sykledust's blog

Anisotropic stiffness of isotropic material

Dear colleagues,

Consider a simple non-linear elastic material with stress given as

σ = D(εdev) εdev + B εiso

where εdev is the norm of εdev, D is a function of εdev and B is constant. The material is isotropic since the principal directions of  σ and ε will coincide.

If we differentiate σ wrt ε to obtain the material stiffness the form of the stiffness tensor will be

Change of basis for deviatoric second order tensors

Dear mechanicians

I remember reading somewhere that someone had a proof of the following:
Given a deviatoric/traceless second order tensor it is possible to find a basis for which all the normal/direct components equal zero.
For 2d this is easy: a basis rotated 45deg wrt. the eigenbasis.
The proof concerned 3d and it may have been Gurtin that had it in one of his books (sometihng tells me "The Linear Theory of Elasticity" (1972) as I don't have access to this one), but I'm not certain.

Can anyone help me in this matter?