constitutive relations (stress-strain) for non-homogeneous materials?

Dear All,

I am student new to this field and I recently found this amazing forum. I have a question that relates to the basic understanding of deformable materials.

I would like to understand better or find references that talk about the constitutive relations (stress-strain) for materials with non homogenous material properties, for

example materials that might have modulus of elasticity of the form E(x), E(x,y), or even E(x,y,z).

First, is a material having E(x,y,z) an anisotropic material?

The books on elasticity or viscoelasticiy  I have read so far talk about elasticity "constants" [C] such that Stress=[C] strain, even for anisotropic materials.

Is it infered that for anisotropic materials these "constants" can change in space (x,y,z) and that they are only constants with respect to time?

If not, how does one model the stress-strain relation for materials with spatially varying material properties (E(x), E(x,y), etc..)?

I would really appreciate being pointed to good references, papers or books that cover this question.

Thanks in advance for you help!

Best regards,