  Two novel phenomena in a weakly coupled granular superconductor under an
applied stress are predicted which are based on recently suggested piezophase
effect (a macroscopic quantum analog of the piezoelectric effect) in
mechanically loaded grain boundary Josephson junctions. Namely, we consider the
existence of stress induced paramagnetic moment in zero applied magnetic field
(piezomagnetism) and its influence on a low-field magnetization (leading to a
mechanically induced paramagnetic Meissner effect). The conditions under which
these two effects can be experimentally measured in high-T_$ granular
superconductors are discussed.
