### How to get displacements from strain tensor at each node?

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4 months ago by
Hi guys,
Sorry about being completely lost in this but how can I get back the node displacements from the strain tensor (Let say in 2D)?
Thanks
Community: FEniCS Project

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4 months ago by
You'd have to integrate ( from a point).
How are you calculating the strain tensor? Usually, one defines a displacement vector as the unknown and expresses the strain as its gradient. In that case you have your displacement directly...
I'm trying to solve a martensitic phase transition problem under elastic deformation. To do it I have defined a traction problem by steps (Incremental traction displacement), where first (As you indicated) the displacement field is calculated, then the strain one (Cauchy strain tensor shown below), which is later part of the phase transition calculation, by splitting elastic strain from transformation strain. The thing is, before starting the next step, the current elastic strain (Accumulated) must be the input for the next traction increment. That is why I need it back in a displacement domain.
def epsilon(u):
return 0.5*(nabla_grad(u) + nabla_grad(u).T)​

Now, you have said "usually" the displacement is the unknown. So, could be possible in Fenics to define the linear elastic problem with the strain tensor as unknown?

written 4 months ago by Matias Tejada