工程应变和对数应变

Engineering Strain vs Logarithmic strain

1、Engineering strain:

We define “Engineering strain” as the change in length by original length- assuming a bar of initial length 100 cms which stretched by 1 cm and becomes 101 cms. Then, Engineering strain = (101-100)/ 101 = 0.01 

2、 logarithmic strain:

Logarithmic strain = ln (L/Lo) = ln (101/100) = 0.00995 IS my interpretation correct if I say: Logaritmic strain is more realistic than engineering strain because here we take the strain as the summation of numerous small differential segments and thus express the final strain whereas in Engineering strain it is just the strain over the whole length (just 1 segment) compared to numerous segments in Logarithmic strain. 

Eng. strain considers only the final state compared to the initial state although the log. strain takes into account the continuous

variation of length. 

 

In fact, the first one can be seen as a simplification of the second one (even if eng strain cannot be always used):

 

If you define the strain as the relative variation of length: dEps = dl / l, and you can integrate it from l0 to l0 + Δl. You get the logarithmic strain Eps = ln( (l0 + Δl)/l0 ) = ln(1 + Δl/l0).

 

Then, if you consider small deformations, this expression can be reduced to EpsEng =  Δl/l0 because the limit of ln(1+X) is X when X --> 0.

So eng. strain and log. strain give the same value for small deformations but they differ a lot if you consider large deformation. (工程应变和对数应变在小变形情况下结果是差不多的，但是在大变形时两者时不同的。)

 

When large deformation is encountered, the initial length can be no more taken as a reference to compute every strain increments (like in eng. strain), one has to take in account the value of length just before each strain increment (that is the idea of the log. strain).

 

参考：

【1】https://imechanica.org/node/6797

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