Variables
Description
What is this formula?
The Modulus of Resilience represents the maximum elastic strain energy per unit volume that a material can absorb before yielding. Graphically, it corresponds to the area under the linear elastic portion of the stress-strain curve.
When to use it
Use this formula when evaluating materials subjected to impacts, cyclic loading, springs, energy storage devices, and structures that must absorb energy without undergoing permanent deformation.
Example
A spring steel has a yield strength of 1200 MPa and a Young's modulus of 210 GPa.
Data:
sigmay = 1200000000 Pa
E = 210000000000 Pa
Formula:
Ur = sigmay² / (2E)
Substitution:
Ur = (1200000000²) / (2 × 210000000000)
Result:
Ur = 3428571 J/m³
The material can absorb approximately 3.43 MJ/m³ of elastic energy before yielding.
Applications
- Spring design
- Impact-resistant components
- Mechanical energy storage
- Structural materials selection
- Automotive suspension systems
- Aerospace structural design