Finding Energy Density from Stress-Strain graph

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Aleksander Krol
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#1
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#1
Stress x Strain gives us Energy density (Jm-3).

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In this case, should I use 0.5 x Stress(y) x Strain(x) to find Energy Density?
Because area under stress-strain graph gives energy density.

Case 2:
If the graph was curved, I will have to count the no. of boxes under the graph. And then look for stress and strain for 1 box. Multiply Stress with Strain, which will give me the energy density for 1 box.
Then multiply this value with the total no. of boxes under the graph to find the total energy demsity for the whole graph, right?
Just want to clear my understanding.
Last edited by Aleksander Krol; 3 months ago
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Stonebridge
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#2
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(Original post by Aleksander Krol)
Stress x Strain gives us Energy density (Jm-3).

Name:  Screenshot_20220117_162801.jpg
Views: 21
Size:  71.6 KB
In this case, should I use 0.5 x Stress(y) x Strain(x) to find Energy Density?
Because area under stress-strain graph gives energy density.

Case 2:
If the graph was curved, I will have to count the no. of boxes under the graph. And then look for stress and strain for 1 box. Multiply Stress with Strain, which will give me the energy density for 1 box.
Then multiply this value with the total no. of boxes under the graph to find the total energy demsity for the whole graph, right?
Just want to clear my understanding.
Yes. It's the area under the graph and so in this case is the area of a triangle.
That is 0.5 x stress x strain for a triangle. That gives the strain energy density for that particular value of stress or strain.
If the graph is not a straight line you have to find the area by other means. (Counting the boxes is one way.)
The energy density is still the total area under the graph. Not half the area.
Last edited by Stonebridge; 3 months ago
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lordaxil
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Yes, that's essentially right, although only strictly true as the size of boxes tend to zero. If you are familiar with integral calculus then what you want to say can be expressed more precisely as E = \int \sigma \,d\epsilon

[referring to OP]
Last edited by lordaxil; 3 months ago
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