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Stress invariants for anisotropic materials

Submitted by Khong Wui Gan on

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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Stress Tensor
Biswajit Banerjee

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

Tue, 08/03/2010 - 22:05 Permalink
Khong Wui Gan

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

Mon, 08/09/2010 - 21:37 Permalink