What property allows a material to undergo permanent deformation without returning to its original shape?

The property that allows a material to undergo permanent deformation without returning to its original shape is plasticity. Plasticity is the ability of a material to experience significant deformation under applied stress, which leads to a permanent change in shape or size once the stress is removed. This characteristic is especially important in processes such as metal forming or molding, where materials must be shaped and retained in their new form.

Elasticity, on the other hand, refers to a material’s ability to return to its original shape after the removal of stress, indicating that the deformation is temporary. Ductility describes a material’s capability to be drawn into a wire or undergo significant plastic deformation before rupture, which is related but not synonymous with general plasticity. Toughness is a measure of a material's ability to absorb energy and plastically deform without fracturing. While all of these properties are important in engineering, plasticity specifically addresses the ability to maintain a new shape after stress is applied, making it the correct choice in this context.