# Assign different materials (composites)
**URL:** https://community.freefem.org/t/assign-different-materials-composites/2002
**Category:** General Discussion
**Created:** [September 12, 2022, 4:05pm UTC](https://community.freefem.org/t/assign-different-materials-composites/2002 "2022-09-12T16:05:54Z")
**Posts on this page:** 8
**Page:** 1
### Author:  [@danmo](https://community.freefem.org/u/danmo)
#### Post date: [September 12, 2022, 4:05pm UTC](https://community.freefem.org/t/assign-different-materials-composites/2002/1 "2022-09-12T16:05:54Z")
Hi,
I want to simulate a composite material made of matrix (E1) and inclusion (E2). I am not sure how to assign two different material properties and integrate over the domain.
Assume a classic elasticity problem…how can I modify the following code to separately define C1 and C2 matrices and integrate them in the “solve” command?
// Material Parameters
real E1 = 100.; // Elastic modulus of matrix
real nu1 = 0.3; // Poisson’s ratio
real mu1 = E1/(2\*(1+nu1)); // Lame’s constants
real lambda1 = E1_nu1/((1+nu1)_(1-2\*nu1)); // Lame’s constants
real E2 = 1; // Elastic modulus of matrix
real nu2 = 0.01; // Poisson’s ratio
real mu2 = E2/(2\*(1+nu2)); // Lame’s constants
real lambda2 = E2_nu2/((1+nu2)_(1-2\*nu2)); // Lame’s constants
func C1 = [[lambda1+2_mu1, lambda1, 0], [lambda1, lambda1+2_mu1, 0], [0, 0, 2_mu1]]; // matrix
func C2 = [[lambda2+2_mu2, lambda2, 0], [lambda2, lambda2+2_mu2, 0], [0, 0, 2_mu2]]; // inclusion
// Geometric Parameters
real L = 1;
real t = 0.1;
// Geometry
border botout(a=-L/2., L/2){x=a; y=-L/2;}
border rightout(a=-L/2, L/2){x=L/2; y=a;}
border topout(a=L/2, -L/2){x=a; y=L/2;}
border leftout(a=L/2, -L/2){x=-L/2; y=a;}
border botin(a=-L/2+t/2., L/2-t/2.){x=a; y=-L/2+t/2.;}
border rightin(a=-L/2+t/2., L/2-t/2.){x=L/2-t/2.; y=a;}
border topin(a=L/2-t/2., -L/2+t/2.){x=a; y=L/2-t/2.;}
border leftin(a=L/2-t/2., -L/2+t/2.){x=-L/2+t/2.; y=a;}
// Meshing
mesh Th = buildmesh(botout(45) + rightout(45) + topout(45) + leftout(45) + botin(25) + rightin(25) + topin(25) + leftin(25));
plot(Th, wait=true);
// FE space
fespace Vh(Th, [P1, P1], periodic=[[rightout,y], [leftout,y], [botout,x], [topout,x]]);
Vh [u1, u2]; //unknowns
Vh [v1, v2]; //test functions
// Definitions
macro epsilon(u1,u2) [dx(u1), dy(u2), dx(u2)+dy(u1)] //EOM
func Ebar = [1., 0., 0.]; // Applied load
solve Elastic([u1, u2], [v1, v2]) = int2d(Th)(epsilon(v1,v2)'_C_epsilon(u1,u2)) + int2d(Th)(epsilon(v1,v2)'_C_Ebar) ;
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [September 12, 2022, 4:19pm UTC](https://community.freefem.org/t/assign-different-materials-composites/2002/2 "2022-09-12T16:19:06Z")
Use a P0 function instead of constant scalars. See, e.g., [aldaas2019multi/elasticity-2d.edp at main · prj-/aldaas2019multi · GitHub](https://github.com/prj-/aldaas2019multi/blob/main/elasticity-2d.edp#L49).
---
### Author:  [@JuillenL](https://community.freefem.org/u/JuillenL)
#### Post date: [September 14, 2022, 11:45am UTC](https://community.freefem.org/t/assign-different-materials-composites/2002/3 "2022-09-14T11:45:10Z")
hello
where C1 and C2 are used in your code ? in “solve Elastic(…” ??
---
### Author:  [@Yangshen](https://community.freefem.org/u/Yangshen)
#### Post date: [September 25, 2022, 6:05am UTC](https://community.freefem.org/t/assign-different-materials-composites/2002/4 "2022-09-25T06:05:08Z")
Have you solved this problem？
I have the same problem as you.
---
### Author:  [@danmo](https://community.freefem.org/u/danmo)
#### Post date: [September 30, 2022, 8:03am UTC](https://community.freefem.org/t/assign-different-materials-composites/2002/5 "2022-09-30T08:03:21Z")
I think @prj has pointed out how this can be done. Yet, the slicing of the domain was not really straightforward to me so I still could not put it into a code for my case.
---
### Author:  [@danmo](https://community.freefem.org/u/danmo)
#### Post date: [September 30, 2022, 8:04am UTC](https://community.freefem.org/t/assign-different-materials-composites/2002/6 "2022-09-30T08:04:36Z")
Yes, they are supposed to appear in my “solve” equation. But I still could not figure out how to divide my domain and assign different materials.
---
### Author:  [@Yangshen](https://community.freefem.org/u/Yangshen)
#### Post date: [September 30, 2022, 9:36am UTC](https://community.freefem.org/t/assign-different-materials-composites/2002/7 "2022-09-30T09:36:09Z")
Thank you very much.
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [October 2, 2022, 5:46am UTC](https://community.freefem.org/t/assign-different-materials-composites/2002/8 "2022-10-02T05:46:03Z")
Something along the following lines.
```auto
fespace Ph(Vh, P0);
Ph lambda = (x < L/4.0 && x > -L/4.0 && y < L/4.0 && y > -L/4.0) ? lambda2 : lambda1;
```