14. Strain Energy Method Theory at a Glance (for IES, GATE, PSU) 1. Resilience (U) •
Resilience is an ability of a material to absorb energy when elastically deformed and to return it when unloaded.
•
The strain energy stored in a specimen when stained within the elastic limit is known as resilience.
U=
σ2 × V o lu m e 2E
or U =
∈2 E × V o lu m e 2
2. Proof Resilience •
Maximum strain energy stored at elastic limit. i.e. the strain energy stored in the body upto elastic limit.
•
This is the property of the material that enables it to resist shock and impact by storing energy. The measure of proof resilience is the strain energy absorbed per unit volume.
3. Modulus of Resilience (u) The proof resilience per unit volume is known as modulus of resilience. If σ is the stress due to gradually applied load, then
σ2 u= 2E
∈2 E or u= 2
4. Application 3 L P2. P2 L P2 L 4 4 U= + = 2 π πd 2 AE 2 (2d ) 2 E E 2. 4 4
L/4
L
2d
P
Strain energy becomes smaller & smaller as the cross sectional area of bar is increased over more & more of its length i.e. A ↑ , U ↓
5. Toughness •
This is the property which enables a material to be twisted, bent or stretched under impact Page be 387 considered of 429 load or high stress before rupture. It may to be the ability of the material to