function [y] = function_root_adot(x,a,p,temp,T_g)
global R_0 x_mesh counter pa sigma_plastic_vec  stress_vec sigma_rubber mechanism_vec T_g_0 stress_profile_vec f_int_vec


for s=1:length(x_mesh) 
    R(s) = x_mesh(s); 
    r_R(s) = (1+(a^3-R_0^3)/R(s)^3)^(1/3); 
    eps(s) = 2*log(r_R(s)); 
    eps_dot(s) = (2*a^2*(x))/(R(s)^3)*r_R(s)^(-3); 

   [stress sigma_plastic sigma_rubber1  mechanism] = stress_function_lowmw(T_g_0,temp,T_g,eps_dot(s),eps(s)); % compute dominant stress at mesh point
   f_int(s) = 2/R(s)*(r_R(s))^(-3)*stress; 

   stress_profile_vec(s) = stress;
   f_int_vec = f_int;
end

int_value = trapz(x_mesh,f_int); 

   
   stress_vec(counter) =  stress(1); 
   sigma_plastic_vec(counter) = sigma_plastic(1);
   sigma_rubber(counter) =  sigma_rubber1(1);
   mechanism_vec(counter) = mechanism(1);
   
   

y = (p-pa) - int_value;

end