  We present new nonlinear, time-dependent convective hydrodynamical models of
RR Lyrae stars computed assuming a constant helium-to-metal enrichment ratio
and a broad range in metal abundances (Z=0.0001--0.02). The stellar masses and
luminosities adopted to construct the pulsation models were fixed according to
detailed central He burning Horizontal Branch evolutionary models. The
pulsation models cover a broad range in stellar luminosity and effective
temperatures and the modal stability is investigated for both fundamental and
first overtones. We predict the topology of the instability strip as a function
of the metal content and new analytical relations for the edges of the
instability strip in the observational plane. Moreover, a new analytical
relation to constrain the pulsation mass of double pulsators as a function of
the period ratio and the metal content is provided. We derive new
Period-Radius-Metallicity relations for fundamental and first-overtone
pulsators. They agree quite well with similar empirical and theoretical
relations in the literature. From the predicted bolometric light curves,
transformed into optical (UBVRI) and near-infrared (JHK) bands, we compute the
intensity-averaged mean magnitudes along the entire pulsation cycle and, in
turn, new and homogenous metal-dependent (RIJHK) Period-Luminosity relations.
Moreover, we compute new dual and triple band optical, optical--NIR and NIR
Period-Wesenheit-Metallicity relations. Interestingly, we find that the optical
Period-W(V,B-V) is independent of the metal content and that the accuracy of
individual distances is a balance between the adopted diagnostics and the
precision of photometric and spectroscopic datasets.
