The strain energy stored in a spring, when subjected to maximum load, without suffering permanent distortion, is known as 

Explanation:

Strain Energy in a Spring:

• Strain energy is the energy stored in a body or structure due to deformation caused by applied forces. For a spring, this energy is stored when the spring is subjected to a load, and it is released when the load is removed. The strain energy stored in the spring is a result of elastic deformation, and the spring returns to its original shape once the load is removed, provided the material does not exceed its elastic limit.
• When a spring is subjected to a maximum load without suffering permanent distortion or plastic deformation, the energy stored is termed as the proof resilience. Proof resilience is the maximum strain energy a material can store within its elastic limit.

Formula for Strain Energy in a Spring:

The strain energy stored in a spring, also known as elastic potential energy, can be calculated using the following formula:

U = ½ × F × δ

Where:

• U = Strain energy (Joules)
• F = Force applied to the spring (Newtons)
• δ = Deflection or displacement of the spring (meters)

Alternatively, in terms of the spring constant (K):

U = ½ × K × δ²

Where:

• K = Spring constant (N/m)
• δ = Deflection (m)

Proof Resilience:

• Proof resilience is the maximum amount of strain energy stored in a material per unit volume without causing permanent deformation. It is a measure of the material's ability to absorb energy elastically. For a spring, it is the strain energy stored when the spring is subjected to its maximum elastic load.

The formula for proof resilience is given by:

Proof Resilience = σ² / (2 × E)

Where:

• σ = Maximum stress within the elastic limit
• E = Modulus of elasticity