The capacity of a material to absorb energy within the elastic limit is known as:

Explanation:

Resilience

• Resilience is defined as the capacity of a material to absorb energy within its elastic limit and to release that energy upon unloading without undergoing permanent deformation. It is a measure of a material's ability to store elastic energy, which can be utilized in applications where materials undergo repeated loading and unloading.
• When a material is subjected to stress, it deforms elastically within its elastic limit. During this elastic deformation, the material stores potential energy. Resilience is the ability of the material to absorb this energy and recover its original shape and size once the stress is removed. This property is crucial in applications requiring materials to withstand cyclic or dynamic loads without permanent deformation.

Elastic Limit:

• The elastic limit is the maximum stress that a material can withstand without undergoing permanent deformation. Beyond this limit, the material enters the plastic deformation region, where it cannot return to its original shape or size upon unloading. Resilience is concerned only with the energy absorbed within the elastic limit.

Mathematical Representation: Resilience is quantitatively represented by the area under the stress-strain curve within the elastic region. Mathematically, it is given by:

Resilience (U) = (σ²) / (2 × E)

Where:

• σ = Stress within the elastic limit
• E = Young's Modulus of the material