# tensor

## 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

## Questions about tensors and matrices

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Hello,

I am having questions with tensors. I know that not all matrices are tensor. Tensor is a homogeneous, linear and vector valued function. So my questions are:

1. Are all 3*3 matrices tensors?
2. Are all anisymmetric second order tensors orthogonal?

Thanks.

## principal directions for 4th order tensor

Is it possible to find eigenvalues and principal directions for a 4th order tensor? How?

For a zero order tensor? for a first order tensor? for a third order tensor.........

many thanks