# yade-users team mailing list archive

## Re: Strain compution in Triaxialstresscontroller

```张林 a écrit :
> Hi everyone
> These days I'm a little puzzled with the strain compution in
> TriaxialstressController.cpp ,just as follows:
> strain[0] = Mathr::Log(width0/width);//Eq(1)
> strain[1] = Mathr::Log(height0/height);//Eq(2)
> strain[2] = Mathr::Log(depth0/depth);//Eq(3)
> volumetricStrain=strain[0]+strain[1]+strain[2];//Eq(4)
> IIRC,Log means not log10 but ln as usual .Is it right?

Yes.
The reason is very simple : d(espilon) = d(L)/L, so the total strain on
the loading is the integral of d(L)/L between L0 and L1, which is ln(L1)
- ln(L0).

> Eq(1 to 3) is different from the common compution of strain like:
> epsilon=(length-length0)/length0
This equation is usual yes, but it is wrong. It is a linear
approximation of Log(width0/width) around 1.

> and, in PFC3D manuals(V3.0)->users' guide->problem solving with pfc3d
> Page 47, I found another Eq for strain compution:
> epsilon=(L-L0)/((L0+L)/2)
I never saw this one before...
Thinking in terms of linear approximation, I have the impression this
third expression is a 2nd order approximation while the second one is
1st order.
We don't need any approximation in Yade, and given the large deformation
of the triaxial cell, approximations would be bad.

Example when height is divided by 2 :

1st expression (exact) : eps = 0.69
2nd : eps = 0.5
3rd : eps = 0.66

Bruno

> Are the 3 methods all right? They're designed for different fields?
> Thanks for any suggestion.
> Regards.
> Zhang Lin
> 　　　　　　　　xtss_0002@xxxxxxxxxxxx
> 　　　　　　　　　　2008-11-25
> ------------------------------------------------------------------------
>
> _______________________________________________
>

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