Why true strain is always smaller than nominal strain in tensile test?

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In tensile testing, true strain is always smaller than nominal strain due to the actual length increase being less than the theoretical increase. This discrepancy arises because, as a material is stretched, its cross-sectional area decreases, affecting the calculations of strain. The relationship ε = δ/L indicates that true strain accounts for the changing dimensions of the specimen during deformation. The discussion also highlights a common misunderstanding of the definitions of nominal and true strain. Overall, the conversation emphasizes the importance of grasping these concepts in the study of Mechanics of Materials.
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Why true strain is always smaller than nominal strain in tensile test?

Is that mean that actual length increase is smaller than theoretical length increase?

Is it related to atomic forces?
Hi everyone.

I'm studying Mechanics of Materials and I got some question about 'nominal/true strain'.

First of all, I agree that in tensile test, nominal stress is always smaller than true stress

σt > σn

cause when the material specimen is being stretched, then the actual area of the specimen at the cross section would be decreased.

However, I wonder why nominal strain is always larger than true strain in tensile test. εt < εn

If I'm right, I guess that statement implies that actual length increase would be smaller than theoretical length increase.

cause ε=δ/L, am I right?

If I'm right, what factor is the main reason for that truth? Is it related to the atomic forces?

p.s. I just started to use this PhysicsForums, so I wonder if it is okay to upload questions here.

If I did wrong, I would appreciate if you tell me where should I upload questions. I'm not very good at english TT.

Anyway, thanks for reading my question.
 
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Ah, I think I misunderstood the definition of each of them. It was a simple thing haha;
 
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