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[Jan Stránský <question670047@xxxxxxxxxxxxxxxxxxxxx>]

Question #670047 on Yade changed:
https://answers.launchpad.net/yade/+question/670047

    Status: Open => Answered

Jan Stránský proposed the following answer:
> From my point of view the linear regression is better

yes, see below

> but which are the "right points"

the right points should be that lying approximately on the elastic line.
In later stages of the simulation there are some non-linearities, which
should not be considered for elastic modulus. You can either set the
last elastic point "visually" or automate it by increasing the last
elastic point until the linear regression slope starts to be
systematically lower than the slopes for previous points. For given
material parameters, it should be a constant, e.g. strain -1e-3

> it makes some "jumps" in some points (I don't know why)

In the case of static simulation, the line would be really a line. In
terms of DEM, the simulation is dynamic and only quasi-static, i.e.
there are still some inertial effects and dynamic stress waves causing
these jumps

> so I took just the initial part where I see a pretty well defined
ascending slope and got the slope from the regression. Do you think that
would be right??

yes

> How would I determine "bulk modulus" and how would I "compute ratio
comparing it to the value of Young's modulus"?

Have a look at 3D Hooke's law [1]. For different stress-strain states the elements of stiffness matrix can be easily evaluated. Below s=stress, e=strain
E.g. for uniaxial stress (s11=something, s22=s33=s23=s31=s12=0) you directly get
e11=(1/E)*s11
and
e22=e33=-(nu/E)*s11

There is also a formula
stressTensor=3K*vol(strainTensor)+2G*dev(strainTensor)
For triaxial stress state dev(strainTensor)=0 and vol(strainTensor)=strainTensor, so stressTensor=3K*strainTensor.
For the case s11=s22=s33, you get s11=3K*e11 and K is easily evaluated.

At the bottom of the page there are conversions between E,K,nu. For
known E and K, nu can be evaluated.

If you have troubles with continuum mechanics, we can point you to some
literature.

cheers
Jan

[1] https://en.wikipedia.org/wiki/Hooke%27s_law , section "Linear
elasticity theory for continuous media"

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