How to model a tendon contracting

[ebdoep22]

Currently I am working with a unique actuator which under the simplest explanation is like a small rope which we can control the contraction of. This actuator can easily be cast in flexible polymers and then used to control the shape/motion of the cast structure. In the past the FE models have simply used forces applied at each attachment point of the actuator. This is no longer really a valid solution due to the longer lengths used and the large deflections needed.

The model can basically be thought of as cylinder approximately the size of a finger with a line element running top and bottom along the axis at the surface. These line elements will represent the contracting actuators. As they contract(strain) the cylinder would bend similar to a finger curling.

I would like to be able to control the strain of the actuators directly in the model. One method I have considered is to model the line elements as truss elements with a material with a thermal expansion constant. Change the temperature of the model and that would control the actuation. Then I would later be able to relate the Abaqus temperature to the fluid pressure that we actually use to control the actuators. The issue with this approach is the actual resulting strain of the actuator is also dependent on its modulus of elasticity. If the modulus were infinite the change in temperature would directly control strain, but of course the whole infinite modulus is an issue. I will also need to know the overall force the actuator needs to maintain that strain level. Note the actuators have no appreciable bending stiffness, so modeling them with 2 force members like trusses should be sufficient.

I realize the problem is a little unorthodox. Is there another element type I could couple with a state variable like temperature/charge/etc. to get this kind of control of a line element?

Thanks,

EBD

 

[DrBwts]

How about defining node sets along the cylinder's surface where you would have your controlling line elements.

You could then control the position of the nodes using displacement boundary conditions.

 

[ebdoep2]

That would cause the curve of the structure to then be directly defined by those BCs. Along the line I need to be able to make each element contract (strain 0%-30%) but otherwise the element should be free to move in the other directions. Now if the BC was setup such that the motion was constrained from one node to the next then that might be viable, but I don't think that is possible.

I guess I could setup a series of constraint eqs from one node to the next which basically takes their initial distance apart then constrains it to the new smaller value. I think this would work but that would get to be a whole lot of constraint equations. I was hoping for something a little less tedious.

 

[DrBwts]

You could script the constraint generation if you are using CAE.

 

[ebdoep2]

I have done something similar when setting up periodic boundary conditions and it is certainly possible. But eventually I would like to consider running many of these contracting actuators and was really hoping for a continuous solution. I will likely start looking at getting those constraint eq scripted if I don't find something soon.

 

[DrBwts]

What do you mean by 'continuous solution'?

 

[ebdoep2]

I don't mean continuous in the usual mechanics of materials way. I mean a method which is less labor intensive, easily integrated to multiple models.

If I could find an element or material property that already exists which couples strain in a line element to some variable I can control that would really be a powerful method for solving this problem. Like thermal expansion couples strain to temperature (but without the previously mentioned issue). I know there is also a piezoelectric coupling but I think I would have a similar issue to the temperature coupling. I was really hoping that someone knew of another similar way to couple this.

 

[ebdoep2]

So I started looking at writing constraint equations to directly control the strain of the line elements representing my contracting tendon-like actuators. The problem I see that the equation editor (interaction module>>constraints>>create>>equation) only allows for linear relationship between nodes. I have previously used these equation constraints to setup periodic boundary conditions, but those are of course a linear relationship between one side of the periodic region to the other.

Any ideas on how to enforce a strain on a line element like this? Basically directly say that each line element must contract X amount of strain?

Thanks

 

[DrBwts]

If you know the original original coordinates of the nodes then why not use a Python script to calculate the position you would like the nodes to end up in and use a displacement boundary condition to move the nodes?

That is use a script to set up your model and not CAE. The equations for nodal displacements would be part of the Python script that sets up the model & not in the model as such.

 

[ebdoep2]

I appreciate you DrBwts for keeping up with this and trying to help out. I think maybe I have not explained the problem well enough. Attached is figure of a very simplified case of a single actuator. As you can see as the actuator changes length (strains) the structure bends, but I don't know its final shape, that is actually what I am trying to figure out.

In the attached figure I have labeled some nodes along the actuator. Concerning appling BC directly to those nodes, if we look at the third element from N3 to N4. All I know is the initial distance between N3 and N4 and that there new distance between them should be less (whatever the strain I tell the actuator). I don't know the new position of N3 or N4, just the new distance between them.

]

 

[DrBwts]

How is the actuator attached? Is it bonded or are there attachment points?

 

[ebdoep2]

The actuator is bonded/cast into the polymer. Additionally in the ends it is anchored. I think the valid assumption is the the polymer is perfectly bonded to it and they strain together. The actuator can directly control its own strain up to 25% length change.

Really this all just boils down to finding a way to directly-control/prescribe/define the axial strain in a line element even through the line element may bend with the structure (Note this would be a truss element so there is zero bending stiffness).

 

[willievanwyk101]

Your problem sounds similar to what I have used in the past to model post tensioning of reinforcement. An easy way of obtaining a solution is to use reduction of temperature. Calculate what change in temperature you require for a given section and coefficient of thermal expansion, to give you the appropriate contraction in your element.