What do we call a material's ability to retain its deformed shape after the load is removed?

The correct answer is plasticity. This term specifically refers to a material's ability to undergo permanent deformation when subjected to stress, allowing it to retain its new shape even after the load is removed.

When a material exhibits plastic behavior, it means that it has passed its yield point and has undergone a change that is not reversible. For example, when modeling clay is shaped and then allowed to harden, it keeps that new shape, demonstrating plasticity.

In contrast, stiffness relates to a material's resistance to deformation under an applied load but does not indicate whether the material will retain that deformation. Ductility refers to a material’s capability to deform under tensile stress, often associated with the ability to be stretched into wires, rather than holding a permanent shape after removal of stress. Hardness measures a material's resistance to localized deformation from a hard object but again does not pertain to maintaining a shape after load removal.