User login


You are here

Stress invariants for anisotropic materials

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.


Free Tags: 
tuhinsinha.25's picture

I think invariants (which mean quantities which are directionally independent) are valid 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.


Integrity basis for a second-order and a
fourth-order tensor

J Betten - International Journal of Mathematics and

Sciences, 1982, 5(1), pp. 87-96.

-- Biswajit

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.



I misunderstood the question, so the previous reply was deleted. Sorry about the confusion.

Subscribe to Comments for "Stress invariants for anisotropic materials"

Recent comments

More comments


Subscribe to Syndicate