Applying force on a particular node on the mesh

Question

I am a newbie in fenics and finite element methods.

I try to implement a method to estimate the elasticity parameters (young modulus and poisson ratio) of a deformable object. What I want to do is this:

An object fixed from the bottom(as a start a cube)
To apply an external force on a particular place on the top of the object and using a method like gradient descent etc. estimate the elasticity parameters by comparing the real displacement and estimated displacement.
I am looking over Hyperelasticity demo in fenics (http://fenicsproject.org/documentation/dolfin/1.0.1/python/demo/pde/hyperelasticity/python/documentation.html) but I couldn't figure out how to apply to on a particular node on the mesh and then deform the object based on that force. I think in that demo a force is applied in the -y direction on the whole mesh. There is body force vector:
B = Constant((0.0, -0.5, 0.0))

Should I change this to a vector in the same size with the mesh and put a force value to on the element of the vector which corresponds to the nodal element on the mesh.

Sorry if I don not make much sense. I may ask very trivial questions. This concepts are new for me so I am having troubles in stating what is in my head.

Answer 1

Hi,
In the hyperelastic demo
demo
T is the surface traction (surface force). B is the body force. If you want to only apply the traction on a specific part of the surface, you will have to define that boundary area precisely and use another ds() to apply it.

Applying a dirichlet displacement is easier, and if you use the 'pointwise' method, you can get it at a specific point.

Comments

Thank you for your answer! That worked.
Is it possible to combine this approach with collision detection? I was looking over to the collision detection demo: demo
As I understand, compute_entity_collisions(tree) returns the list of indices where the two entities collide.
Let's say I get the list of the entity indices and calculated the corresponding area where collision occurs. If I give this area as input to a new boundary definition and apply the traction force there, is it the right way of doing it?

#the area where collusion occurs
a=0.5 
b=0.7
class Obstacle(SubDomain):
    def inside(self, x, on_boundary):
           return (between(x[2],(a,b)) and between(x[0],(a,b)) )

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Sorry, I haven't done collision detection, so I really don't know if that is the right (best) way to do that. You might consider posting another question mentioning collision detection in the title to get the right attention.