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Attempting to Understand Plasticity with Textbook Case
Posted 15.11.2016, 13:26 GMT-5 2 Replies
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Hi,
I am attempting to understand the workflow when implementing the nonlinear material module so that plastic deformation can be observed. I am trying to gain this understanding by analyzing a standard textbook problem which I have attached in as a picture. The problem consists of an axially loaded bar, 7 ft in total length. At the base of the bar, it is pinned such that no deflection occurs. At 5 ft along the bar, an 8 kip load is applied axially such that it places the member in tension. At the tip of the bar (7 ft along the length), a 5 kip load is applied such that it places the bar in tension. The material of the bar is provided as a stress strain diagram which is a bilinear curve. The yield stress occurs at 20 ksi and 0.001 strain. A point on the hardening portion of the curve is given at 40 ksi and 0.021 strain.
To analyze this problem in COMSOL, I have the following in my tree:
1) Geometry - Two rectangles joined together of lengths 5 ft and 2 ft to form the bar.
2) Material - Basic properties for Young's modulus calculated from the given curve. Poisson's ratio density are set to 0.3 and 7500 kg/m^3 respectively although these are not part of the given to the problem. Elastoplastic material model assigned with initial yield stress provided as the yield stress from the diagram and hardening function set to a piecewise function which defines the given material curve. This function operates on the effective plastic strain.
3) Solid mechanics - Roller applied to the pinned in, a boundary load applied at the interface between rectangles as a total force of 8000 lbf, a boundary load applied at the free end as a total force of 5000 lbf. Linear elastic material default assigned with subnode for Plasticity. Hardening function is set to "From material".
4) Mesh is mapped an very fine as it is a simple problem.
5) Stationary study computed.
The issue I am having is that I feel that the problem has been properly setup but it is differing by a large amount from the book when it comes to deflection. At the interface between rectangles a deflection of 0.420 in is expected and 0.432 in is expected at the free end. The solution from COMSOL rather says around 0.08in and 0.095 in respectively. Examining the stress plot shows the proper stress values calculated in each segment of 26 ksi in the segment nearest the wall and 10 ksi in the segment with the free end.
Can a problem be identified in my setup at all? I have been unable to figure out why I can not reproduce results close to that of a classical solution in terms of deflection. I'd like to be able to run and understand this workflow with confidence so that I can build more complicated models using the Plasticity model.
Thank you for assistance in advance.
I am attempting to understand the workflow when implementing the nonlinear material module so that plastic deformation can be observed. I am trying to gain this understanding by analyzing a standard textbook problem which I have attached in as a picture. The problem consists of an axially loaded bar, 7 ft in total length. At the base of the bar, it is pinned such that no deflection occurs. At 5 ft along the bar, an 8 kip load is applied axially such that it places the member in tension. At the tip of the bar (7 ft along the length), a 5 kip load is applied such that it places the bar in tension. The material of the bar is provided as a stress strain diagram which is a bilinear curve. The yield stress occurs at 20 ksi and 0.001 strain. A point on the hardening portion of the curve is given at 40 ksi and 0.021 strain.
To analyze this problem in COMSOL, I have the following in my tree:
1) Geometry - Two rectangles joined together of lengths 5 ft and 2 ft to form the bar.
2) Material - Basic properties for Young's modulus calculated from the given curve. Poisson's ratio density are set to 0.3 and 7500 kg/m^3 respectively although these are not part of the given to the problem. Elastoplastic material model assigned with initial yield stress provided as the yield stress from the diagram and hardening function set to a piecewise function which defines the given material curve. This function operates on the effective plastic strain.
3) Solid mechanics - Roller applied to the pinned in, a boundary load applied at the interface between rectangles as a total force of 8000 lbf, a boundary load applied at the free end as a total force of 5000 lbf. Linear elastic material default assigned with subnode for Plasticity. Hardening function is set to "From material".
4) Mesh is mapped an very fine as it is a simple problem.
5) Stationary study computed.
The issue I am having is that I feel that the problem has been properly setup but it is differing by a large amount from the book when it comes to deflection. At the interface between rectangles a deflection of 0.420 in is expected and 0.432 in is expected at the free end. The solution from COMSOL rather says around 0.08in and 0.095 in respectively. Examining the stress plot shows the proper stress values calculated in each segment of 26 ksi in the segment nearest the wall and 10 ksi in the segment with the free end.
Can a problem be identified in my setup at all? I have been unable to figure out why I can not reproduce results close to that of a classical solution in terms of deflection. I'd like to be able to run and understand this workflow with confidence so that I can build more complicated models using the Plasticity model.
Thank you for assistance in advance.
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2 Replies Last Post 15.11.2016, 15:02 GMT-5
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Posted:
8 years ago
Hello,
It looks like your textbook solution is a 1D one, but you are comparing it to a 2D model. That may be the source of the discrepancy. For instance, you'll want to check that the cross section in the textbook in the same as in your 2D model. Along the same lines, by default in COMSOL a 2D structural analysis is in plane strain, which is not a good representation of a bar, so you may want to switch to plane stress. There could be other issues as well, for instance, since this is a plasticity situation, are you ramping up the loads progressively enough, etc.
Jeff
It looks like your textbook solution is a 1D one, but you are comparing it to a 2D model. That may be the source of the discrepancy. For instance, you'll want to check that the cross section in the textbook in the same as in your 2D model. Along the same lines, by default in COMSOL a 2D structural analysis is in plane strain, which is not a good representation of a bar, so you may want to switch to plane stress. There could be other issues as well, for instance, since this is a plasticity situation, are you ramping up the loads progressively enough, etc.
Jeff
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Posted:
8 years ago
Hi Jeff,
Thanks for the response. I expected there to likely be some error introduced by being a 2-D model vs 1-D. I have attempted to help to encourage 1-D axial deformation only by also running a case where the bar has additional roller constraints applied to all edges except for the free edge to restrict the y-direction. Additionally I have also set the case to be Plane Stress rather than Plane Strain. The problem only provides the cross sectional area of the bar but I ensure that the product of the bar height in the y-direction and the depth set in the Solid Mechanics node equal the same cross sectional area. I think I have mitigated much of the errors that could be introduced by a 2-D model. I would not expect the error introduced to cause a 6x difference in calculated deflection?
I will attempt ramping the loads as I have not done that and see what effect that has.
Thank you.
Thanks for the response. I expected there to likely be some error introduced by being a 2-D model vs 1-D. I have attempted to help to encourage 1-D axial deformation only by also running a case where the bar has additional roller constraints applied to all edges except for the free edge to restrict the y-direction. Additionally I have also set the case to be Plane Stress rather than Plane Strain. The problem only provides the cross sectional area of the bar but I ensure that the product of the bar height in the y-direction and the depth set in the Solid Mechanics node equal the same cross sectional area. I think I have mitigated much of the errors that could be introduced by a 2-D model. I would not expect the error introduced to cause a 6x difference in calculated deflection?
I will attempt ramping the loads as I have not done that and see what effect that has.
Thank you.