Does the syntax Grad(U) exist in FEnics
I am trying to compute deformation with respect to reference coordinates. I have found Grad(U) in some of the links while search on internet.
Can anyone please clarify if the syntax Grad(U) exists ? i mean can i compute F = I+Grad(U) directly using FEnics ?
Where U represents the reference coordinates
fenics solves a differential equation in space x, the physical meaning of this x depends on your formulation. For elastostatics, if the differential equation is the divergence of Cauchy stress then the physical meaning of x is the current configuration. If the differential equation is the divergence of Piola (or nominal) stress, then u[i].dx(j) means Grad(u) such that Grad means a derivative in the space representing the reference configuration.
dim = 3 I = identity(dim) F = I + nabla_grad(u)
nabla_ prefix in front of
grad. This gives the correct index ordering, cf. the red box in this chapter of the tutorial.
For this definition of the deformation gradient to be correct, however,
u has to be the displacement and not the reference coordinates.