The total strain energy stored in a body within elastic limit is termed as
resilience
Resilience: Understanding Total Strain Energy
When a material is subjected to a force, it deforms. If this deformation is temporary and the material returns to its original shape upon removal of the force, the energy absorbed during this process is called strain energy. The question asks for the specific term that describes the total strain energy stored in a body, provided the deformation occurs within the elastic limit.
Defining Key Terms
Let's explore the different terms provided in the options:
- Resilience: This is defined as the total strain energy stored in a body when it is deformed up to the elastic limit. It represents the capacity of the material to absorb energy elastically. Mathematically, if $P$ is the load and $\delta$ is the deformation, the total strain energy ($U$) is given by $U = \frac{1}{2} P \delta$ for gradually applied loads, assuming linear elasticity. Resilience refers to this total stored energy for the entire body.
- Proof Resilience: This term refers to the maximum strain energy a unit volume of the material can absorb without undergoing permanent deformation. It is essentially the resilience per unit volume at the elastic limit.
- Impact Energy: This is the energy required to cause fracture in a material when a load is applied suddenly or dynamically. It's related to toughness and energy absorption during fracture, not specifically the energy stored within the elastic limit.
- Modulus of Resilience: This is numerically equal to Proof Resilience. It represents the maximum strain energy per unit volume that a material can withstand without permanent damage. It's calculated as the area under the stress-strain curve up to the elastic limit (or yield point), often expressed as $\frac{\sigma_y^2}{2E}$, where $\sigma_y$ is the yield stress and $E$ is the Young's modulus.
Why Resilience is the Correct Term
The question specifically asks for the term representing the total strain energy stored within the elastic limit for the entire body. Based on the definitions:
- Resilience perfectly matches this description.
- Proof Resilience and Modulus of Resilience refer to energy stored *per unit volume*, not the total energy stored in the body.
- Impact energy relates to fracture under dynamic loading, which goes beyond the elastic limit concept mentioned.
Therefore, resilience is the correct term for the total strain energy stored in a body within the elastic limit.
| Term | Definition | Units |
| Resilience | Total strain energy stored within the elastic limit | Energy (e.g., Joules) |
| Proof Resilience / Modulus of Resilience | Maximum strain energy absorbed per unit volume without permanent deformation (at elastic limit) | Energy per Volume (e.g., J/m³) |
| Impact Energy | Energy absorbed during fracture under sudden load | Energy (e.g., Joules) |
Important Questions from Stress and Strain
The ultimate tensile stress of mild steel compared to ultimate compressive stress is ______.
Which of the following is a proper sequence?
- The stress induced in a body, when suddenly loaded, is _________ the stress induced when the same load is applied gradually.
The ratio of the magnitude of the applied force to the cross-sectional area of the wire is called
A metal rod has a diameter of 8 mm and a true stress-strain relationship is given by \({\sigma } = 900 \times \epsilon^{0.6}\) is under the action of tensile loading. The minimum diameter in mm that can be achieved is:
