Short Answer:

Resilience is the ability of a material to absorb energy when it is deformed elastically and to release that energy upon unloading without any permanent deformation. It represents the capacity of a material to store elastic strain energy under stress and regain its original shape once the load is removed.

In simple terms, resilience is the property of a material to resist shock or impact loads without being permanently deformed. Materials with high resilience, such as spring steel, can absorb large amounts of energy and are used in applications like springs, shock absorbers, and impact-resistant components.

Detailed Explanation :

Resilience

When a body is subjected to external forces, it deforms and stores energy internally. If the applied load is within the elastic limit, the body regains its original shape after the removal of the load, and the energy stored during deformation is completely recovered. The energy stored in the material within this elastic range is called strain energy, and the capacity to absorb and release this energy is known as resilience.

Resilience is one of the most important mechanical properties of materials, especially for those subjected to impact or shock loading. It indicates how much energy per unit volume a material can store and release elastically before yielding.

For example, a spring or suspension component must be highly resilient to absorb shocks without permanent deformation. On the other hand, brittle materials like cast iron have low resilience and break suddenly when subjected to impact.

Definition

The term resilience can be defined as:

“Resilience is the property of a material to absorb energy within the elastic limit and to release it upon unloading.”

In other words, resilience is the measure of a material’s elastic strain energy capacity.

The energy stored per unit volume within the elastic limit is called the modulus of resilience.

Mathematical Expression

Let a material be subjected to a stress–strain relationship within the elastic region as shown in a linear stress-strain diagram.

The strain energy per unit volume (u) stored up to the elastic limit is equal to the area under the stress-strain curve from zero to the elastic limit.

where,

= yield stress (limit of proportionality)
= strain corresponding to yield stress

Using Hooke’s Law (), we can express strain in terms of stress:

Substitute this value in the above equation:

Thus,

\boxed{\text{Modulus of Resilience (U_r)} = \frac{\sigma_y^2}{2E}}

This represents the maximum strain energy per unit volume that can be absorbed without permanent deformation.

Units

SI Unit: Joule per cubic meter (J/m³)
CGS Unit: Erg/cm³

Since strain energy is a form of work or energy, it has the same units as work or potential energy.

Physical Meaning

The modulus of resilience indicates how much energy a material can store elastically per unit volume before it begins to yield.

A high modulus of resilience means the material can absorb a large amount of elastic energy before deformation.
A low modulus of resilience means the material can store only a small amount of energy before reaching its yield point.

Hence, materials like spring steel, copper, and bronze are highly resilient, whereas cast iron, glass, and concrete are not.

Factors Affecting Resilience

Elastic limit:
A higher elastic limit increases resilience, as more stress can be applied within the elastic range.
Modulus of elasticity (E):
Materials with lower E (more flexible) tend to have higher resilience for the same stress value.
Yield stress:
Resilience increases with yield stress since the material can sustain higher elastic stress before plastic deformation.
Temperature:
Increase in temperature may reduce resilience as materials become softer and lose elastic strength.
Material type:
Ductile materials (like steel, bronze) have high resilience, whereas brittle materials (like glass, ceramics) have low resilience.

Importance of Resilience

Energy absorption:
Resilient materials can absorb shocks and impacts effectively without failure.
Spring and suspension design:
Resilience is a key factor in designing springs, leaf suspensions, and elastic couplings.
Safety in machinery:
Helps prevent sudden failure of machine parts subjected to fluctuating or impact loads.
Selection of materials:
Determines the suitability of a material for dynamic loading conditions.
Engineering applications:
Used in automotive, aerospace, and mechanical systems where repeated energy absorption and release occur.

Comparison Between Resilience and Toughness

While both terms relate to energy absorption, they differ in nature:

Resilience refers to the energy absorbed within the elastic limit.
Toughness refers to the total energy absorbed before fracture, including both elastic and plastic deformation.

Hence, a resilient material may not necessarily be tough if it fractures easily after the elastic range.

Example

Let us calculate the modulus of resilience for a mild steel specimen having:

Thus, the material can store 0.156 MPa (or 0.156 N·mm/mm³) of strain energy per unit volume within its elastic limit.

Applications of Resilience

Springs and shock absorbers in vehicles.
Buffers and bumpers in railways and cranes.
Suspension systems in automobiles.
Sports equipment such as bows, golf clubs, and rackets.
Machine components subjected to repeated or impact loads.

These applications demand materials that can store and release energy efficiently without permanent deformation.

Conclusion

The resilience of a material is its ability to absorb and release elastic strain energy under loading and unloading within the elastic limit. It is an essential property for components subjected to impact, vibration, or cyclic stresses. The modulus of resilience, given by , measures the energy stored per unit volume before yielding. Materials like spring steel and bronze have high resilience, making them ideal for springs, suspensions, and energy-absorbing devices. Understanding resilience ensures safe and efficient design of mechanical systems that experience dynamic loading.