David,
I'm trying to compute the effective elastic properties of a heterogeneous,
linear and a bi-periodic system (i.e., left-right and top-bottom periodic
displacement fields). To this system, I would like to apply a global shearing
by prescribing the displacement field of the surfaces in the form of Dirichlet
BCs. This seems slightly contradictory since a bi-periodic system doesn't have
surfaces.
However, we can still think of the global shearing as an average surface
displacement around which periodic fluctuations occur (the origin of such
fluctuations is due to heterogeneous elastic properties). This is illustrated
in the picture below.
bitmap.png
I would like to know which is the best way to do this in deal.II (I have tried
with make_periodicity_constraints and interpolate_boundary_values, but the
problem is that, as I explain before, we set apparently contradictory
constraints).
It seems to me like the correct boundary values are of the form
u(left) = u(right) + offset
and similarly for the bottom/top. The point is that you encode the shearing in
the 'offset', so you have a variation of periodic boundary conditions that
includes this nonzero offset.
I believe that the make_periodicity_constraints() function takes such an
offset argument. Have you tried that?
Best
W.
--
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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