Talk:Finite deformation tensors

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Help with this template Comments: edit – history – watch – refresh The notation and terminology used here was introduced in the "Non-Linear Field Theories of Mechanics” by C.Truesdell and myself, published in 1965. I invented much of the notation and terminology, but I now realize that some of it is misleading and should be changed. For example “Deformation Gradient” should be replaced by “Transplacement Gradient”. A modern, frame-free analysis of the mathematical concept of deformation can be found in the first four parts of my "Five Contributions to Natural Philosophy", available on my website www.math.cmu.edu/~wn0g/noll .

In the process of formulating the Finger tensor, in the equation - F= V R

i believe R is a ROTATION tensor, (as implied by R R^T =I), and NOT an antisymmetric one.

BTW, it's worth mentioning that such a decomposition isn't unique: for F= (-1)I, e.g., the rotation factor R can be extracted at least in 3 different ways. this, of course, does not affect the uniqueness of the Finger tensor, as seen from the definition B = F F^T.

(Ofek Shilon, 7.8.05)

[edit] Cleanup

To mention just one issue: the matrix exponential and logarithmic derivative provide the passage between finite and infinitesimal deformations. The discussion of "uni-axial extension" of an "incompressible material" should be clarified: this just means pulling the body from either end along one axis, with the material responding by extending along that axis, while keeping volume constant, so that its cross section shrinks. Then the Finger tensor can be related via logarithmic derivative to the "Cauchy form" of the tidal tensor near a typical compact massive body in Newtonian gravitation (infinitesimal deformation). This will help both physics and engineering students see how two subjects relate to one another, by removing artificial barriers of notation and terminology.

• This is very nice, but I am affraid it is above my command in the clestial mechanics. Can you be bold and made the neccessary changes youself? abakharev 07:22, 13 November 2005 (UTC)

It should also be helpful to write out how the strain deformation tensor defines the linear transformation relating the rest shape to the deformed shape of the body. In one of these articles, the author mentions (but does not explain) that we can regard this as the first term in a Taylor series for a more general transformation. This also should be clarified.

In addition to these, individual articles often use terms without defining them, which makes them much less useful for students, and generally speaking are insufficiently linked to each other and to relevant articles over in the applied math categories.---CH (talk) 00:47, 13 November 2005 (UTC)

[edit] Notation

I don't use it myself, but a common and cleaner notation is to use upper-case letters for initial configuration quantities. Primes seem to be more commonly used for a transformation to a new coordinate basis.RDT2 20:21, 19 August 2006 (UTC)