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Stress invariants for anisotropic materials
Tue, 2010-08-03 07:21 - Khong Wui Gan
Hello everyone,
Does anyone know how to obtain stress invariants for an anisotropic materials, for example a composite material and there are how many of them? Could you pinpoint me to the correct reference?
Thanks a lot.
Khong
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I think invariants (which
I think invariants (which mean quantities which are directionally independent) are valid only for isotropic materials.
Re: Do invariants exist only for isotropic materials?
1) Stress invariants are relations for a stress tensor and therefore independent of whether a material is anisotropic or not.
2) Invariants of the stiffness tensor also exist irrespective of whether the stiffness is isotropic or aniostropic.
The following papaer may help clarify why.
http://www.emis.ams.org/journals/HOA/IJMMS/Volume5_1/96.pdf
Integrity basis for a second-order and a
fourth-order tensor
J Betten - International Journal of Mathematics and
Mathematical
Sciences, 1982, 5(1), pp. 87-96.
-- Biswajit
Thanks
Thanks Biwajit for your reply.
So you are saying that the concept of stress invariants are the same for both isotropic and anisotropic materials?
I raise this question up because I came across this paper of Christensen RM
Stress based yield/failure criteria for fiber composites
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Volume: 34 Issue: 5 Pages: 529-543 Published: FEB 1997
in which he separated the fiber dominated stress σ11 from the other stress invariants (matrix dominated) and ended up with 7 stress invariants up to the second order. I wonder if anyone could elaborate on this.
Regards,
Khong
I misunderstood the
I misunderstood the question, so the previous reply was deleted. Sorry about the confusion.