# Calculating Modulus of Resilience: Yield Stress, Yield Strain, E

• Nick Goodson
In summary, The person is having trouble with getting different answers when using two different equations for calculating the Modulus of Resilience. The values used are Yield Stress = 1880 MPa, Yield Strain = 0.0068, and E = 401 GPa. The first equation, [U(r) = (Yield Stress x Yield Strain) / 2], gives an answer of 6.39 MJ/m^3 while the second equation, [U(r) = Yield Stress^2 / (2 x E)], gives an answer of 4.4 MJ/m^3. The person is wondering if there is additional information needed to resolve the discrepancy and suggests that the linear relationship between E, yield stress
Nick Goodson
TL;DR Summary
Differing answers for modulus of resilience
Hi,
I have a problem, using the 2 different equations for calculating the Modulus of Resilience, I get 2 different answers. It seems simple, but I’m a little perplexed.
For the following values:

• Yield Stress = 1880 MPa
• Yield Strain = 0.0068
• E = 401 GPa
[U(r) = (Yield Stress x Yield Strain) / 2] - answer = 6.39 MJ/m^3
[U(r) = Yield Stress^2 / (2 x E)] - answer = 4.4 MJ/m^3
Many thanks

Both of those formulas assume linear elastic behavior up to yield. Is there additional information for the problem?

Frabjous said:
Both of those formulas assume linear elastic behavior up to yield. Is there additional information for the problem?
That's all the info I have.
I guess the assumption is that the value for E would need to be defined using yield stress and yield strain to resolve, but is defined by a linear relationship.

For linear elastic 1D stress, E=σ/e=276GPa so there is a discrepancy.

Frabjous said:
For linear elastic 1D stress, E=σ/e=276GPa so there is a discrepancy.
Yes, that's why I was a bit perplexed

## 1. What is the modulus of resilience?

The modulus of resilience is a measure of a material's ability to absorb and store energy when it is deformed elastically. It represents the maximum amount of energy that a material can absorb without undergoing permanent deformation.

## 2. How is yield stress related to modulus of resilience?

Yield stress is the amount of stress required to cause a material to start deforming plastically. The higher the yield stress, the more energy a material can absorb before reaching its yield point, and therefore the higher its modulus of resilience.

## 3. What is the significance of yield strain in calculating modulus of resilience?

Yield strain is the amount of strain a material experiences at its yield point. It is an important factor in calculating modulus of resilience because it indicates how much a material can deform before reaching its yield point and undergoing permanent deformation.

## 4. How is the modulus of resilience calculated?

The modulus of resilience is calculated by taking the area under the stress-strain curve up to the yield point. This can be done by using the formula E = σ^2/2ε, where E is the modulus of resilience, σ is the yield stress, and ε is the yield strain.

## 5. What is the unit of measurement for modulus of resilience?

The unit of measurement for modulus of resilience is joules per cubic meter (J/m^3). This unit represents the amount of energy that can be absorbed per unit volume of material before reaching its yield point.

• Materials and Chemical Engineering
Replies
4
Views
1K
• Engineering and Comp Sci Homework Help
Replies
3
Views
956
• Introductory Physics Homework Help
Replies
4
Views
295
• Materials and Chemical Engineering
Replies
1
Views
1K
• Mechanical Engineering
Replies
5
Views
819
• Introductory Physics Homework Help
Replies
19
Views
1K
• Mechanical Engineering
Replies
2
Views
4K
• Materials and Chemical Engineering
Replies
1
Views
1K
• Mechanical Engineering
Replies
16
Views
1K
• Mechanical Engineering
Replies
3
Views
1K