%% Function name
%       alpha_micro

%% Revised:
%       13 January 2014

%% Author
%       Trey Moore & Autar Kaw
%       Section: All
%       Semester: Fall 2013

%% Purpose
%       Given elastic modulii, Poisson's ratios, and coefficients of 
%       thermal expansion for a fiber and matrix, as well as a fiber volume
%       ratio, output coefficient of thermal expansion in the local
%       directions for the specified unidirectional lamina.

%% Usage 
%       function [alpha12] = alpha_micro(Ef,Em,nuf,numm,alphaf,alpham,Vf)
% Input variables
%       Ef=fiber modulus
%       Em=matrix modulus
%       nuf=fiber Poisson's ratio
%       numm=matrix Poisson's ratio
%       alphaf=thermal expansion of fiber
%       alpham=thermal expansion of matrix
%       Vf=fiber volume fraction
% Output variables 
%       alpha12=vector of thermal expansion of unidirectional lamina
%       [alpha12]=[alpha1 alpha2 alpha12]
% Keywords
%       coefficient of thermal expansion

%% License Agreement
%       http://www.eng.usf.edu/~kaw/OCW/composites/license/limiteduse.pdf

%% Code 
function [alpha12] = alpha_micro(Ef,Em,nuf,numm,alphaf,alpham,Vf)
% Finding Longitudinal Elastic Modulus in Local Direction
E1=Ef*Vf+Em*(1-Vf);
% Finding Major Poisson's Ratio in Local Direction
nu12=nuf*Vf+numm*(1-Vf);
% Finding Coefficient of Thermal Expansions in Local Longitudinal and Local
% Transverse Directions
alpha1=(alphaf*Ef/E1)*Vf+(alpham*Em/E1)*(1-Vf);
alpha2=(1+nuf)*alphaf*Vf+(1+numm)*alpham*(1-Vf)-alpha1*nu12;
% Results in vector form
[alpha12]=[alpha1;alpha2;0];
end