  We consider a generalized Brans-Dicke model in which the scalar field has a
potential function and is also allowed to couple non-minimally with the matter
sector. This anomalous gravitational coupling can in principle avoid the model
to pass local gravity experiments. One then usually assumes that the scalar
field has a chameleon behavior in the sense that it acquires a
density-dependent effective mass. While it can take a small effective mass in
cosmological (low-density environment) scale, it has a sufficiently heavy mass
in Solar System (large-density environment) and then hides gravity tests. We
will argue that such a chameleon behavior can not be generally realized and
depends significantly on the forms attributed to the potential and the coupling
functions.
