Introduction:
The property of a material to retain deformation permanently is known as plasticity. Plasticity is an important mechanical property that determines the ability of a material to undergo plastic deformation under load without fracture.

Explanation:
When a material is subjected to external forces or loads, it undergoes deformation. Depending on the nature of deformation, materials can be classified as either elastic or plastic. Elastic deformation is reversible, meaning the material returns to its original shape once the load is removed. On the other hand, plastic deformation is irreversible, and the material retains the deformation even after the load is removed.

Difference between ductility and plasticity:
Ductility and plasticity are related but distinct properties of materials. Ductility refers to the ability of a material to undergo plastic deformation without fracture. It is the measure of how much a material can be stretched or drawn into wires without breaking. Ductile materials like metals can withstand large amounts of plastic deformation without losing their ability to retain the deformation. On the other hand, plasticity is a broader term that encompasses both ductility and malleability.

Brittleness:
Brittleness is the opposite of plasticity. A brittle material is one that fractures or breaks under stress without significant plastic deformation. Brittle materials are characterized by their lack of ductility and malleability. When a brittle material experiences stress beyond its strength, it fails suddenly without any warning.

Malleability:
Malleability is another property related to plasticity. It refers to the ability of a material to be hammered or rolled into thin sheets without fracturing. Malleable materials can undergo plastic deformation under compression without breaking. Unlike ductility, malleability is specific to deformation under compressive forces.

Conclusion:
In summary, the property of a material that enables it to retain deformation permanently is called plasticity. Plasticity is a broader term that encompasses both ductility and malleability. Ductility refers to the ability of a material to undergo plastic deformation without fracture, while malleability refers to the ability to be hammered or rolled into thin sheets.