function [STRESS,D] = MOONEY(F,PROP,LTAN) %****************************************************************************** % Calculate 2nd PK stress and stiffness for Mooney-Rivlin material % %****************************************************************************** %% % A10=PROP(1); A01=PROP(2); K=PROP(3); % Material properties X12=1/2; X13=1/3; X23=2/3; X43=4/3; X53=5/3; X89=8/9; % Constants D=eye(6); C=F'*F; % Tangent stiffness & Right C-G tensor C1=C(1,1); C2=C(2,2); C3=C(3,3); C4=C(1,2); C5=C(2,3); C6=C(1,3); % Voigt I1=C1+C2+C3; I2=C1*C2+C1*C3+C2*C3-C4^2-C5^2-C6^2; I3=det(C); % Invariants J3=sqrt(I3); % Reduced invariants I1E=2*[1 1 1 0 0 0]'; % Derivatives of invariants I2E=2*[C2+C3, C3+C1, C1+C2, -C4, -C5, -C6]'; % I3E=2*[C2*C3-C5^2, C3*C1-C6^2, C1*C2-C4^2, ... % C5*C6-C3*C4, C6*C4-C1*C5, C4*C5-C2*C6]'; % W1=I3^(-X13); W2 = X13*I1*I3^(-X43); W3 = I3^(-X23); % Parameters W4=X23*I2*I3^(-X53); W5 = X12*I3^(-X12); % J1E=W1*I1E-W2*I3E; J2E=W3*I2E-W4*I3E; J3E=W5*I3E; % Derivatives of invariants STRESS=A10*J1E + A01*J2E + K*(J3-1)*J3E; % 2nd P-K Stress if ~LTAN, return; end % Do not calculate tangent stiffness I2EE=[0 4 4 0 0 0; 4 0 4 0 0 0; 4 4 0 0 0 0; % 2nd derivatives 0 0 0 -2 0 0; 0 0 0 0 -2 0; 0 0 0 0 0 -2]; % I3EE=[ 0 4*C3 4*C2 0 -4*C5 0; % 2nd derivatives 4*C3 0 4*C1 0 0 -4*C6; % 4*C2 4*C1 0 -4*C4 0 0; % 0 0 -4*C4 -2*C3 2*C6 2*C5; % -4*C5 0 0 2*C6 -2*C1 2*C4; % 0 -4*C6 0 2*C5 2*C4 -2*C2]; % W1=X23*I3^(-X12); W2 = X89*I1*I3^(-X43); W3 = X13*I1*I3^(-X43);% Parameters W4=X43*I3^(-X12); W5 = X89*I2*I3^(-X53); W6 = I3^(-X23); % W7=X23*I2*I3^(-X53); W8 = I3^(-X12); W9 = X12*I3^(-X12); % J1EE=-W1*(J1E*J3E' + J3E*J1E') + W2*(J3E*J3E') - W3*I3EE; % 2nd derivatives J2EE=-W4*(J2E*J3E' + J3E*J2E') + W5*(J3E*J3E') + W6*I2EE - W7*I3EE; % J3EE=-W8*(J3E*J3E') + W9*I3EE; % D=A10*J1EE + A01*J2EE + K*(J3E*J3E') + K*(J3-1)*J3EE; % Tangent stiffness end %