Talk:Cauchy stress tensor
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|The content of Euler-Cauchy stress principle was merged into Cauchy stress tensor. For the contribution history and old versions of the redirected page, please see ; for the discussion at that location, see its talk page.|
Definition of couple stress
Article created from "stress" section
This article used to be a section of stress (mechanics); it has been split off because that article was way too long, difficult to read and edit. Another part of that article was split off as Euler-Cauchy stress principle. There are still many rough edges, especially on the partition between these two sister articles. Hopefully we can fix them soon. All the best, --Jorge Stolfi (talk) 22:23, 23 February 2013 (UTC)
- The Cauchy stress tensor and Euler-Caucy stress priciple articles are better placed together. The principle is needed to explain where the Cauchy tensor comes from. I merged both articles. sanpaz (talk) 19:34, 30 May 2013 (UTC)
Shouldn't "octahedral stress" have its own article? (Consider readers who find the term somewhere and want to know what it is. It does not seem useful to redirect them to this article, even if it is to a section.) --Jorge Stolfi (talk) 22:26, 23 February 2013 (UTC)
- You may be right. The octahedral stress section does not fit in the Cauchy stress tensor article. I do not have any suggestions on where to place it at the moment. I have to think about it. sanpaz (talk) 19:43, 30 May 2013 (UTC)
LaTeX vs HTML
I've changed the tensor type from (2,0) into (1,1) as it is a linear mapping and not a bilinear form!! Do you agree?
- No. The section Transformation rule of the stress tensor refers to the stress tensor as contravariant in both indices, so I'm reverting this change for consistency, although the phrasing could still be improved. Since the stress tensor is almost always discussed in the presence of a metric, one may refer to contravariant, covariant, or mixed forms, and this article specifically chose the contravariant form. 126.96.36.199 (talk) 08:14, 17 January 2014 (UTC)
- OK, I see the problem. The index placement on the stress tensor is a matter of convention. Indices of the stress tensor may be raised or lowered with abandon by balanced application of the metric tensor. There are 4 valid choices of index placement. The historical choice is to caste vectors as column vectors, which are implicitly contravariant vectors. If T and n are column vectors, the stress tensor must be type (1,1).
- What is lacking in this article is a declaration of the convention to be used, as well as the choice of dimensional assignments. This should be stated at the very beginning in a section of its own. The same applies to the mother article "Stress (mechanics)".
- The section Transformation rule of the stress tensor is peppered with notational errors but I haven't yet put in the hard work to fathom whether the transformation equations given are consistent with the transformation of a type(0,2) tensor. 2001:5B0:2BFF:3EF0:0:0:0:39 (talk) 09:29, 21 January 2015 (UTC)
- In your texts do tensor products use the Einstein summation convention, but where both indices are lower indices or both are upper indices?Craigde (talk)
- This is one reference Continuum mechanics by Spencer . Please see other references at the bottom of the article. I understand that proper tensor notation has upper and lower indices. But because of the nature of the stress tensor, authors usually only use lower indices. You are right in saying that it is necessary to explain why the convention in the article is the way it is presented.sanpaz (talk) 04:19, 22 January 2015 (UTC)
- Wow. That text is a Dover reprint of a 1929 publication. It's time to move into the 21 century.Craigde (talk)
Contrary to convention, throughout the entire article, lower indices are used exclusively in tensor equations. I attempt to mentally edit every tensor equation I see, yet there seems to be insufficient information to do so.
- The notation used in the article is standard in the continuum mechanics literature and has evolved into this form over the past 60 years to avoid unnecessary complication. The underlying assumption is that the components of the tensor are with respect to an orthonormal basis, i.e., the metric tensor is the rank-2 identity tensor. That means that raising or lowering the indices does not change the values of the components. The expressions get much more complicated in general curvilinear bases. In general, direct tensor notation is preferred so that coordinate systems can be avoided altogether. But that's not useful for understanding the concepts discussed in this article. Bbanerje (talk) 22:09, 14 April 2016 (UTC)