The energy stored in a body when strained within elastic limit is known as
Resilience
Energy Stored in Materials within Elastic Limit
When a material is subjected to external forces, it undergoes deformation. If this deformation is within the material's elastic limit, the material stores internal energy. This stored energy is recoverable once the external forces are removed, meaning the material returns to its original shape. The specific term for this stored energy, when a body is strained within its elastic limit, is resilience.
Resilience Defined
Resilience refers to the total amount of energy that a material can absorb per unit volume when it is deformed elastically. In simpler terms, it is the energy stored in a body when it is strained up to its elastic limit. Beyond this limit, the material undergoes permanent deformation.
- It represents the ability of a material to absorb energy without permanent deformation.
- This energy is released when the load is removed, and the material returns to its original shape.
Distinguishing Related Concepts: Proof Resilience and Modulus of Resilience
It's important to differentiate resilience from closely related terms in mechanics of materials:
- Proof Resilience: This is the maximum amount of strain energy that can be stored in a body without causing permanent deformation. It is essentially the strain energy at the elastic limit. For practical purposes, it often refers to the same concept as resilience when emphasizing the maximum elastic energy storage capacity.
- Modulus of Resilience: This is defined as the proof resilience per unit volume of the material. It indicates the capacity of a material to absorb energy in the elastic range. It is a specific material property and can be calculated using the following formula:
| Term | Definition | Formula (where applicable) |
|---|---|---|
| Resilience | Total energy stored in a body when strained within the elastic limit. | \(\text{U} = \int_0^{\delta_e} \text{P d}\delta\) or \(\text{U} = \frac{1}{2} \text{P}_e \delta_e\) where \(\text{U}\) is energy, \(\text{P}\) is load, \(\delta\) is deformation, and subscript 'e' denotes elastic limit. |
| Proof Resilience | Maximum strain energy stored in a body up to the elastic limit without permanent deformation. | Same as Resilience when considering the maximum elastic energy. |
| Modulus of Resilience | Proof resilience per unit volume. | \(\text{U}_r = \frac{\text{Proof Resilience}}{\text{Volume}} = \frac{\sigma_e^2}{2\text{E}}\) where \(\sigma_e\) is stress at elastic limit and \(\text{E}\) is Young's Modulus. |
The question precisely asks for the "energy stored in a body when strained within elastic limit". Based on the definitions provided, this perfectly aligns with the concept of Resilience.
Important Questions from Mechanical Properties
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