Hello everyone, 

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.


[image: 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).

Thank you in advance.


P.S.: suggestions of alternative procedures to achieve the same goal are 
welcome.

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