  We numerically investigate the dynamics of an one-dimensional disordered
lattice using the Hertzian model, describing a granular chain, and the
$\alpha+\beta $ Fermi-Pasta-Ulam-Tsingou model (FPUT). The most profound
difference between the two systems is the discontinuous nonlinearity of the
granular chain appearing whenever neighboring particles are detached. We
therefore sought to unravel the role of these discontinuities in the
destruction of Anderson localization and their influence on the system's
chaotic dynamics. Our results show that both models exhibit an energy range
where localization coexists with chaos. However, the discontinuous nonlinearity
is found to be capable of triggering energy spreading of initially localized
modes, at lower energies than the FPUT model. A transition from Anderson
localization to chaotic dynamics and energy equipartition is found for the
granular chain and is associated with the"propagation" of the discontinuous
nonlinearity in the chain. On the contrary, the FPUT chain exhibits an
alternate behavior between localized and delocalized chaotic behavior which is
strongly dependent on the initial energy of excitation.
