%% Function name
%       moduli_halphin

%% Revised
%       30 January 2014

%% Authors
%       Michael Cohen, Trey Moore, & Autar Kaw
%       Section: All
%       Semester: Fall 2013

%% Purpose
%       Given the elastic modulii, Poisson's ratios, of a fiber and matrix,
%       as well as the fiber volume fraction, output the elastic modulii
%       and Poisson's ratios of the lamina using the Halphin and Tsai
%       method

%% Usage 
%       function [moduli] = moduli_halphin(Ef,Em,nuf,numm,Vf,xi)
% Input Variables
%       Ef=fiber elastic modulus
%       Em=matrix elastic modulus
%       nuf=fiber Poisson's ratio
%       numm=matrix Poisson's ratio
%       Vf=fiber volume fraction
%       xi=Halphin Tsai reinforcing factor
% Output Variables 
%       moduli=vector of elastic modulii and Poisson's ratio of unidirectional lamina
%       [E1 E2 nu12 G12]
% Keyword
%       elastc modulii
%       Poisson's ratio
%       Halphin and Tsai method

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

%% Code
function [moduli] = moduli_halphin(Ef,Em,nuf,numm,Vf,xi)
% Fiber shear modulus
Gf=Ef/(2*(1+nuf));
% Matrix shear modulus
Gm=Em/(2*(1+numm));
% Stress partitioning parameter for elastic modulii
Eta1=((Ef/Em)-1)/((Ef/Em)+xi(1));
% Stress partitioning parameter for shear modulus
Eta2=((Gf/Gm)-1)/((Gf/Gm)+xi(2));
% Longitudional elastic modulus
E1=Ef*Vf+Em*(1-Vf);
% Transverse elastic modulus
E2=Em*((1+xi(1)*Eta1*Vf)/(1-Eta1*Vf));
% Shear modulus
G12=Gm*((1+xi(2)*Eta2*Vf)/(1-Eta2*Vf));
% Major Poisson Ratio
nu12=nuf*Vf+numm*(1-Vf);
% Vector of elastic modulii and Poisson's ratio of unidirectional lamina
[moduli]=[E1 E2 nu12 G12];
end