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Comparison of natural vs. engineering strain
1) Engineering stress is defined as:
σ F/
S
0
and engineering strain as:
ε
∫
L
L0
1 ∆L
L−
L L
dl
L L L L
0
= = = −
0 0 0 0
1
2) Natural (Cauchy) stress is defined as:
s F / S
and natural strain as:
e
∫
L
L0
1 L
dl = ln
L L
0
3) We have thus the relationships:
L +∆L
e= = + = −
L
0
ln ln (1 ε) and ε exp ( e) 1
0
These functions have the following shape:
L/
L
0
L/
L0
∆ ε e Graph
0.0 -1.0 -1.0 −∞
0.5 -0.5 -0.5 -0.693
1.0 0.0 0.0 0.000
1.5 0.5 0.5 0.405
2.0 1.0 1.0 0.693
8