function out = model % % OneTet.m % % Model exported on Jun 29 2025, 15:48 by COMSOL 6.3.0.420. import com.comsol.model.* import com.comsol.model.util.* model = ModelUtil.create('Model'); model.modelPath('/Users/rth/Desktop/Comsol for IST/Smallest'); model.modelNode.create('comp1', true); model.geom.create('geom1', 3); model.geom('geom1').model('comp1'); model.geom('geom1').geomRep('cadps'); model.geom('geom1').designBooleans(false); model.mesh.create('mesh1', 'geom1'); model.mesh('mesh1').contribute('geom/detail', true); model.physics.create('solid', 'SolidMechanics', 'geom1'); model.physics('solid').model('comp1'); model.study.create('std1'); model.study('std1').create('stat', 'Stationary'); model.study('std1').feature('stat').setSolveFor('/physics/solid', true); model.geom('geom1').create('tet1', 'Tetrahedron'); model.geom('geom1').runPre('fin'); model.geom('geom1').run; model.material.create('mat1', 'Common', 'comp1'); model.material('mat1').label('UNS C10300 [solid]'); model.material('mat1').info.create('UNS'); model.material('mat1').info('UNS').body('C10300'); model.material('mat1').info('UNS').title('UNS'); model.material('mat1').info.create('EN_DIN'); model.material('mat1').info('EN_DIN').body('CW021A/Cu-PHC'); model.material('mat1').info('EN_DIN').title('EN_DIN'); model.material('mat1').info.create('Composition'); model.material('mat1').info('Composition').body('bal. Cu, (0.001-0.006) P, small amount of Ag (wt %)'); model.material('mat1').info('Composition').title('Composition'); model.material('mat1').propertyGroup('def').set('thermalconductivity', 'k(T)'); model.material('mat1').propertyGroup('def').setPropertyInfo('thermalconductivity', ['Reference: "Standards Handbook, Part 2, Wrought Copper and Copper Alloy Mill Products", Copper Development Association, New York, 8th Edition (1985) https://www.copper.org/resources/standards/uns-standard-designations.html' newline 'Note: T' native2unicode(hex2dec({'00' '98'}), 'unicode') native2unicode(hex2dec({'00' '9a'}), 'unicode') ' = 1083 ' native2unicode(hex2dec({'00' 'b0'}), 'unicode') 'C (1356 K), room temperature value from the reference, the temperature dependence was estimated from similar materials']); model.material('mat1').propertyGroup('def').set('thermalexpansioncoefficient', '(alpha_solid_1(T)+(Tempref-293[K])*if(abs(T-Tempref)>1e-3,(alpha_solid_1(T)-alpha_solid_1(Tempref))/(T-Tempref),d(alpha_solid_1(T),T)))/(1+alpha_solid_1(Tempref)*(Tempref-293[K]))'); model.material('mat1').propertyGroup('def').setPropertyInfo('thermalexpansioncoefficient', ['Reference: N.J. Simon, E.S. Drexler, and R.P. Reed, "Properties of Copper and Copper Alloys at Cryogenic Temperatures", NIST Monograph 177 (1992) https://nvlpubs.nist.gov/nistpubs/Legacy/MONO/nistmonograph177.pdf; T.A. Hahn, "Thermal Expansion of Copper from 20 to 800 K-Standard Reference Material 736", Journal of Applied Physics, v41, No. 13, p5096 (1970) https://doi.org/10.1063/1.1658614; G.K. White and R.B. Roberts, "Problems in presenting key values: linear expansivity of copper", High Temperatures-High Pressures, v12, No. 3, p311 (1980); D.L. Thornburg, E.S. Thall, and J. Brous, "A Manual of Materials For Microwave Tubes", WADD Technical Report 60-325 (1961) https://apps.dtic.mil/sti/tr/pdf/AD0267327.pdf' newline 'Note: the reference temperature is 20 ' native2unicode(hex2dec({'00' 'b0'}), 'unicode') 'C (293 K), T' native2unicode(hex2dec({'00' '98'}), 'unicode') native2unicode(hex2dec({'00' '9a'}), 'unicode') ' = 1083 ' native2unicode(hex2dec({'00' 'b0'}), 'unicode') 'C (1356 K), 3% error, same data as elemental copper, calculated from the linear expansion' newline 'Reference temperature: 293.00[K]']); model.material('mat1').propertyGroup('def').set('heatcapacity', 'C_solid_1(T)'); model.material('mat1').propertyGroup('def').setPropertyInfo('heatcapacity', ['Reference: G.K. White and S.J. Collocott, "Heat Capacity of Reference Materials: Cu and W", Journal of Physical and Chemical Reference Data, v13, No. 4, p1251 (1984) https://srd.nist.gov/JPCRD/jpcrd263.pdf; "Pub TN27 - High Conductivity Coppers Technical Data", Copper Development Association (1972) http://copperalliance.org.uk/resource-library/pub-tn26---the-brasses---nickel-brass-and-nickel-silver---technical-data' newline 'Note: T' native2unicode(hex2dec({'00' '98'}), 'unicode') native2unicode(hex2dec({'00' '9a'}), 'unicode') ' = 1083 ' native2unicode(hex2dec({'00' 'b0'}), 'unicode') 'C (1356 K), error less than 2%']); model.material('mat1').propertyGroup('def').set('density', 'rho_solid_1(T)'); model.material('mat1').propertyGroup('def').setPropertyInfo('density', ['Reference: N.J. Simon, E.S. Drexler, and R.P. Reed, "Properties of Copper and Copper Alloys at Cryogenic Temperatures", NIST Monograph 177 (1992) https://nvlpubs.nist.gov/nistpubs/Legacy/MONO/nistmonograph177.pdf; T.A. Hahn, "Thermal Expansion of Copper from 20 to 800 K-Standard Reference Material 736", Journal of Applied Physics, v41, No. 13, p5096 (1970) https://doi.org/10.1063/1.1658614; G.K. White and R.B. Roberts, "Problems in presenting key values: linear expansivity of copper", High Temperatures-High Pressures, v12, No. 3, p311 (1980); D.L. Thornburg, E.S. Thall, and J. Brous, "A Manual of Materials For Microwave Tubes", WADD Technical Report 60-325 (1961) https://apps.dtic.mil/sti/tr/pdf/AD0267327.pdf' newline 'Note: T' native2unicode(hex2dec({'00' '98'}), 'unicode') native2unicode(hex2dec({'00' '9a'}), 'unicode') ' = 1083 ' native2unicode(hex2dec({'00' 'b0'}), 'unicode') 'C (1356 K), calculated from the linear expansion and the room temperature density']); model.material('mat1').propertyGroup('def').set('TD', 'TD_solid_1(T)'); model.material('mat1').propertyGroup('def').setPropertyInfo('TD', ['Reference: "Standards Handbook, Part 2, Wrought Copper and Copper Alloy Mill Products", Copper Development Association, New York, 8th Edition (1985) https://www.copper.org/resources/standards/uns-standard-designations.html; K.K. Kelley, "Contributions to the Data on Theoretical Metallurgy, Pt. XIII", US Bureau of Mines, Bulletin No. 584 (1960) http://pbadupws.nrc.gov/docs/ML1212/ML12124A257.pdf' newline 'Note: T' native2unicode(hex2dec({'00' '98'}), 'unicode') native2unicode(hex2dec({'00' '9a'}), 'unicode') ' = 1083 ' native2unicode(hex2dec({'00' 'b0'}), 'unicode') 'C (1356 K), calculated from the thermal conductivity, density, and specific heat']); model.material('mat1').propertyGroup('def').func.create('k', 'Piecewise'); model.material('mat1').propertyGroup('def').func('k').set('funcname', 'k'); model.material('mat1').propertyGroup('def').func('k').set('arg', 'T'); model.material('mat1').propertyGroup('def').func('k').set('extrap', 'constant'); model.material('mat1').propertyGroup('def').func('k').set('pieces', {'293.0' '373.16' '411.679601-0.0875993192*T^1'}); model.material('mat1').propertyGroup('def').func('k').label('Piecewise'); model.material('mat1').propertyGroup('def').func('k').set('fununit', 'W/(m*K)'); model.material('mat1').propertyGroup('def').func('k').set('argunit', 'K'); model.material('mat1').propertyGroup('def').func.create('alpha_solid_1', 'Piecewise'); model.material('mat1').propertyGroup('def').func('alpha_solid_1').set('funcname', 'alpha_solid_1'); model.material('mat1').propertyGroup('def').func('alpha_solid_1').set('arg', 'T'); model.material('mat1').propertyGroup('def').func('alpha_solid_1').set('extrap', 'constant'); model.material('mat1').propertyGroup('def').func('alpha_solid_1').set('pieces', {'4.0' '100.0' '1.104402E-5+4.812192E-8*T^1-1.223083E-10*T^2'; ... '100.0' '210.0' '1.27655838E-5+1.849516E-8*T^1+1.203963E-11*T^2-1.023671E-13*T^3'; ... '210.0' '800.0' '1.472580288E-5+8.137386E-9*T^1-4.58414E-12*T^2'; ... '800.0' '1273.16' '1.834200656E-5-1.577095E-9*T^1+1.908643E-12*T^2'}); model.material('mat1').propertyGroup('def').func('alpha_solid_1').label('Piecewise 1'); model.material('mat1').propertyGroup('def').func('alpha_solid_1').set('fununit', '1/K'); model.material('mat1').propertyGroup('def').func('alpha_solid_1').set('argunit', 'K'); model.material('mat1').propertyGroup('def').func.create('C_solid_1', 'Piecewise'); model.material('mat1').propertyGroup('def').func('C_solid_1').set('funcname', 'C_solid_1'); model.material('mat1').propertyGroup('def').func('C_solid_1').set('arg', 'T'); model.material('mat1').propertyGroup('def').func('C_solid_1').set('extrap', 'constant'); model.material('mat1').propertyGroup('def').func('C_solid_1').set('pieces', {'223.0' '300.0' '-215.2814022+8.23639228*T^1-0.04732108184*T^2+1.29111169E-4*T^3-1.357031447E-7*T^4'; '300.0' '1300.0' '342.8111259+0.1338348214*T^1+5.535252088E-5*T^2-1.97122089E-7*T^3+1.140747098E-10*T^4'}); model.material('mat1').propertyGroup('def').func('C_solid_1').label('Piecewise 2'); model.material('mat1').propertyGroup('def').func('C_solid_1').set('fununit', 'J/(kg*K)'); model.material('mat1').propertyGroup('def').func('C_solid_1').set('argunit', 'K'); model.material('mat1').propertyGroup('def').func.create('rho_solid_1', 'Piecewise'); model.material('mat1').propertyGroup('def').func('rho_solid_1').set('funcname', 'rho_solid_1'); model.material('mat1').propertyGroup('def').func('rho_solid_1').set('arg', 'T'); model.material('mat1').propertyGroup('def').func('rho_solid_1').set('extrap', 'constant'); model.material('mat1').propertyGroup('def').func('rho_solid_1').set('pieces', {'4.0' '90.0' '9028.160747+0.001936185*T^1-4.310034E-4*T^2-8.227902E-6*T^3'; ... '90.0' '250.0' '9034.26758-0.05885933*T^1-0.001406238*T^2+1.736657E-6*T^3'; ... '250.0' '800.0' '9062.239466-0.3913962*T^1-8.947644E-5*T^2'; ... '800.0' '1273.16' '9038.962-0.3593546*T^1-9.31574E-5*T^2'}); model.material('mat1').propertyGroup('def').func('rho_solid_1').label('Piecewise 3'); model.material('mat1').propertyGroup('def').func('rho_solid_1').set('fununit', 'kg/m^3'); model.material('mat1').propertyGroup('def').func('rho_solid_1').set('argunit', 'K'); model.material('mat1').propertyGroup('def').func.create('TD_solid_1', 'Piecewise'); model.material('mat1').propertyGroup('def').func('TD_solid_1').set('funcname', 'TD_solid_1'); model.material('mat1').propertyGroup('def').func('TD_solid_1').set('arg', 'T'); model.material('mat1').propertyGroup('def').func('TD_solid_1').set('extrap', 'constant'); model.material('mat1').propertyGroup('def').func('TD_solid_1').set('pieces', {'293.0' '373.16' '1.32769513E-4-7.85151051E-8*T^1+3.59693251E-11*T^2'}); model.material('mat1').propertyGroup('def').func('TD_solid_1').label('Piecewise 4'); model.material('mat1').propertyGroup('def').func('TD_solid_1').set('fununit', 'm^2/s'); model.material('mat1').propertyGroup('def').func('TD_solid_1').set('argunit', 'K'); model.material('mat1').propertyGroup('def').addInput('temperature'); model.material('mat1').propertyGroup('def').addInput('strainreferencetemperature'); model.material('mat1').propertyGroup.create('ThermalExpansion', 'ThermalExpansion', 'Thermal expansion'); model.material('mat1').propertyGroup('ThermalExpansion').set('dL', '(dL_solid_1(T)-dL_solid_1(Tempref))/(1+dL_solid_1(Tempref))'); model.material('mat1').propertyGroup('ThermalExpansion').setPropertyInfo('dL', ['Reference: N.J. Simon, E.S. Drexler, and R.P. Reed, "Properties of Copper and Copper Alloys at Cryogenic Temperatures", NIST Monograph 177 (1992) https://nvlpubs.nist.gov/nistpubs/Legacy/MONO/nistmonograph177.pdf; T.A. Hahn, "Thermal Expansion of Copper from 20 to 800 K-Standard Reference Material 736", Journal of Applied Physics, v41, No. 13, p5096 (1970) https://doi.org/10.1063/1.1658614; G.K. White and R.B. Roberts, "Problems in presenting key values: linear expansivity of copper", High Temperatures-High Pressures, v12, No. 3, p311 (1980); D.L. Thornburg, E.S. Thall, and J. Brous, "A Manual of Materials For Microwave Tubes", WADD Technical Report 60-325 (1961) https://apps.dtic.mil/sti/tr/pdf/AD0267327.pdf' newline 'Note: the reference temperature is 20 ' native2unicode(hex2dec({'00' 'b0'}), 'unicode') 'C (293 K), T' native2unicode(hex2dec({'00' '98'}), 'unicode') native2unicode(hex2dec({'00' '9a'}), 'unicode') ' = 1083 ' native2unicode(hex2dec({'00' 'b0'}), 'unicode') 'C (1356 K), 3% error, same data as elemental copper' newline 'Reference temperature: 293.00[K]']); model.material('mat1').propertyGroup('ThermalExpansion').set('alphatan', 'CTE_solid_1(T)'); model.material('mat1').propertyGroup('ThermalExpansion').setPropertyInfo('alphatan', ['Reference: N.J. Simon, E.S. Drexler, and R.P. Reed, "Properties of Copper and Copper Alloys at Cryogenic Temperatures", NIST Monograph 177 (1992) https://nvlpubs.nist.gov/nistpubs/Legacy/MONO/nistmonograph177.pdf; T.A. Hahn, "Thermal Expansion of Copper from 20 to 800 K-Standard Reference Material 736", Journal of Applied Physics, v41, No. 13, p5096 (1970) https://doi.org/10.1063/1.1658614; G.K. White and R.B. Roberts, "Problems in presenting key values: linear expansivity of copper", High Temperatures-High Pressures, v12, No. 3, p311 (1980); D.L. Thornburg, E.S. Thall, and J. Brous, "A Manual of Materials For Microwave Tubes", WADD Technical Report 60-325 (1961) https://apps.dtic.mil/sti/tr/pdf/AD0267327.pdf' newline 'Note: T' native2unicode(hex2dec({'00' '98'}), 'unicode') native2unicode(hex2dec({'00' '9a'}), 'unicode') ' = 1083 ' native2unicode(hex2dec({'00' 'b0'}), 'unicode') 'C (1356 K), 3% error, same data as elemental copper, calculated from the linear expansion']); model.material('mat1').propertyGroup('ThermalExpansion').func.create('dL_solid_1', 'Piecewise'); model.material('mat1').propertyGroup('ThermalExpansion').func('dL_solid_1').set('funcname', 'dL_solid_1'); model.material('mat1').propertyGroup('ThermalExpansion').func('dL_solid_1').set('arg', 'T'); model.material('mat1').propertyGroup('ThermalExpansion').func('dL_solid_1').set('extrap', 'constant'); model.material('mat1').propertyGroup('ThermalExpansion').func('dL_solid_1').set('pieces', {'4.0' '80.0' '-0.003272612414-6.837087E-8*T^1+1.574823E-8*T^2+3.040518E-10*T^3'; ... '80.0' '250.0' '-0.003491521746+2.12144E-6*T^1+5.197613E-8*T^2-6.339761E-11*T^3'; ... '250.0' '800.0' '-0.004355177043+1.293125E-5*T^1+7.341229E-9*T^2-2.541027E-12*T^3'; ... '800.0' '1273.16' '-0.004359809427+1.427188E-5*T^1+3.639858E-9*T^2'}); model.material('mat1').propertyGroup('ThermalExpansion').func('dL_solid_1').label('Piecewise'); model.material('mat1').propertyGroup('ThermalExpansion').func('dL_solid_1').set('fununit', ''); model.material('mat1').propertyGroup('ThermalExpansion').func('dL_solid_1').set('argunit', 'K'); model.material('mat1').propertyGroup('ThermalExpansion').func.create('CTE_solid_1', 'Piecewise'); model.material('mat1').propertyGroup('ThermalExpansion').func('CTE_solid_1').set('funcname', 'CTE_solid_1'); model.material('mat1').propertyGroup('ThermalExpansion').func('CTE_solid_1').set('arg', 'T'); model.material('mat1').propertyGroup('ThermalExpansion').func('CTE_solid_1').set('extrap', 'constant'); model.material('mat1').propertyGroup('ThermalExpansion').func('CTE_solid_1').set('pieces', {'4.0' '13.0' '-8.574809E-9+4.13567E-9*T^1-5.673583E-10*T^2+5.520915E-11*T^3'; ... '13.0' '60.0' '2.193883887E-7-2.662325E-8*T^1+4.800942E-10*T^2+6.093443E-11*T^3-6.195564E-13*T^4'; ... '60.0' '250.0' '-8.809400408E-6+3.292355E-7*T^1-1.773823E-9*T^2+4.545667E-12*T^3-4.483983E-15*T^4'; ... '250.0' '800.0' '1.104881709E-5+2.743089E-8*T^1-3.159431E-11*T^2+1.370433E-14*T^3'}); model.material('mat1').propertyGroup('ThermalExpansion').func('CTE_solid_1').label('Piecewise 1'); model.material('mat1').propertyGroup('ThermalExpansion').func('CTE_solid_1').set('fununit', '1/K'); model.material('mat1').propertyGroup('ThermalExpansion').func('CTE_solid_1').set('argunit', 'K'); model.material('mat1').propertyGroup('ThermalExpansion').addInput('temperature'); model.material('mat1').propertyGroup('ThermalExpansion').addInput('strainreferencetemperature'); model.material('mat1').propertyGroup.create('Enu', 'Enu', 'Young''s modulus and Poisson''s ratio'); model.material('mat1').propertyGroup('Enu').set('E', 'E(T)'); model.material('mat1').propertyGroup('Enu').setPropertyInfo('E', ['Reference: N.J. Simon, E.S. Drexler, and R.P. Reed, "Properties of Copper and Copper Alloys at Cryogenic Temperatures", NIST Monograph 177 (1992) https://nvlpubs.nist.gov/nistpubs/Legacy/MONO/nistmonograph177.pdf; H.M. Ledbetter, "Elastic constants of polycrystalline copper at low temperatures. Relationship to single-crystal elastic constants", Physica Status Solidi (a), v66, p477 (1981) https://doi.org/10.1002/pssa.2210660209; H.M. Ledbetter and E.R. Naimon, "Elastic Properties of Metals and Alloys. II. Copper", Journal of Physical and Chemical Reference Data, v3, No. 4, p897 (1974) https://srd.nist.gov/jpcrdreprint/1.3253150.pdf' newline 'Note: T' native2unicode(hex2dec({'00' '98'}), 'unicode') native2unicode(hex2dec({'00' '9a'}), 'unicode') ' = 1083 ' native2unicode(hex2dec({'00' 'b0'}), 'unicode') 'C (1356 K), high purity, annealed, 2% error, data above 27 ' native2unicode(hex2dec({'00' 'b0'}), 'unicode') 'C (300 K) was multiplied by 0.975 to match the low temperature data, dynamic method']); model.material('mat1').propertyGroup('Enu').set('nu', 'nu(T)'); model.material('mat1').propertyGroup('Enu').setPropertyInfo('nu', ['Reference: N.J. Simon, E.S. Drexler, and R.P. Reed, "Properties of Copper and Copper Alloys at Cryogenic Temperatures", NIST Monograph 177 (1992) https://nvlpubs.nist.gov/nistpubs/Legacy/MONO/nistmonograph177.pdf; H.M. Ledbetter, "Elastic constants of polycrystalline copper at low temperatures. Relationship to single-crystal elastic constants", Physica Status Solidi (a), v66, p477 (1981) https://doi.org/10.1002/pssa.2210660209; H.M. Ledbetter and E.R. Naimon, "Elastic Properties of Metals and Alloys. II. Copper", Journal of Physical and Chemical Reference Data, v3, No. 4, p897 (1974) https://srd.nist.gov/jpcrdreprint/1.3253150.pdf' newline 'Note: T' native2unicode(hex2dec({'00' '98'}), 'unicode') native2unicode(hex2dec({'00' '9a'}), 'unicode') ' = 1083 ' native2unicode(hex2dec({'00' 'b0'}), 'unicode') 'C (1356 K), assumed linear over the temperature range, this is in broad agreement with several studies within the experimental error']); model.material('mat1').propertyGroup('Enu').func.create('E', 'Piecewise'); model.material('mat1').propertyGroup('Enu').func('E').set('funcname', 'E'); model.material('mat1').propertyGroup('Enu').func('E').set('arg', 'T'); model.material('mat1').propertyGroup('Enu').func('E').set('extrap', 'constant'); model.material('mat1').propertyGroup('Enu').func('E').set('pieces', {'4.0' '1330.0' '1.396274E11-5077626.0*T^1-191131.5*T^2+290.7333*T^3-0.2058552*T^4+5.385261E-5*T^5'}); model.material('mat1').propertyGroup('Enu').func('E').label('Piecewise'); model.material('mat1').propertyGroup('Enu').func('E').set('fununit', 'Pa'); model.material('mat1').propertyGroup('Enu').func('E').set('argunit', 'K'); model.material('mat1').propertyGroup('Enu').func.create('nu', 'Piecewise'); model.material('mat1').propertyGroup('Enu').func('nu').set('funcname', 'nu'); model.material('mat1').propertyGroup('Enu').func('nu').set('arg', 'T'); model.material('mat1').propertyGroup('Enu').func('nu').set('extrap', 'constant'); model.material('mat1').propertyGroup('Enu').func('nu').set('pieces', {'4.0' '20.0' '0.3413950726-9.643661E-5*T^1+2.151898E-6*T^2'; '20.0' '1330.0' '0.339846+2.405498E-5*T^1'}); model.material('mat1').propertyGroup('Enu').func('nu').label('Piecewise 1'); model.material('mat1').propertyGroup('Enu').func('nu').set('fununit', ''); model.material('mat1').propertyGroup('Enu').func('nu').set('argunit', 'K'); model.material('mat1').propertyGroup('Enu').addInput('temperature'); model.material('mat1').propertyGroup.create('KG', 'KG', 'Bulk modulus and shear modulus'); model.material('mat1').propertyGroup('KG').set('G', 'mu(T)'); model.material('mat1').propertyGroup('KG').setPropertyInfo('G', ['Reference: N.J. Simon, E.S. Drexler, and R.P. Reed, "Properties of Copper and Copper Alloys at Cryogenic Temperatures", NIST Monograph 177 (1992) https://nvlpubs.nist.gov/nistpubs/Legacy/MONO/nistmonograph177.pdf; H.M. Ledbetter, "Elastic constants of polycrystalline copper at low temperatures. Relationship to single-crystal elastic constants", Physica Status Solidi (a), v66, p477 (1981) https://doi.org/10.1002/pssa.2210660209; H.M. Ledbetter and E.R. Naimon, "Elastic Properties of Metals and Alloys. II. Copper", Journal of Physical and Chemical Reference Data, v3, No. 4, p897 (1974) https://srd.nist.gov/jpcrdreprint/1.3253150.pdf' newline 'Note: T' native2unicode(hex2dec({'00' '98'}), 'unicode') native2unicode(hex2dec({'00' '9a'}), 'unicode') ' = 1083 ' native2unicode(hex2dec({'00' 'b0'}), 'unicode') 'C (1356 K), calculated from E and v, errors may be large']); model.material('mat1').propertyGroup('KG').set('K', 'kappa(T)'); model.material('mat1').propertyGroup('KG').setPropertyInfo('K', ['Reference: N.J. Simon, E.S. Drexler, and R.P. Reed, "Properties of Copper and Copper Alloys at Cryogenic Temperatures", NIST Monograph 177 (1992) https://nvlpubs.nist.gov/nistpubs/Legacy/MONO/nistmonograph177.pdf; H.M. Ledbetter, "Elastic constants of polycrystalline copper at low temperatures. Relationship to single-crystal elastic constants", Physica Status Solidi (a), v66, p477 (1981) https://doi.org/10.1002/pssa.2210660209; H.M. Ledbetter and E.R. Naimon, "Elastic Properties of Metals and Alloys. II. Copper", Journal of Physical and Chemical Reference Data, v3, No. 4, p897 (1974) https://srd.nist.gov/jpcrdreprint/1.3253150.pdf' newline 'Note: T' native2unicode(hex2dec({'00' '98'}), 'unicode') native2unicode(hex2dec({'00' '9a'}), 'unicode') ' = 1083 ' native2unicode(hex2dec({'00' 'b0'}), 'unicode') 'C (1356 K), calculated from E and v, errors may be large']); model.material('mat1').propertyGroup('KG').func.create('mu', 'Piecewise'); model.material('mat1').propertyGroup('KG').func('mu').set('funcname', 'mu'); model.material('mat1').propertyGroup('KG').func('mu').set('arg', 'T'); model.material('mat1').propertyGroup('KG').func('mu').set('extrap', 'constant'); model.material('mat1').propertyGroup('KG').func('mu').set('pieces', {'4.0' '1330.0' '5.208306E10-2585817.0*T^1-71978.63*T^2+110.2355*T^3-0.07807297*T^4+2.043615E-5*T^5'}); model.material('mat1').propertyGroup('KG').func('mu').label('Piecewise'); model.material('mat1').propertyGroup('KG').func('mu').set('fununit', 'Pa'); model.material('mat1').propertyGroup('KG').func('mu').set('argunit', 'K'); model.material('mat1').propertyGroup('KG').func.create('kappa', 'Piecewise'); model.material('mat1').propertyGroup('KG').func('kappa').set('funcname', 'kappa'); model.material('mat1').propertyGroup('KG').func('kappa').set('arg', 'T'); model.material('mat1').propertyGroup('KG').func('kappa').set('extrap', 'constant'); model.material('mat1').propertyGroup('KG').func('kappa').set('pieces', {'4.0' '1330.0' '1.459784E11+4948257.0*T^1-132451.5*T^2+114.0737*T^3+0.02475104*T^4-9.178407E-5*T^5+3.51125E-8*T^6'}); model.material('mat1').propertyGroup('KG').func('kappa').label('Piecewise 1'); model.material('mat1').propertyGroup('KG').func('kappa').set('fununit', 'Pa'); model.material('mat1').propertyGroup('KG').func('kappa').set('argunit', 'K'); model.material('mat1').propertyGroup('KG').addInput('temperature'); model.material('mat1').set('family', 'copper'); model.physics('solid').create('fix1', 'Fixed', 2); model.physics('solid').feature('fix1').selection.set([2]); model.physics('solid').create('pl1', 'PointLoad', 0); model.physics('solid').feature('pl1').selection.set([3]); model.physics('solid').feature('pl1').set('forcePoint', [0 0 -500]); model.mesh('mesh1').create('ftet1', 'FreeTet'); model.mesh('mesh1').feature('size').set('hauto', 9); model.mesh('mesh1').run; model.mesh('mesh1').feature('size').set('custom', true); model.mesh('mesh1').feature('size').set('hmax', 1); model.mesh('mesh1').run; model.mesh('mesh1').feature('size').set('hmax', 2); model.mesh('mesh1').run; model.study('std1').createAutoSequences('all'); model.sol('sol1').runAll; model.result.create('pg1', 'PlotGroup3D'); model.result('pg1').set('data', 'dset1'); model.result('pg1').label('Stress (solid)'); model.result('pg1').set('frametype', 'spatial'); model.result('pg1').create('vol1', 'Volume'); model.result('pg1').feature('vol1').set('expr', {'solid.misesGp'}); model.result('pg1').feature('vol1').set('threshold', 'manual'); model.result('pg1').feature('vol1').set('thresholdvalue', 0.2); model.result('pg1').feature('vol1').set('colortable', 'Rainbow'); model.result('pg1').feature('vol1').set('colortabletrans', 'none'); model.result('pg1').feature('vol1').set('colorscalemode', 'linear'); model.result('pg1').feature('vol1').set('resolution', 'custom'); model.result('pg1').feature('vol1').set('refine', 2); model.result('pg1').feature('vol1').set('colortable', 'Prism'); model.result('pg1').feature('vol1').create('def', 'Deform'); model.result('pg1').feature('vol1').feature('def').set('expr', {'u' 'v' 'w'}); model.result('pg1').feature('vol1').feature('def').set('descr', 'Displacement field'); model.result('pg1').run; out = model;