  In this paper, we investigate the stabilization of a linear Bresse system
with one discontinuous local internal viscoelastic damping of Kelvin-Voigt type
acting on the axial force, under fully Dirichlet boundary conditions. First,
using a general criteria of Arendt-Batty, we prove the strong stability of our
system. Finally, using a frequency domain approach combined with the multiplier
method, we prove that the energy of our system decays polynomially with
different rates.
