  We present a formalism to compute Lagrangian displacement fields for a wide
range of cosmologies in the context of perturbation theory up to third order.
We emphasize the case of theories with scale dependent gravitational strengths,
such as chameleons, but our formalism can be accommodated to other modified
gravity theories. In the non-linear regime two qualitative features arise. One,
as is well known, is that nonlinearities lead to a screening of the force
mediated by the scalar field. The second is a consequence of the transformation
of the Klein-Gordon equation from Eulerian to Lagrangian coordinates, producing
frame-lagging terms that are important especially at large scales, and if not
considered, the theory does not reduce to the $\Lambda$CDM model in that limit.
We apply our formalism to compute the 1-loop power spectrum and the correlation
function in $f(R)$ gravity by using different resummation schemes. We further
discuss the IR divergences of these formalisms.
