We have systematically explored the pressure dependence of magnetism, electronic structure, elasticity and lattice dynamics of the ferromagnetic L10-FePd crystalline alloy by employing first-principles calculations. All predicted properties of the ground state are well consistent with available experimental and theoretical results. The total magnetic moment decreases slowly with pressure before the ferromagnetic collapse critical pressure of about 164 GPa and then sharply decreases near the 164 GPa, and the (C44-C66) value changed from positive to negative. The phonon dispersion relations and phonon densities of state are also investigated at zero and high pressures. Owing to the spontaneous magnetization of the system, the ferromagnetic L10-FePd crystalline alloy is dynamically stable at pressures below 171 GPa (above which the magnetism completely disappears). When the pressure was greater than 171.4 GPa, the system dynamics became unstable. The calculated elastic properties indicate that the L10-FePd alloy is mechanically stable up to 180 GPa. The ferromagnetic L10-FePd crystalline alloy has good ductility and metallicity outside the ferromagnetic collapse pressure region, but the L10-FePd crystalline alloy has an abnormal phenomenon of a sudden sharp increase in brittleness near 162 GPa. We found this anomaly from the Pugh ratio B/G and Poisson's ratio of the system and the change of Cauchy pressures (C12-C66) and (C13-C44) with pressure, and this anomaly was analyzed with compression factor and magnetoelastic force.
