Displacement gradient componenets and macroscopic strain 6

[frztrb]

Hi All

I need some clarification of the terms : displacement gradient with components H_ij=du_i/dX_j , from which the Average strain ( is it macroscopic strain ??)

is achieved : E_ij = 0.5 *(du_i/dx_j + du_j/dx_i). that will always display symmetries since E_ij=E_ji.

I am searching to find the relationship of H and E , the proof how we get E from H .

I also would like to know , how the displacement gradient matrice change for different loading types for example when we say for a simple shear we have ( for deformation gradient) we have :

F11=F22=1, F21=0, F12=gamma(t)

and H11=H22=0 and H21=0, H12=gamma(t).

how can we reason this ??

 

[frztrb]

This question is very urgent for me , please be very kind to me and if you know a good reference , please refer me to that source , I will be very grateful

 

[ztengguy]

What function are you using this for structural engineering? What are you designing?

 

[jayrod12]

Perhaps it could be that you really don't outline the problem. You haven't began to describe the problem you are trying to solve, what material you are working with, or really anything that anyone could comment on. I for one have absolutely no idea what you are talking about except I recognize the words displacement, gradient, strain and shear. What are F11 and F22 and F21 etc.

 

[KootK]

It's got to be continuum mechanics or FEM right? Try this: Link. It sounds like we're talking about the fancy math version of why shear stresses are the same in both directions etc. If so, imagine the element as comprised of a bunch of stacked plates.



The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[frztrb]

thanks a lot , well I am talking about homogenization of periodic materials , there to relate the micro mechanics to Macro , we use the concept of displacemnet = macro displacement gradient * coordinat >>>>>

u = H * x , so here is my problem , in applying shear load case , I need to know how the matrices are built up exactly and how each load case is defined , and yes KootK , right , I also think it is related to continuum mechancis

thank you Ztengguy , is there more info needed I should give ?

 

[frztrb]

and Thanks a lot , that was a perfect and nice link !! thanks !!!!

 

[BAretired]

Does that mean your question is answered?

BA

 

[KootK]

I'd love to help with this frztrb but I'm afraid that I'm not knowledgeable enough in this area to do so. You'd be amazed at how little periodic material homogenization takes place in routine structural engineering these days.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[frztrb]

Baretired : thank you , but I think not exaxtly yet , due to some difference in expressing the displacement vectors , the one I have mentioned , in conventional periodic materials , is u = E * x , that E is actually the displacement gradient , as I knew later , not the macroscopic strain

so the thing is when you have a periodic material , you should state the condition of the displcement gradient , which is NOT symmetric . that can be done regarding to loading conditions , in the link Above , there was a bit of difference , since there is a y also added as displacement , as well as u (x,y) . and it doesn't look similar to what I mentioned in the first comment , maybe I need some unification of parameters here , if you could help me , could be great

KootK : well I did not know that and can you please tell me the reason ? due to the manufacturability ? you mean it's too early , or no appropriate useage?

 

[KootK]

Nothing like that OP. Your audience here is mostly building and bridge structural engineers. Our day to day work usually does not involve continuum mechanics at the detailed level that you are dealing with it. We mostly just use FEM software utilizing pretty straight forward beam/shell/membrane elements.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[Brad805]

Honestly, I think you have posted in the wrong section. There are engineers on this forum that have interest in this; however, most of them do not post here. As Koot suggests, the Structural Engineering group is comprised mostly of day to day practitioners. I suggest you post the question on the FEA forum or another section where most of the mechanical (aerospace/automotive...) engineers tend to go.

 

[frztrb]

Anyway thanks a lot for your help and kind attention , still you helped with with some good info , regards