This document describes advances made to a MATLAB code for calculating properties of composite materials. The original code (Advance 1) calculates properties like modulus of elasticity, thermal coefficients, and shear modulus based on input fiber and matrix properties. Advance 2 upgrades the code to also calculate strains and stresses in global and local coordinate systems, including the transformation matrices needed. The upgraded code is tested on sample problems from homework assignments.

1. Smart Materials 4th
year
Report: Project (1) Advance (2)
Report No: 2 Date: 18/4/2013
Submitted to: Dr. Mohammad Tawfik
Name
 Mohammad Tawfik Eraky
‫عراقي‬ ‫أحمد‬ ‫توفيق‬ ‫محمد‬
2013/2014

2. Advance 1
The project is MATLAB code that calculate all the properties of composite
materials so the input GF, , 𝑬 𝒎 , 𝑬 𝒇 ,𝝂 𝒎 ,𝝂 𝒇 , 𝜶 𝒇, 𝜶 𝒎
𝑬 𝟏, 𝑬 𝟐 , 𝑮 𝟏𝟐 , 𝝂 𝟏𝟐, G23, 𝜶 𝟏 , 𝜶 𝟐
MATLAB code
clc;clear all;close all;
%given the following properities
e_f=55; % modlus of elasticty of Fibers [input in GPa]
e_m= 3.4 ; % Modlus of elasticty of matrix [input in GPa]
v_m= 0.22; % Representative volume of the matrix [input]
v_f=0.78; % Reprenstative volume of the fibers [input]
alpha_m= 60/1000000; % Thermal coefficient of the matrix [input/c]
alpha_f=5.4/1000000 ; % Thermal coeffient of the fibers [input/c]
new_m=0.38;
new_f=0.22;
g_m=e_m/(2*(1+new_m)); % modlus of regidity of the matrix
[input in Gpa]
g_f= e_f/(2*(1+new_f)); % modlus of regidity of the
fibers[input in Gpa]
%outputs
e_1=v_m*e_m+v_f*e_f; %
Modlus of elastisity in fiber direction
e_2=(e_m*e_f)/(v_f*e_m+v_m*e_f); %
modlus of elasticty in direction transverse to the fibers
alpha_1=(v_f*e_f*alpha_f+v_m*e_m*alpha_m)/(v_f*e_f+v_m*e_m); %
thermal coeffiecient in direction 1
alpha_2=alpha_f*v_f+alpha_m*v_m ; %
thermal coeffient in direction 2
new_12=new_f*v_f+new_m*v_m ;
new_21=(e_2*new_12)/e_1; %
inplane shear modlus
g12=(g_m*g_f)/(v_m*g_f+v_f*g_m);
eta_23=(3-4*v_m+(g_m/g_f))/(4*(1-v_m));
g_23=g_m*((v_f+eta_23*(1-v_f))/(eta_23*(1-v_f)+(v_f*g_m/g_f)));
%display outputs
display(e_1);
display(e_2);
display(alpha_1);
display(alpha_2);
display(g12);

3. display(new_12);
display(new_21);
display(g_23);
The code is tested on many problems in homework 4
Pb 4.5
Compute, 𝑬 𝟏, 𝑬 𝟐 , 𝑮 𝟏𝟐 and , 𝝂 𝟏𝟐 given that EF=230Gpa, Em =EF/50,
GF=EF/2.5, GM=EM/2.6, 𝝂 𝒇 = 𝟎. 𝟐𝟓 , 𝝂 𝒎 = 𝟎. 𝟑, and Vf = 40%.the fibers
have circular cross section .Assume there is no voids
Solution
Using MATLAB code project (1)
We get the following results
𝑬 𝟏 = 𝟗𝟒. 𝟕𝟔 𝐆𝐩𝐚
𝑬 𝟐 = 𝟕. 𝟓𝟔𝟓𝟖 𝐆𝐩𝐚
𝑮 𝟏𝟐 = 𝟐. 𝟗𝟏𝟏𝟒 𝑮𝒑𝒂
𝝂 𝟏𝟐 = 𝟎. 𝟐𝟖

4. Advance 2
Now the code is upgraded to calculate the strain and stresses in global and
local axes and transformation matrixes needed
It has been tested on homework many problems
Upgrade 2
clc;clear all;close all;
%calculating(local)stresses
ceta=10*pi/180;
c=ceta;
e_1=35;
e_2=3.5;
new_12=0.3;
g_12=1.75;
g_23=0.35;
%Transformations Matrixes
t=[cos(c)^2 sin(c)^2 2*sin(c)*cos(c);
sin(c)^2 cos(c)^2 -2*sin(c)*cos(c);
-sin(c)*cos(c) sin(c)*cos(c) cos(c)^2-sin(c)^2];
new_21=new_12*e_2/e_1;
delta=1-new_12*new_21;
q=[e_1/delta new_12*e_2/delta 0;
new_12*e_2/delta e_2/delta 0;
0 0 2*g_12];
t_inv=inv(t);
q_bar=(t_inv)*q*t;
% stresses in global axes
sigma_global=[200/20 ; 0 ; 0];
%stresses in local axes
sigma_local=t*sigma_global;
%strains in local axes
strain_local=10^-3*(inv(q))*sigma_local;
%strains in Global Axes
strain_global=(t_inv)*strain_local;

5. %display ouputs
display (q_bar);
display(sigma_local);
display(strain_local);
display(strain_global);
problem 5.3 in barber composite materials
Using MATLAB code (project1) we got the following results
(a) Strains in local axes
[
ϵx′x′
εy′y′
τx′y′
] = [
0.2745
0.003
−0.4886
] x 𝟏𝟎−𝟑
(b) Strains in global axes
[
ϵxx
εyy
τxy
] = [
0.4334
−0.1559
−0.4127
] x 𝟏𝟎−𝟑