Hi Folks,
How difficult would it be for the developers to extend ex7 of system of
equations for nonlinear elasticity to include variation in surface traction in
the
Jacobian formation?
https://github.com/libMesh/libmesh/blob/master/examples/systems_of_equations/systems_of_equations_ex7/systems_of_equations_ex7.C#L230-L256
In theory its straightforward (I think), but for the life of me I cannot figure
out how to play with the indices to get terms like
D traction [u] = (D F[u] S N). V + (F(u) D S[u] N). V
= (D F[u] S N). V + (F(u) (C : D E[u]) N). V
in which D [u] is the linearization in the direction u, F is deformation
gradient, S is PK2 tensor, N is normal vector in reference frame, E is Green
strain
C is elasticity tensor, and V is a test function.
Also, how bad is the nonlinear convergence if one leaves traction part from
Jacobian in general?
Thanks,
— Amneet
=====================================================
Amneet Bhalla
Postdoctoral Research Associate
Department of Mathematics and McAllister Heart Institute
University of North Carolina at Chapel Hill
Email: [email protected]<mailto:[email protected]>
Web: https://abhalla.web.unc.edu<https://abhalla.web.unc.edu/>
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