Auricchio F., Petr<strong>in</strong>i F., Extension and solution algorithm for a three-<strong>di</strong>mensionalmodel for stress-<strong>in</strong>duced solid phase transformations, International Journal forNumerical Methods <strong>in</strong> Eng<strong>in</strong>eer<strong>in</strong>g, 55, 1255-1284, 2002.Auricchio F., Petr<strong>in</strong>i L., A three <strong>di</strong>mensional model describ<strong>in</strong>g stress-temperature<strong>in</strong>duced solid phase transformations: solution algorithm and boundary valueproblems, International Journal for Numerical Methods <strong>in</strong> Eng<strong>in</strong>eer<strong>in</strong>g, 61, 807-836, 2004.Auricchio F., Reali A., <strong>Shape</strong> <strong>Memory</strong> <strong>Alloys</strong>: material modell<strong>in</strong>g and Device <strong>F<strong>in</strong>ite</strong>element simulations, Materials Science Forum, 583, 257-275, 2008.Auricchio F., Sacco E., A superelastic shape-memory alloy beam model, Journal ofIntelligent Material Systems and Structures, 8, 489-501, 1997.Auricchio F., Sacco E., A one-<strong>di</strong>mensional model for superelastic shape-memoryalloys with <strong>di</strong>fferent elastic properties between austenite and martensite,International Journal of Non-L<strong>in</strong>ear Mechanics, 32, 1101-1114, 1997.Auricchio F., Sacco E., A temperature-dependant beam for shape-memory alloys:constitutive modell<strong>in</strong>g, f<strong>in</strong>ite-element implementation and numerical simulations,Computer Methods <strong>in</strong> Applied Mechanics and Eng<strong>in</strong>eer<strong>in</strong>g, 174, 171-190, 1999.Auricchio F., Sacco E., On the thermo-mechanical response of a superelastic shapememorywire under cyclic stretch<strong>in</strong>g-ben<strong>di</strong>ng loa<strong>di</strong>ngs, Journal of InternationalJournal of Solids and Structures, 38, 6123-6145, 2001.Auricchio F., Taylor R., <strong>Shape</strong>-memory alloys: modell<strong>in</strong>g and numerical simulationsof the f<strong>in</strong>ite-stra<strong>in</strong> superelastic behavior, Computer Methods <strong>in</strong> AppliedMechanics and Eng<strong>in</strong>eer<strong>in</strong>g, 143, 175-194, 1997.162
Auricchio F., Taylor R., A return-map algorithm for general associative isotropicelasto-plastic materials <strong>in</strong> large deformation regimes, International Journal ofPlasticity, 15, 1359-1378, 1999.Auricchio F., Taylor R., Lubl<strong>in</strong>er J., <strong>Shape</strong>-memory alloys: macromodell<strong>in</strong>g andnumerical simulations of the superelastic behavior, Computer Methods <strong>in</strong> AppliedMechanics and Eng<strong>in</strong>eer<strong>in</strong>g, 146, 281-312, 1997.Barret D.J., A one-<strong>di</strong>mensional constitutive model for shape-memory alloys, Journalof Intelligent Materials Systems and Structures, 6, 329-337, 1995.Barret D.J., Sullivan B.J., A three-<strong>di</strong>mensional phase transformation model forshape-memory alloys, Journal of Intelligent Materials Systems and Structures, 6,831-839, 1995.Bathe K.J., <strong>F<strong>in</strong>ite</strong> element procedures <strong>in</strong> eng<strong>in</strong>eer<strong>in</strong>g analysis. Prentice-Hall, 1982.Bo Z., Lagoudas D., Thermomechanical model<strong>in</strong>g of polycrystall<strong>in</strong>e SMA undercyclic loa<strong>di</strong>ng. Part II. Material characterization and experimental results for astable transformation cycle, International Journal of Eng<strong>in</strong>eer<strong>in</strong>g Science, 37,1141-1173, 1999a.Bo Z., Lagoudas D., Thermomechanical model<strong>in</strong>g of polycrystall<strong>in</strong>e SMA undercyclic loa<strong>di</strong>ng. Part III. Evolution of plastic stra<strong>in</strong>s and two-way shape memoryeffect, International Journal of Eng<strong>in</strong>eer<strong>in</strong>g Science, 37, 1175-1203, 1999b.Bo Z., Lagoudas D., Thermomechanical model<strong>in</strong>g of polycrystall<strong>in</strong>e SMA undercyclic loa<strong>di</strong>ng. Part VI. <strong>Model<strong>in</strong>g</strong> of m<strong>in</strong>or hysteresis loops, International Journalof Eng<strong>in</strong>eer<strong>in</strong>g Science, 37, 1205-1249, 1999c.163
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University of CassinoFaculty of Eng
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Contents1. INTRODUCTION ...........
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5.2.1.2. Finite Element Approximati
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1 INTRODUCTIONScience and technolog
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The implementations of the model in
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applications are presented in order
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2 SHAPE MEMORY ALLOYS2.1 Introducti
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transformation (M→A), indicated r
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Fig. 2.2: SuperelasticityFig. 2.3:
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The Differential Scanning Calorimet
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2.3 Biocompatibility of Shape-Memor
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only in the angioplasty procedure,
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micropumps used to unblock blood ve
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introduction of a multi-well free-e
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spectral decomposition allowing the
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Fig. 3.1: Reference and deformed co
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δ δ = δ and δ δ = δ(3.6)iI iJ
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and it is a two-point tensor since
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Furthermore,( ) 2 2Jdet b= det F =
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3.2.3 Polar DecompositionThe deform
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which can now be interpreted as fir
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Fig. 3.2: Representation of the pol
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ecause, as time progresses, the spe
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It can be introduced the rotated ra
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traction vector. For the Cauchy’s
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Nt per unit area acting on the boun
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transforms according to a= Qa. Velo
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∂∂t=−∂F∂t−1 −1 −1F
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where the direct dependency upon X
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3.4.2 Isotropic Hyperelasticity - M
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such phenomena as the Bauschinger e
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superposed to intermediate configur
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whereΨerepresents the elastic stra
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( )( ) E 1 ( )Ψ = h ω β T − M
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4.2.2 Clausius-Duhem InequalityIn o
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−1∂Ψe−TS− 2FtFt= 0∂Ce(4.
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qφ = T : dt− ⋅gradT≥0(4.30)T
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fact the values of ϕ andenergy usu
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4.2.5 Final Format of the Constitut
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1 ( C )*1t−1α = ( β T − M ( )
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5 FINITE STRAIN CONSTITUTIVE MODEL:
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2 3ζ 2 ζ 3exp( ζ g) = 1+ ζ g+ g
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where d is a user-defined parameter
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⎡R R Rt⎢⎢RR Rt⎢⎣R R RtC C
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γ• R,Ct=12EEtt(5.28)• R γ ,
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The spatial virtual work equation s
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[ E E E 2 E 2 E 2 E ]δE = δ δ δ
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ˆNLB = B + B (5.51)a a ain whichBa
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Kirchhoff stress and converting int
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DF( φ)[ u]d=dεε = 0( φ εu)∂
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In terms of the linear strain tenso
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6.2 3D Constitutive Model for Stres
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T − Mf Tη = η0− ⎡⎣h( ω)
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assumed to be ruled by the limit fu
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♦The limit function is assumed fu
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6.3.1.1 Time Integration of the 3D
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⎧∂f∂ ε⎪ C ⎡⎤⎣ ⎦⎪
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- Page 121 and 122: 7 3D-1D Constitutive Model with 1D
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- Page 127 and 128: (7.21)σ3 1.5R=− βc( T − Mf)+2
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- Page 151 and 152: PhLFig. 8.7: Geometry and boundary
- Page 153 and 154: 250200150100Axial force [N]500-50-1
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- Page 167: REFERENCESAdler P.H., Yu W., Pelton
- Page 171 and 172: Ciarlet P.G., The Finite Element Me
- Page 173 and 174: Huang M.S., Brinson L.C., A multiva
- Page 175 and 176: Raniecki B., Lexcellent Ch., Thermo
- Page 177: Taylor G.I., Plastic strain in meta