lot!
Sincerely,
Changyeol