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Large deformation of a 2-D square
Posted Sep 17, 2013, 6:53 p.m. EDT Structural Mechanics Version 4.3b 2 Replies
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Hello All
I am trying to apply a large shear strain on a square domain. The geometry is very simple, just a square where on the upper and lower edges, opposite velocities are applied. In order to prevent any rotation, I assume that the upper edge is fixed vertically, and I turn on the nonlinear geometry option.
I get divergence problems and to solve it I have tried every possible method (adaptive mesh, automatic refinement and even mesh displacement physics), nothing works. The process stops at 13% progress.
Thank you,
Hossein
I am trying to apply a large shear strain on a square domain. The geometry is very simple, just a square where on the upper and lower edges, opposite velocities are applied. In order to prevent any rotation, I assume that the upper edge is fixed vertically, and I turn on the nonlinear geometry option.
I get divergence problems and to solve it I have tried every possible method (adaptive mesh, automatic refinement and even mesh displacement physics), nothing works. The process stops at 13% progress.
Thank you,
Hossein
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2 Replies Last Post Sep 18, 2013, 1:28 p.m. EDT
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Posted:
1 decade ago
Hello Hossein,
The cause of your problem has a general interest, since it often turns up in support cases. To identify it, plot the smallest principal strain in the last converged time or parameter step. It is of the order -0.4.
When using geometric nonlinearity with a Linear Elastic material, the linearity actually says that the 2:nd Piola-Kirchhoff stress is proportional to the Green-Lagrange strain. (This is sometimes called a St. Venant-Kichhoff material). If you would model uniaxial tension with the same data, the force vs. displacement relation is far from linear at larger strains. It can actually be shown that the force is not unique at high compressive strains, and the limit is approximately -0.4.
Conclusion: If there are high compressive strains in your model, a Linear Elastic material will break down when the smallest principal strain is of the order of -0.4. It is necessary to use another material model.
Regards,
Henrik
The cause of your problem has a general interest, since it often turns up in support cases. To identify it, plot the smallest principal strain in the last converged time or parameter step. It is of the order -0.4.
When using geometric nonlinearity with a Linear Elastic material, the linearity actually says that the 2:nd Piola-Kirchhoff stress is proportional to the Green-Lagrange strain. (This is sometimes called a St. Venant-Kichhoff material). If you would model uniaxial tension with the same data, the force vs. displacement relation is far from linear at larger strains. It can actually be shown that the force is not unique at high compressive strains, and the limit is approximately -0.4.
Conclusion: If there are high compressive strains in your model, a Linear Elastic material will break down when the smallest principal strain is of the order of -0.4. It is necessary to use another material model.
Regards,
Henrik
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Posted:
1 decade ago
Dear Henrik
Thank you for your kind reply. I had thought of every possible issue except the material. The point is that now by hyper elastic material (Neo-Hookean, with Lambda=0 , Mu=10^6) still I see the divergence when the principal strain is around -0.45. Do you have any suggestion on a more proper material choice?
Thank you,
Hossein
Thank you for your kind reply. I had thought of every possible issue except the material. The point is that now by hyper elastic material (Neo-Hookean, with Lambda=0 , Mu=10^6) still I see the divergence when the principal strain is around -0.45. Do you have any suggestion on a more proper material choice?
Thank you,
Hossein