  We consider the elasticity problem in a %heterogeneous domain with contact on
multiple periodic open cracks. The contact is described by the Signorini and
Coulomb-friction conditions. Problem is non-linear, the dissipative functional
depends on the un-known solution and the existence of the solution for fixed
period of the structure is usually proven by the fix-point argument in the
Sobolev spaces with a little higher regularity, $H^{1+\alpha}$. We rescaled
norms, trace, jump and Korn inequalities in fractional Sobolev spaces with
positive and negative exponent, using the unfolding technique, introduced by
Griso, Cioranescu and Damlamian. Then we proved the existence and uniqieness of
the solution for friction and period fixed. Then we proved the continuous
dependency of the solution to the problem with Coulomb's friction on the given
friction and then estimated the solution using fixed point theorem. However, we
were not able to pass to the strong limit in the frictional dissipative term.
For this reason, we regularized the problem by adding a fourth-order term,
which increased the regularity of the solution and allowed the passing to the
limit. This can be interpreted as micro-polar elasticity.
