%% Function name
%       maximumstrain

%% Revised
%       16 January 2014

%% Author
%       Mahdi M. Dewan, Trey Moore, & Autar Kaw
%       Section : All
%       Semester : Fall 2012

%% Purpose
%       Given elastic modulii and ultimate strengths of a unidirectional lamina, angle of the 
%       ply in degrees, and the global strains acting on the lamina, output
%       the strength ratio of the lamina based on maximum strain theory

%% Usage
%       function [SR] = maximumstrain(strain_glo,angle,moduli,strength)
% Input variables
%       moduli=vector with four elastic moduli of unidirectional lamina
%       [moduli]=[E1 E2 nu12 G12]
%       angle=angle of ply in degrees
%       E1=longitudinal elastic modulus
%       E2=transverse elastic modulus
%       nu12=major Poisson's ratio
%       G12=in-plane shear modulus
%       strain_glo=vector of global strain applied to unidirectional lamina
%       [strain_glo]=[epsx;epsy;epsxy]
%       epsx=longitudinal global strain
%       epsy=transverse global strain
%       epsxy=in-plane global strain
%       strength=vector of the five ultimate strain strengths of the 
%                unidirectional lamina
%       [strength]=[s1tu s1cu s2tu s2cu s12u] 
%       s1tu=ultimite longitudinal tensile strength
%       s1cu=ultimite longitudinal compressive strength
%       s2tu=ultimite transverse tensile strength
%       s2cu=ultimite transverse compressive strength
%       s12u=ultimite in-plane shear strength
% Output variable
%       SR=Strength Ratio
% Keyword
%       maximum strain failure theory
%       strength ratio
%       angle ply

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

%% Code
function [SR] = maximumstrain(strain_glo,angle,moduli,strength)
% Sine of the angle of the lamina
s=sind(angle);
% Cosine of the angle of the lamina
c=cosd(angle);
% Inverse Transformation Matrix
T=[c^2 s^2 2*s*c; s^2 c^2 -2*s*c; -s*c s*c c^2-s^2];
% Reuter Matrix
R=[1 0 0; 0 1 0; 0 0 2];
% Calculating the local strains
strain_loc=R*T*inv(R)*strain_glo;
e1tu=strength(1)/moduli(1); 
e1cu=strength(2)/moduli(1); 
e2tu=strength(3)/moduli(2);  
e2cu=strength(4)/moduli(2);  
e12u=strength(5)/moduli(4);  
if strain_loc(1)>0 
    SRp(1)=e1tu/strain_loc(1);
end
if strain_loc(1)<0
    SRp(1)=-e1cu/strain_loc(1);
end
if strain_loc(2)>0
    SRp(2)=e2tu/strain_loc(2);
end
if strain_loc(2)<0
    SRp(2)=-e2cu/strain_loc(2);
end
if strain_loc(3)>0
    SRp(3)=e12u/strain_loc(3);
end
if strain_loc(3)<0
    SRp(3)=-e12u/strain_loc(3);
end
% Defining the Strength Ratio Vector
SR=min(SRp);
end