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### Help to apply shear force at boundary

Posted: **04 Jan 2016, 08:30**

by **LizR**

Hello,

I am working on modelling a very small rectangular prism of ice. Imagine a block of ice with larger sheets of some other material firmly attached to the top and bottom. If you pull on the top and bottom in opposite directions the result will be a shear force experienced by the ice block.

*Ice block with shear forces applied at top and bottom surfaces* - ShearedBlock.png (2.9 KiB) Viewed 6037 times

I need to model a shear force applied to the top and bottom surfaces of my small ice block, as in the picture. I have made the ‘box’ in ElmerGrid and I have most of my .sif file written but I am having trouble with the boundary conditions for the Navier Stokes solver.

In summary, I would like help to apply a tangential force to two surfaces of a ‘box’ and leave the other surfaces free. I have made an attempt at the BC for the free surfaces but I am not sure where to even start with the sheared surface. I am new to Elmer so any help would be very much appreciated.

Thank you for your time,

Liz

Code: Select all

```
Boundary Condition 1
Name = "sides"
Target Boundaries(4) = 2 4 5 6
Depth = Real 0.0
Free Surface = Logical True
End
Boundary Condition 2
Name = "sheared surfaces"
Target Boundaries(2) = 1 3
End
```

### Re: Help to apply shear force at boundary

Posted: **04 Jan 2016, 09:43**

by **tzwinger**

Hi Liz,

tangential forces can be applied with the keywords

for directional applied surface stresses (force/unit-area) or

for normal external pressure (I know, the naming is unfortunate, but this is something from old Elmer history).

In your particular case I'd split Boundary 2 into Boundary 2 and 3 and apply the externally applied shear with different signs, i.e.,

Code: Select all

```
Boundary Condition 2
Name = "sheared surface up"
Target Boundaries(1) = 1
Pressure 1 = $shearstress
End
Boundary Condition 3
Name = "sheared surface low"
Target Boundaries(1) = 3
Pressure 1 = $-shearstress
End
```

you can define the numerical value of shearstress somewhere outside a section within the SIF. This assumes your shear-stress is aligned with the x-direction.

Nevertheless, I have two issues:

1) you are assuming incompressibility (which is correct for pure ice). How realistic is it to assume that the geometry doesn't change vertically if shearing the block? I would have the feeling that the vertical distance between the surfaces where the shear-stress is applied will come closer together - but of course this links to the design of the apparatus which I do not know.

2) I do not get the point on setting the pressure constant in the body-force for the whole domain. In fact, I think that is a problem.

Best Regards,

Thomas

### Re: Help to apply shear force at boundary

Posted: **05 Jan 2016, 01:43**

by **LizR**

Hello Thomas,

Thank you for your detailed help, I really appreciate it. With what you have told me I can move forward now.

To answer your first question, I realise that this test case is unrealistic. At the moment I am just aiming to create a block and put some forces on it as a step towards a more advanced model. Creating a moving mesh so the geometry can move when force is applied will come later, after I can get simple code to run. I will also be changing the geometry in future.

Second, the constant body force was part of an earlier attempt to apply the shear and I forgot to remove it. My .sif file is unfinished and will be cleaned up before I run it, I just included it for more context if needed. Sorry if it confused you.

Kind regards,

Liz

### Re: Help to apply shear force at boundary

Posted: **04 Mar 2016, 01:01**

by **LizR**

Hello Thomas,

I have run into some more issues with this ice block case. To answer your previous question, in our lab experiment the top and bottom faces can be held in place so they don’t move vertically. I am having some trouble introducing the horizontal motion though.

I have implemented free surface solvers on the four sides of the ice block, using the undocumented rotated free surface solver. This gives the mesh update perpendicular to each wall, and works well for the two end walls.

The problem is related to the larger side panels. When shear is applied to the top of the block the side panels can move outward (which is solved for by the rotated free surface solver), but they need to be able to move in the direction of shear also. If I don’t include this sideways motion the side panel elements can’t move in the direction of shear and so the mesh becomes very stretched at the edges.

I can’t think of a way to include this sideways motion while making sure mass is properly conserved. It is possible to run the model for one timestep and see the problem as shown in the picture (the color is the horizontal Mesh Update – and shows how the edges of the side panel move, while the centre remains fixed, leading to distorted elements after a couple of timesteps).

Do you know of a way to make the side walls move?

Liz

- Screen Shot 2016-03-04 at 8.59.02 am.png (66.5 KiB) Viewed 5909 times

### Re: Help to apply shear force at boundary

Posted: **15 Apr 2016, 09:33**

by **tzwinger**

Hi Liz,

somehow I missed your reply from March 4th, sorry. If you really have an apparatus where two parallel plates to which the ice is attached are pushed with a shear stress and not vertically displaced (I still wonder how you can achieve that without cracking the ice), I would deploy the FreeSurfaceSolver only to the side boundaries (guess that is what we mean with "boundaries

not attached to the apparatus") and on the boundaries resembling the plates simply in parallel direction apply the stress and in vertical direction set the velocity component to zero. I do not see any need to solve for a kinematic boundary there. You will have to set the Mesh Update in the parallel direction to be the velocity multiplied with the timestep-size (dt):

Code: Select all

```
! outside any block
$dt = 0.1 ! or whatever your timestep-size is
...
! in Simulation
Timestep Sizes = $dt
...
! at boundary
Mesh Update 1 = Variable Velocity 1
Real MATC "tx * dt"
Velocity 2 = 0.0
```

Another issue, if your mesh deforms is, that the FreeSurfaceSolver would need to know that it has to take the Mesh Velocity into account (this is the ALE - Arbitrary Eulerian Lagrangian - formulation). In order to do so, you might have to include a

Code: Select all

`ALE Formulation = Logical True ! we can have a sidewards moving mesh`

in the solver section.

Best wishes,

THomas