### Strain Calculation by Gradient

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Hello everyone,

Normally we calcucate the elastic strain as

Regards,

Normally we calcucate the elastic strain as

`sym(grad(u))`

. Even if we does not use quadrature functionspace, does FeniCS calculates the strain directly at nodes or at quadrature points due to integrals ? Another question is if we are using linear elements for displacements, then the strain and stress will be piecewise continious on the elements. On that situation, strains and stresses will be different for each of the element even the node is the same. While representing the stress and strains globally, does FEniCS taking the average of them in the node ? Is there any way to see the stress/strains in locally on elements ?Regards,

Community: FEniCS Project

### 1 Answer

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FEniCS calculates the strain at the quadrature points when you have

Yes, strain and stress are piecewise constants when using linear elements. In this situation, if you wanted to know the value at the nodes, you would have to project the stress or strain onto a finite element space that is continuous at the nodes, see for instance: https://fenicsproject.org/pub/tutorial/sphinx1/._ftut1006.html#flux-computations . You would use

`sym(grad(u))`

in a form and you are integrating it.Yes, strain and stress are piecewise constants when using linear elements. In this situation, if you wanted to know the value at the nodes, you would have to project the stress or strain onto a finite element space that is continuous at the nodes, see for instance: https://fenicsproject.org/pub/tutorial/sphinx1/._ftut1006.html#flux-computations . You would use

`TensorFunctionSpace`

instead of `VectorFunctionSpace`

. If you don't really mind that the stress are not continuous at the nodes and just want to see them piecewise constant, you would still have to project them, but in this case, to a DG order 0 space.
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