Hi all,
I am confused about which stress measure to use in the momentum balance. The divergence for the Cauchy stress is often written with a small d, whereas the divergence for the 1st Piola Kirchhoff stress is written with a big D.
Which divergence is the one that Fenics takes? Which of these two equations should I solve in FEM? I am investigating big deformations.
Many thanks in advance!
Hi, the small d divergence of the Cauchy stress refers to derivatives with respect to the current unknown configuration. The derivatives computed in FEniCS in a Lagrangian setting are computed with respect to the initial configuration (big D divergence). However, it is also possible to problems in an Eulerian setting (as in fluid mechanics). The Lagrangian setting with the first Piola Kirchhoff stress is a bit more natural for solid mechanics.
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Okay I see, thank you!