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How is compliance tensor calculated in comsol for isotropic materials?

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I have been working on a piezoelectric cantilever.
At some point I wanted to see what would be the difference if the piezoelectric material was considered isotropic regarding his compliance matrix (strain-charge form in the material definition).
What surprises me is that for isotropic materials, comsol does not take into account, nor does it ask, for Poisson's ration, Shear moduli or anything else.
If I understood correctly, isotropic material do have non diagonal terms in their compliance matrix and they depend on Poisson's ratio.
How come comsol doesn't need any of theses terms ?

Regards,
Pierre

3 Replies Last Post 2017年7月25日 GMT-4 11:53
Henrik Sönnerlind COMSOL Employee

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Posted: 9 years ago 2016年2月22日 GMT-5 02:33
HI,

In the piezoelectric material you always enter the full compliance (or stiffness) tensor. So if the material is isotropic, you have to fill in the off-diagonal terms too (which of course all are the same). So you have to calculate the three different numbers which appear in the matrix from E and nu.

Regards,
Henrik
HI, In the piezoelectric material you always enter the full compliance (or stiffness) tensor. So if the material is isotropic, you have to fill in the off-diagonal terms too (which of course all are the same). So you have to calculate the three different numbers which appear in the matrix from E and nu. Regards, Henrik

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Posted: 9 years ago 2016年2月22日 GMT-5 11:45
Ok, that's what I tought but the isotropic option threw me off-guard.
Thank you Henrik.
Regards,
Pierre
Ok, that's what I tought but the isotropic option threw me off-guard. Thank you Henrik. Regards, Pierre

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Posted: 7 years ago 2017年7月25日 GMT-4 11:53
Please, how can I output global displacement (U) in Comsol? I want to calculate the compliance of my model. (Please, see the attached Matlab code).

compliance = U transpose x Global stiffness matrix x U

I have used these lines of code to obtain the global stiffness matrix (Kf).

MA = mphmatrix(model, 'sol1', 'out', {'K','E'})
K = MA.K; % stiffness vector
Kf = full(K);

Thank you.

Complete codes
%..............................

function [Kf,compliance] = examplestudy
%
% examplestudy.m
%
% Model exported on Jul 24 2017, 18:50 by COMSOL 5.2.1.152.

import com.comsol.model.*
import com.comsol.model.util.*

model = ModelUtil.create('Model');

model.modelPath('C:\Users\sayinde\Dropbox\Comsol stuffs new');

model.label('examplestudy.mph');

model.comments(['Untitled\n\n']);

model.modelNode.create('comp1');

model.geom.create('geom1', 2);

model.mesh.create('mesh1', 'geom1');

model.geom('geom1').create('b1', 'BezierPolygon');
model.geom('geom1').feature('b1').set('p', {'-0.7' '-0.7' '0.05' '0.05' '0.5' '0.5' '-0.7'; ...
'-0.3' '0.3' '0.3' '0.6' '0.6' '-0.3' '-0.3'});
model.geom('geom1').feature('b1').set('w', {'1' '1' '1' '1' '1' '1' '1' '1' '1' '1' ...
'1' '1'});
model.geom('geom1').feature('b1').set('degree', {'1' '1' '1' '1' '1' '1'});
model.geom('geom1').run;

model.material.create('mat1', 'Common', 'comp1');
model.material('mat1').propertyGroup.create('Enu', 'Young''s modulus and Poisson''s ratio');

model.physics.create('solid', 'SolidMechanics', 'geom1');
model.physics('solid').create('fix1', 'Fixed', 1);
model.physics('solid').feature('fix1').selection.set([1]);
model.physics('solid').create('disp1', 'Displacement0', 0);
model.physics('solid').create('disp2', 'Displacement0', 0);
model.physics('solid').feature('disp2').selection.set([5]);

model.mesh('mesh1').create('fq1', 'FreeQuad');

model.view('view1').axis.set('ymax', '1.7435424327850342');
model.view('view1').axis.set('xmax', '1.561381220817566');
model.view('view1').axis.set('ymin', '-1.7435424327850342');
model.view('view1').axis.set('xmin', '-1.561381220817566');

model.material('mat1').label('solid material 1');
model.material('mat1').propertyGroup('Enu').set('youngsmodulus', '1');
model.material('mat1').propertyGroup('Enu').set('poissonsratio', '0.3');

model.physics('solid').feature('disp1').set('Direction', {'1'; '1'; '0'});
model.physics('solid').feature('disp1').set('U0', {'-12.44'; '-3.45'; '0'});
model.physics('solid').feature('disp2').set('Direction', {'1'; '1'; '0'});
model.physics('solid').feature('disp2').set('U0', {'14.257'; '3.457'; '0'});

model.mesh('mesh1').run;

model.study.create('std1');
model.study('std1').create('stat', 'Stationary');

model.sol.create('sol1');
model.sol('sol1').study('std1');
model.sol('sol1').attach('std1');
model.sol('sol1').create('st1', 'StudyStep');
model.sol('sol1').create('v1', 'Variables');
model.sol('sol1').create('s1', 'Stationary');
model.sol('sol1').feature('s1').create('fc1', 'FullyCoupled');
model.sol('sol1').feature('s1').feature.remove('fcDef');

model.result.create('pg1', 'PlotGroup2D');
model.result.create('pg2', 'PlotGroup2D');
model.result('pg1').create('surf2', 'Surface');
model.result('pg2').create('surf1', 'Surface');

model.sol('sol1').attach('std1');
model.sol('sol1').runAll;

model.result('pg1').label('Stress (solid)');
model.result('pg1').feature('surf2').set('resolution', 'normal');
model.result('pg2').label('total disp');
model.result('pg2').feature('surf1').label('total displacement');
model.result('pg2').feature('surf1').set('resolution', 'normal');

MA = mphmatrix(model, 'sol1', 'out', {'K','E'})
K = MA.K; % stiffness vector
Kf = full(K);

% How can I output the global displacement in comsol
compliance = u'*Kf*u; % u is the global displacement I want to use to compute the compliance

out = model;
Please, how can I output global displacement (U) in Comsol? I want to calculate the compliance of my model. (Please, see the attached Matlab code). compliance = U transpose x Global stiffness matrix x U I have used these lines of code to obtain the global stiffness matrix (Kf). MA = mphmatrix(model, 'sol1', 'out', {'K','E'}) K = MA.K; % stiffness vector Kf = full(K); Thank you. Complete codes %.............................. function [Kf,compliance] = examplestudy % % examplestudy.m % % Model exported on Jul 24 2017, 18:50 by COMSOL 5.2.1.152. import com.comsol.model.* import com.comsol.model.util.* model = ModelUtil.create('Model'); model.modelPath('C:\Users\sayinde\Dropbox\Comsol stuffs new'); model.label('examplestudy.mph'); model.comments(['Untitled\n\n']); model.modelNode.create('comp1'); model.geom.create('geom1', 2); model.mesh.create('mesh1', 'geom1'); model.geom('geom1').create('b1', 'BezierPolygon'); model.geom('geom1').feature('b1').set('p', {'-0.7' '-0.7' '0.05' '0.05' '0.5' '0.5' '-0.7'; ... '-0.3' '0.3' '0.3' '0.6' '0.6' '-0.3' '-0.3'}); model.geom('geom1').feature('b1').set('w', {'1' '1' '1' '1' '1' '1' '1' '1' '1' '1' ... '1' '1'}); model.geom('geom1').feature('b1').set('degree', {'1' '1' '1' '1' '1' '1'}); model.geom('geom1').run; model.material.create('mat1', 'Common', 'comp1'); model.material('mat1').propertyGroup.create('Enu', 'Young''s modulus and Poisson''s ratio'); model.physics.create('solid', 'SolidMechanics', 'geom1'); model.physics('solid').create('fix1', 'Fixed', 1); model.physics('solid').feature('fix1').selection.set([1]); model.physics('solid').create('disp1', 'Displacement0', 0); model.physics('solid').create('disp2', 'Displacement0', 0); model.physics('solid').feature('disp2').selection.set([5]); model.mesh('mesh1').create('fq1', 'FreeQuad'); model.view('view1').axis.set('ymax', '1.7435424327850342'); model.view('view1').axis.set('xmax', '1.561381220817566'); model.view('view1').axis.set('ymin', '-1.7435424327850342'); model.view('view1').axis.set('xmin', '-1.561381220817566'); model.material('mat1').label('solid material 1'); model.material('mat1').propertyGroup('Enu').set('youngsmodulus', '1'); model.material('mat1').propertyGroup('Enu').set('poissonsratio', '0.3'); model.physics('solid').feature('disp1').set('Direction', {'1'; '1'; '0'}); model.physics('solid').feature('disp1').set('U0', {'-12.44'; '-3.45'; '0'}); model.physics('solid').feature('disp2').set('Direction', {'1'; '1'; '0'}); model.physics('solid').feature('disp2').set('U0', {'14.257'; '3.457'; '0'}); model.mesh('mesh1').run; model.study.create('std1'); model.study('std1').create('stat', 'Stationary'); model.sol.create('sol1'); model.sol('sol1').study('std1'); model.sol('sol1').attach('std1'); model.sol('sol1').create('st1', 'StudyStep'); model.sol('sol1').create('v1', 'Variables'); model.sol('sol1').create('s1', 'Stationary'); model.sol('sol1').feature('s1').create('fc1', 'FullyCoupled'); model.sol('sol1').feature('s1').feature.remove('fcDef'); model.result.create('pg1', 'PlotGroup2D'); model.result.create('pg2', 'PlotGroup2D'); model.result('pg1').create('surf2', 'Surface'); model.result('pg2').create('surf1', 'Surface'); model.sol('sol1').attach('std1'); model.sol('sol1').runAll; model.result('pg1').label('Stress (solid)'); model.result('pg1').feature('surf2').set('resolution', 'normal'); model.result('pg2').label('total disp'); model.result('pg2').feature('surf1').label('total displacement'); model.result('pg2').feature('surf1').set('resolution', 'normal'); MA = mphmatrix(model, 'sol1', 'out', {'K','E'}) K = MA.K; % stiffness vector Kf = full(K); % How can I output the global displacement in comsol compliance = u'*Kf*u; % u is the global displacement I want to use to compute the compliance out = model;

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