Which property enables a material to undergo considerable plastic deformation under compressive load before rupture?

The property that enables a material to undergo considerable plastic deformation under compressive load before rupture is malleability. Malleability refers to the capability of a material, often metals, to deform and change shape significantly without breaking when subjected to compressive forces. This characteristic allows materials such as gold or aluminum to be formed into thin sheets or intricate shapes through processes like rolling or hammering.

When considering the other options, brittleness describes materials that fracture easily under stress without significant deformation, which is opposite to the concept of malleability. Stiffness indicates a material's resistance to deformation under load, but it does not address the ability to undergo plastic deformation specifically. Resilience pertains to the capacity of a material to absorb energy when deformed elastically and then return to its original shape, but it does not concern itself with plastic deformation or the material’s behavior under compressive loads. Therefore, malleability is the correct choice as it directly relates to the material's ability to sustain significant plastic deformation before failing.