MechanicalLinearElastic Class

This class defines an linear elastic stress-strain constitutive law. The class provides methods to compute the stress vector, constitutive matrix, elastic constants (shear modulus and bulk modulus), and elastic tensors (constitutive and flexibility matrices). It also includes a method to determine if the material is elasto-plastic.

Contents

Methods

Author

Danilo Cavalcanti

Version History

Version 1.00.

Class Definition

classdef MechanicalLinearElastic < MechanicalLaw

Constructor method

    methods
        %------------------------------------------------------------------
        function this = MechanicalLinearElastic()
            this = this@MechanicalLaw();
        end
    end

Public methods

    methods

        %------------------------------------------------------------------
        % Compute the stress vector and the constitutive matrix
        function [stress,De] = eval(this,material,ip)

            % Constitutive matrix
            De = this.elasticConstitutiveMatrix(material,ip);

            % Stress vector
            stress = De * (ip.strain - ip.strainOld) + ip.stressOld;

        end

Elastic constants

        %------------------------------------------------------------------
        % Computes the shear modulus of the material
        function G = shearModulus(~,material)
            G = material.Young / (2.0 * (1.0 + material.nu));
        end

        %------------------------------------------------------------------
        % Computes the bulk modulus of the material
        function K = bulkModulus(~,material)
            K = material.Young / (3.0 * (1.0 - 2.0*material.nu));
        end

    end

Public methods

    methods (Static)

        function flag = isElastoPlastic()
            flag = false;
        end

Elastic tensors

        %------------------------------------------------------------------
        % Compute the elastic constitutive matrix
        function De = elasticConstitutiveMatrix(material,ip)

            % Elastic material properties
            E  = material.Young;
            nu = material.nu;

            if strcmp(ip.anm,'PlaneStress')

                c = E/(1.0 - (nu*nu));
                De = [  c   ,   c*nu , 0.0  ,  0.0;
                       c*nu ,    c   , 0.0  ,  0.0;
                       0.0  ,   0.0  , 1.0  ,  0.0;
                       0.0  ,   0.0  , 0.0  , c*(1-nu)/2.0 ];


            elseif strcmp(ip.anm,'PlaneStrain')

                De = [ 1.0-nu ,   nu   ,   nu   ,    0.0;
                         nu   , 1.0-nu ,   nu   ,    0.0;
                         nu   ,  nu    , 1.0-nu ,    0.0;
                        0.0   ,  0.0   ,   0.0  , (1-2.0*nu)/2.0 ];

                De = De * E/(1.0 + nu)/(1.0 - 2.0*nu);

            else
                De = [];
            end
        end

        %------------------------------------------------------------------
        % Compute the elastic flexibility matrix
        function Ce = elasticFlexibilityMatrix(material,ip)

            % Elastic material properties
            E  = material.Young;
            nu = material.nu;

            if strcmp(ip.anm,'PlaneStress')

                Ce = [  1.0/E ,  -nu/E  ,  0.0  ,  0.0;
                        -nu/E ,  1.0/E  ,  0.0  ,  0.0;
                         0.0  ,  0.0    ,  1.0  ,  0.0;
                         0.0  ,  0.0    ,  0.0  , 2.0*(1+nu)/E ];

            elseif strcmp(ip.anm,'PlaneStrain')

                Ce = [  1.0/E ,  -nu/E  ,  -nu/E ,  0.0;
                        -nu/E ,  1.0/E  ,  -nu/E ,  0.0;
                        -nu/E ,  -nu/E  ,  1.0/E ,  0.0;
                         0.0  ,  0.0    ,  0.0   , 2.0*(1+nu)/E ];
            else
                Ce = [];
            end
        end

    end

end

Published with MATLAB® R2022a