Could there exist a material that resistively dissipates gravitational flux more strongly than normally, in the same sense that ferromagnetic materials resistiv

Could there exist a material that resistively dissipates gravitational flux more strongly than normally, in the same sense that ferromagnetic materials resistively dissipate magnetic flux more strongly than normally? Something something "gravitational permeability"? (I guess such a material would interact with gravitational waves as if it had more mass than it does, without that affecting its inertial mass?)