I'm trying to solve a variant of a simple linear elastic problem. The variation is that the sub-domains have an intrinsic residual stress, and the goal of the simulation is to find the relaxed shape. Although there is internal structure, the external boundary is (nearly) a cube.
Assuming for the moment that region is the unit cube, the problem requires Dirichlet conditions on the faces where x=0 and y=0. The face x=1 requires the boundary condition that the face is constrained to remain planar. Similarly, the face y=1 requires the boundary conditioni that the face is constrained to remain planar.
I believe that part of the solution is to create a mixed element formulation with DOFs for the plane equations:
element = VectorElement("Lagrange", "tetrahedron", 1 )
plane = FiniteElement( "R", "tetrahedron", 4 )
V = element * plane * plane
Unfortunately, I do not see how to connect those additional DOFs to impose the required boundary condition. Some advice would be appreciated.
