MechanicalElastoPlasticVonMises Class
This class implements an elasto-plastic constitutive law based on the Von Mises yield criterion. It extends the MechanicalElastoPlastic base class and provides methods for defining the yield condition, flow rule, and hardening behavior.
Contents
Methods
- yieldCondition: Computes the yield condition based on the Von Mises stress and the yield stress.
- yieldStressGradient: Computes the gradient of the yield function with respect to the stress vector.
- flowVector: Computes the flow direction vector based on the deviatoric stress.
- flowVectorGradient: Computes the gradient of the flow vector with respect to the stress vector.
- hardening: Returns the hardening modulus from the material properties.
- hardeningStressGradient: Returns the gradient of the hardening law with respect to the stress vector.
Author
Danilo Cavalcanti
Version History
Version 1.00.
Class Definition
classdef MechanicalElastoPlasticVonMises < MechanicalElastoPlastic
Constructor method
methods
%------------------------------------------------------------------
function this = MechanicalElastoPlasticVonMises()
this = this@MechanicalElastoPlastic();
this.nstVar = 5; % Hardening + Kinematic hardening
end
end
Public methods
methods
%------------------------------------------------------------------
% Yield function definition
function f = yieldCondition(this,material,ip,stress)
sVM = this.vonMisesStress(stress);
sy = material.sy0;% + material.Kp * ip.statevar(1);
f = sVM - sy;
end
%------------------------------------------------------------------
% Gradient of the yield function wrt to the stress vector
function df = yieldStressGradient(this,~,~,stress)
df = this.vonMisesStressGradient(stress);
end
%------------------------------------------------------------------
% Flow vector
function n = flowVector(this,~,~,stress)
% n = this.vonMisesStressGradient(stress);
sd = this.deviatoricStress(stress);
n = sd / norm(sd);
end
%------------------------------------------------------------------
% Flow vector gradient
function dn = flowVectorGradient(this,~,~,stress)
dn = this.vonMisesStressHessian(stress);
end
%------------------------------------------------------------------
% Hardening law
function h = hardening(~,material,~,~)
h = material.Kp;
end
%------------------------------------------------------------------
% Gradient of the hardening law wrt to the stress vector
function dh = hardeningStressGradient(~,~,~,~)
dh = 0.0;
end
end
end