Displacement gradient componenets and macroscopic strain
Displacement gradient componenets and macroscopic strain
(OP)
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 ??
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 ??






RE: Displacement gradient componenets and macroscopic strain
RE: Displacement gradient componenets and macroscopic strain
RE: Displacement gradient componenets and macroscopic strain
RE: Displacement gradient componenets and macroscopic strain
The greatest trick that bond stress ever pulled was convincing the world it didn't exist.
RE: Displacement gradient componenets and macroscopic strain
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 ?
RE: Displacement gradient componenets and macroscopic strain
RE: Displacement gradient componenets and macroscopic strain
BA
RE: Displacement gradient componenets and macroscopic strain
The greatest trick that bond stress ever pulled was convincing the world it didn't exist.
RE: Displacement gradient componenets and 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?
RE: Displacement gradient componenets and macroscopic strain
The greatest trick that bond stress ever pulled was convincing the world it didn't exist.
RE: Displacement gradient componenets and macroscopic strain
RE: Displacement gradient componenets and macroscopic strain