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The material and content of Engineering Archives is designed to be subject to change and alteration at all times. Therefore, it may not be assumed that any presented material herein is static. The material is constantly subject to change for the purpose of maximizing the ability of the learner to comprehend and absorb the material. The changing and alteration is conducted based on user feedback. Therefore, effective changes cannot take place without the user feedback. Please go to the forum for questions and feedback. See more…

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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.

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The material and content of Engineering Archives is designed to be subject to change and alteration at all times. Therefore, it may not be assumed that any presented material herein is static. The material is constantly subject to change for the purpose of maximizing the ability of the learner to comprehend and absorb the material. The changing and alteration is conducted based on user feedback. Therefore, effective changes cannot take place without the user feedback. Please go to the forum for questions and feedback. See more…
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