  We consider a linearly elastic material with a periodic set of voids. On the
boundaries of the voids we set a Robin-type traction condition. Then we
investigate the asymptotic behavior of the displacement solution as the Robin
condition turns into a pure traction one. To wit, there will be a matrix
function {$b[k](\cdot)$ that depends analytically on a real parameter $k$ and
vanishes for $k=0$ and we multiply the Dirichlet-like part of the Robin
condition by $b[k](\cdot)$}. We show that the displacement solution can be
written in terms of power series of $k$ that converge for $k$ in a whole
neighborhood of $0$. For our analysis we use the Functional Analytic Approach.
