**Proof Resilience**

The maximum strain energy stored in a body without permanent deformation is known as proof resilience. It is a measure of the ability of a material to absorb energy up to the elastic limit without undergoing permanent deformation. Proof resilience is an important property of materials used in engineering applications as it determines their ability to withstand impact or sudden loads without deforming or breaking.

**Explanation:**

When a load is applied to a material, it deforms elastically up to a certain point. This elastic deformation is reversible, meaning that the material can return to its original shape once the load is removed. The energy stored in the material during this elastic deformation is known as strain energy.

However, if the load exceeds a certain threshold, the material will undergo plastic deformation, which is irreversible and leads to permanent deformation. The energy required to cause this permanent deformation is known as the yield strength of the material.

The proof resilience is defined as the maximum strain energy that a material can absorb up to the yield point without permanent deformation. It is calculated as the area under the stress-strain curve up to the yield point.

By definition, the proof resilience is a measure of the material's ability to absorb energy without permanent deformation. It represents the maximum amount of energy that can be stored in the material and released when the load is removed without causing any permanent changes in the material's structure.

In practical terms, materials with high proof resilience are desirable in applications where they are subjected to impact or sudden loads. For example, in the construction of bridges, buildings, or automotive components, materials with high proof resilience are preferred as they can withstand sudden loads or impacts without permanent deformation or failure.

In conclusion, the maximum strain energy stored in a body without permanent deformation is known as proof resilience. It represents the ability of a material to absorb energy up to the elastic limit without undergoing permanent deformation.