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Modulus of Resilience

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Quick
The modulus of resilience is the maximum elastic energy absorbed by a material when a load is applied.


Details

The modulus of resilience E_r is the area contained under the elastic portion of the stress-strain curve. It is the elastic energy that a material absorbs during loading and subsequently releases when the load is removed. For linear elastic behavior:

Er =

1 2

(yield strength)(strain at yielding)

The ability of a spring or a golf ball to perform satisfactorily depends on a high modulus of resilience.

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If the stress σ_x from the lesson Strain-Energy Density remains within the proportional limit of the material, Hooke's law applies and:

σ_x = Eε_x

Substituting for σ_x from Eq1 into Eq1 of the lesson Strain-Energy Density, the following results:

u =

∫

ε1   0

Eεx dεx =

Eε12 2

or, using Eq1 to express ε₁ in terms of the corresponding stress σ₁:

u =

σ12 2E

The value of u_Y of the strain-energy density obtained by setting σ₁ = σ_Y in Eq2, where σ_Y is the yield strength, is called the modulus of resilience of the material. Then:

uY =

σY2 2E

The modulus of resilience is equal to the area under the portion of OY of the stress-strain diagram as shown:



and represents the energy per unit volume that a material can absorb without yielding. The capacity of a structure to withstand an impact load without being permanently deformed clearly depends upon the resilience of the material used.

The units of the modulus of resilience are in J/m³ (SI), or in*lb/in³ (US customary).

The modulus of resilience is related to strain-energy density.