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Non-Zero Net Forces when using Moving Mesh with Solid Deformation

Posted Jan 8, 2024, 4:13 p.m. EST Studies & Solvers, Structural Mechanics, Physics Interfaces Version 6.1 2 Replies

Mike Yan Michelis
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Dear Forum,

Recently, I tried to model some contractile muscle elements, which in practice can be done with spring forces on specific body part boundaries (using their normal vectors). However, while exploring modeling these in COMSOL, I ran into the issue that while the normal vectors always sum up to zero on this simple cube (for the sake of simplicity), the resulting force is non-zero and causes a net displacement.

The simplified time-dependent experiment is a unit cube, where on two opposite faces we apply a sinusoidal force that is always along the normal (akin to a pressure). When solving this problem using just a solid mechanics interface, everything happens as expected. When adding a moving mesh, as if doing fluid-structure-interaction but not adding the fluid yet, the equations for the solid mechanics change and include the deformation gradient on the right hand side for the transient problem. This, in turn, seem to cause this non-zero net force. I'm curious if this is just expected, and it should not balance at all, or is there some numerical error or tweaking I should be doing?

Thanks a lot if anyone has encountered this before, and/or is willing to have a look and run the attached scenarios.

Cheers, Mike

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2 Replies Last Post Jan 17, 2024, 3:37 a.m. EST
Henrik Sönnerlind COMSOL Employee

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Posted: 4 months ago Jan 9, 2024, 9:12 a.m. EST

The model does not have any constraints. It is thus unstable, except as balanced by inertial effects. Small errors will accumulate over time. When the normal vectors change due to the small deformation errors (the analysis is geometrically nonlinear), there will no longer be force balance and the cube will start spinning. In the first model, however, the analysis is geometrically linear, and less sensitive to drift.

Is the analysis really time dependent? That is, do you want to see wave propagation? If not, you should use a Stationary study step with an auxiliary sweep to change the loads parametrically. In this case, you will get a singular stiffness matrix error due to the lack of constraints, though.

If you have loads that cancel each other, the Rigid Motion Suppression boundary condition is useful.

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Henrik Sönnerlind
COMSOL
The model does not have any constraints. It is thus unstable, except as balanced by inertial effects. Small errors will accumulate over time. When the normal vectors change due to the small deformation errors (the analysis is geometrically nonlinear), there will no longer be force balance and the cube will start spinning. In the first model, however, the analysis is geometrically linear, and less sensitive to drift. Is the analysis really time dependent? That is, do you want to see wave propagation? If not, you should use a Stationary study step with an auxiliary sweep to change the loads parametrically. In this case, you will get a singular stiffness matrix error due to the lack of constraints, though. If you have loads that cancel each other, the Rigid Motion Suppression boundary condition is useful.
Mike Yan Michelis
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Posted: 3 months ago Jan 17, 2024, 3:37 a.m. EST

Dear Henrik,

Thanks a lot for the extensive reply! That clarifies a lot of points indeed. The final idea of the study is to submerge for example a rectangular block in water and have it actuate based on a sinusoidal (or some other time-dependent signal) force that is applied on two sides of half the block for example (such that it contracts based on a left-right flapping motion). Hence it should be somewhat free-floating to observe displacement based on FSI. How would this experiment be best done with more constraints? As indeed, the nonlinear solve regularly runs into singular stiffness matrices (or does not converge within the iterations given). And that happens already with a fixed Dirichlet boundary condition on one end of the block, so I can only imagine it becoming worse in FSI when there is no fixed boundary conditions.

Kind regards, Mike

Dear Henrik, Thanks a lot for the extensive reply! That clarifies a lot of points indeed. The final idea of the study is to submerge for example a rectangular block in water and have it actuate based on a sinusoidal (or some other time-dependent signal) force that is applied on two sides of half the block for example (such that it contracts based on a left-right flapping motion). Hence it should be somewhat free-floating to observe displacement based on FSI. How would this experiment be best done with more constraints? As indeed, the nonlinear solve regularly runs into singular stiffness matrices (or does not converge within the iterations given). And that happens already with a fixed Dirichlet boundary condition on one end of the block, so I can only imagine it becoming worse in FSI when there is no fixed boundary conditions. Kind regards, Mike

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