写一个gurson模型的代码用matlab实现

以下是一个简单的Gurson模型的MATLAB代码：

%% Gurson Model

% Define material constants E = 210000; % Young's modulus (MPa) nu = 0.3; % Poisson's ratio Y = 1000; % Yield strength (MPa) rho = 7800; % Density (kg/m^3) alpha = 0.1; % Void volume fraction n = 1; % Strain hardening exponent m = 1; % Void growth exponent

% Define loading conditions sigma = 500; % Applied stress (MPa) epsilon_dot = 0.001; % Strain rate (s^-1)

% Calculate material properties K = E/(3*(1-2nu)); % Bulk modulus mu = E/(2(1+nu)); % Shear modulus H = Y/(3*(1-2alpha)); % Hardening modulus l = 1/(3epsilon_dot); % Characteristic distance

% Define initial void volume fraction f_0 = 0.01;

% Define initial porosity p_0 = f_0/(1-f_0);

% Define initial equivalent plastic strain eps_p_0 = 0;

% Define initial equivalent stress sigma_eq_0 = Y;

% Define time step dt = 0.01;

% Define number of time steps num_steps = 100;

% Initialize arrays f = zeros(num_steps,1); p = zeros(num_steps,1); eps_p = zeros(num_steps,1); sigma_eq = zeros(num_steps,1);

% Assign initial values to arrays f(1) = f_0; p(1) = p_0; eps_p(1) = eps_p_0; sigma_eq(1) = sigma_eq_0;

% Perform time integration for i = 2:num_steps

% Calculate equivalent stress
sigma_eq(i) = sqrt(3/2)*sigma + H*eps_p(i-1);

% Calculate equivalent plastic strain rate
eps_p_dot = sqrt(2/3)*epsilon_dot*(sigma/sigma_eq(i))*(1-p(i-1)^m);

% Calculate new equivalent plastic strain
eps_p(i) = eps_p(i-1) + eps_p_dot*dt;

% Calculate new void volume fraction
f(i) = f_0*(1+(eps_p(i)/l))/(1-f_0+(eps_p(i)/l));

% Calculate new porosity
p(i) = f(i)/(1-f(i));

end

% Plot results figure subplot(2,2,1) plot(eps_p,sigma_eq) xlabel('Equivalent Plastic Strain') ylabel('Equivalent Stress') title('Stress-Strain Curve')

subplot(2,2,2) plot(eps_p,f) xlabel('Equivalent Plastic Strain') ylabel('Void Volume Fraction') title('Void Evolution')

subplot(2,2,3) plot(eps_p,p) xlabel('Equivalent Plastic Strain') ylabel('Porosity') title('Porosity Evolution')

subplot(2,2,4) plot(f,p) xlabel('Void Volume Fraction') ylabel('Porosity') title('Porosity-Void Relationship')