Timeline for Strain-Displacement relationship symmetrization
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 5, 2015 at 19:42 | answer | added | rdt2 | timeline score: 3 | |
| Oct 22, 2014 at 13:15 | comment | added | Jon Custer | Oh, absolutely, for any non-trivial strain field (i.e. not uniaxial strain, modes of plates, etc.) you need to consider it if looking at strain maps. In the sense of finite element calculations, the element can rotate but there is not stress/strain as a result, which is different from the shear deformations. | |
| Oct 22, 2014 at 4:20 | comment | added | diffeomorphism | but it is a quantity that in principle can be different at different points of the solid | |
| Oct 21, 2014 at 22:01 | comment | added | Jon Custer | I'd say rather that they are rotation without strain... | |
| Oct 21, 2014 at 21:38 | comment | added | diffeomorphism | so they can be interpreted as a rigid rotation strain? | |
| Oct 21, 2014 at 21:12 | comment | added | Jon Custer | Indeed, I spaced. The $\omega_{ij}$ are called the 'components of rotation'. For the displacement vector $u$ = (u,v,w), and $\omega$ the vector of ($\omega_{x},\omega_{y},\omega_{z}$), than $2\omega = curl u$. If $\omega_{x} = \omega_{y} = \omega_{z} = 0$, than the strain is irrotational. But the rotations don't affect the strains, it just can drive you nuts trying to see what is going on. | |
| Oct 21, 2014 at 19:12 | comment | added | diffeomorphism | but in this case the anti-symmetric components of displacements are in principle invariant under such relabeling or axis reorientation. The anti-symmetric component of a 3x3 matrix transforms as an axial vector | |
| Oct 21, 2014 at 19:10 | comment | added | diffeomorphism | you are referring to the Voigt notation: en.wikipedia.org/wiki/Voigt_notation | |
| Oct 21, 2014 at 18:53 | comment | added | Jon Custer | Most engineering elasticity texts end up with $\sigma_{i} = c_{i,j}\epsilon_{j}$, using $i$ and $j$ = $x,y,z,xy,xz,yz$ (only 6 elements) and throwing in the appropriate factors of 2 or 1/2 on the off-diagonal terms to make it work out right. That is, they assume that $xy = yx$ and shove it into one index. Physics folk would recognize this better as $\sigma_{ij} = c_{ij,kl}\epsilon_{kl}$. This eliminates the need for the seemingly random factors of 2 or 1/2 on the off-diagonal elements, and makes it straightforward to use Euler formalism to rotate the axes to what you'd like them to be. | |
| Oct 21, 2014 at 17:59 | comment | added | diffeomorphism | can you point a reference for this and elaborate a bit? | |
| Oct 21, 2014 at 17:36 | comment | added | Jon Custer | If you wish to rotate your principal axis around, you will find it much easier to do with the real, physically meaningful tensor formalism. I've never liked the reduced engineering format - I think it is a relic from the dinosaur ages (much like secant and cosecant for that matter). | |
| Oct 21, 2014 at 16:36 | history | asked | diffeomorphism | CC BY-SA 3.0 |