Recent content by FQVBSina_Jesse

The Hencky strain, AKA true strain, logarithmic strain, can be related to displacement tensor as follows: $$ E = ln(U) $$ However, Hencky strain is typically done only for principal strains. This can be easily shown by actually trying to calculate the full displacement tensor using the above...

That makes sense. Thanks!

Sorry, let me be clearer with my question: You said above "I find it better not to talk about “curl” at all in this case but instead specify what you actually mean." So if I don't mean to calculate a curl with these expressions, then what does it mean? I guess it is a spatial derivative, but...

Could you please elaborate a bit more on "avoid calling this curl"?

Firstly, thank you for sticking with me and helping me with these concepts. We are not super well trained in these mathematic topics in the mechanical engineering field so we have to try to learn it on our own and there are so many different notations especially when used in a different...

The differences between your equation and the one in Wikipedia are: - You added the arrows on the LHS, is it to indicate rank? - Using the left expression as an example, the free index, ##i##, is the first index in the ##\epsilon## symbol, while the Wikipedia expression's free index, ##k##, is...

Ok, please allow me to try asking this: could you give me a correct example of a curl of a second-rank tensor in indicial notation? So far your replies have not given me an example of a correct equation, only asking me for clarifications and corrections which have been made clear to me that I...

Ok so from what you and @Orodruin have said so far, it seems that I have dropped an index, and need to clarify which part of R that I am taking the curl of. If we go by what I wrote above, it seems the curl is applied on the second index of R, since I wrote: $$ \nabla \times R_{ij} =...

Can we look at them one at a time so I can understand why? For the gradient, I write the nabla symbol as: $$ \nabla = \frac{\partial}{\partial x_k} $$ As it is the spatial derivative. That makes the right side as I wrote them, no?

I am sorry but I don't follow what is the problem. The Levi-Cavita symbol gives a +1 if ijk indices follow forward ordering such as 123, 231, 312, gives -1 if ijk indices are reverse such as 321, 213, 132, and zero otherwise. So it does not contract the RHS. Therefore my second equation's RHS is...

Are the following two equations expressing the gradient and curl of a second-rank tensor correct? $$ \nabla R_{ij} = \frac{\partial R_{ij}}{\partial x_k} $$ $$ \nabla \times R_{ij} = \epsilon_{ijk} \frac{\partial R_{ij}}{\partial x_k} $$ If so, then the two expressions only differ by the...

Thanks a lot! That makes sense. Just to circle this back to the task at hand that sparked my question, if I apply trilinear interpolation for each component of the quaternion or rotation matrix, and the resulting matrix of functions gives a quaternion or rotation matrix given any arbitrary...

The difficulty for me is that I am not as familiar with forms of rotation. What's the rationale that each component can be treated as an independent scalar field? From here, if I express the quaternions as rotation matrices, can each component of the 3x3 rotation matrix also be interpolated...

Thanks for sharing! However, as I read it, I feel like it is more about expressing normal function values in terms of quaternions, which was a thing when quaternions were introduced. It was why we still sometimes see i j k for x y z in vectors.

I have a 5x5x5 set of grid points in space. I can describe each point with p(x,y,z), and I can convert them to spherical or other coordinates. At each point, I have a quaternion assigned to it. So, numerically, I can describe a q(x,y,z) quaternion field. The goal is to obtain a functional form...