Displacement gradient componenets and macroscopic strain 1

[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 ??

 

[Andries]

frtztrb,

You should consult a good text on continuum mechanics. Google Amazon; the books have customer reviews.

Andries

 

[frztrb]

thank you very much

 

[Andries]

Hi frztrb,

Expanding on my previous post. If you need the continuum mechanics as background for finite element analysis a very good introduction to continuum mechanics is in the book "Non-Linear Continuum Mechanics for Finite Element Analysis", by Javier Bonet and Richard D. Wood, published by Cambridge University Press.

Andries