# Ph or ? for anisotropic property by region

**URL:** <https://community.freefem.org/t/ph-or-for-anisotropic-property-by-region/3227>\
**Category:** General Discussion\
**Created:** [May 7, 2024, 9:58am UTC](https://community.freefem.org/t/ph-or-for-anisotropic-property-by-region/3227 "2024-05-07T09:58:01Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![bcaval](https://avatars.discourse-cdn.com/v4/letter/b/d26b3c/32.png) [@bcaval](https://community.freefem.org/u/bcaval)\
**Post date:** [May 7, 2024, 9:58am UTC](https://community.freefem.org/t/ph-or-for-anisotropic-property-by-region/3227/1 "2024-05-07T09:58:01Z")

</div>

Dear freefem community,

I would like to have your advices for the best implementation of anisotropic physical property for each material.

In fact I imagine this for attributing physical property to each material, see below, is it correct ?

real [int, int][int] z(4)  
for (i=1;i\<=3;i++) {  
z[i].resize(4,4); z[i] = 0.; // for instance 3 materials (I don’t use 0 index)  
}

// Def for a physical property to whatever i material  
macro Z(i) [[z[i] (1,1), z[i] (1,2), z[i] (1,3) ],  
[z[i] (2,1), z[i] (2,2), z[i] (2,3) ],  
[z[i] (3,1), z[i] (3,2), z[i] (3,3) ]] // EOM

// and the varf for each material…1,2,3  
varf VZ(u,v) = int3d(Th,1)( grad(v)’ \*(Z(1)\*grad(u)) )  
+ int3d(Th,2)( grad(v)’ \*(Z(2)\*grad(u)) )  
+ int3d(Th,3)( grad(v)’ \*(Z(3)\*grad(u)) );  
Is the proposal of my previous post correct ?

Or should I use definition with

Ph Phy = Phy1\*(region==1)+Phy2\*(region==2) + etc. But the latter definition is well documented only for scalar values even for elasticity in isotropic conditions with E, nu or lambda, mu.

In fact, I am searching for the best way to properly model these anisotropic properties, especially when some solution fields are dependent of such region property (for instance stress field).

Best regards.