Modulus of Resilience
Modulus of Resilience
The modulus of resilience is the strain energy stored per unit volume when a material is loaded to its yield point — how good a spring material it is.
It is U_r = σ_y²/(2·E). where σ_y is the yield strength and E Young’s modulus.
Inputs
sigma_y := 400 MPa=400 MPa
E := 200 GPa=200000 MPa
Apply the modulus-of-resilience formula.
U_r := sigma_y^2/(2·E)=400000 Pa
Results
A high yield strength and low modulus store more elastic energy — why spring steels are strong but not especially stiff. The result is an energy density.
Assumptions & limitations
- Linear-elastic up to yield.
- Uniaxial loading.
- Energy per unit volume.