Finite Strain Shape Memory Alloys Modeling - Scuola di Dottorato in ...

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Simo J.C., Marsden J.E., On the Rotated Stress Tensor and the Material Version ofthe Doyle-Ericksen Formula, Archive for Rotational Mechanics and Analysis,104, 125-183, 1984.Simo J.C., A framework for finite strain elastoplasticity based on maximum plasticdissipation and the multiplicative decomposition: Part I. Continuum formulation,Computer Methods in Applied Mechanics and Engineering, 66, 199-219, 1998a.Simo J.C., A framework for finite strain elastoplasticity based on maximum plasticdissipation and the multiplicative decomposition: Part II. Computational Aspects,Computer Methods in Applied Mechanics and Engineering, 68, 1-31, 1998b.Souza A.C., Mamiya E.N., Zouain N.. Three-dimensional model for solidsundergoing stress-induced phase transformations. European Journal of MechanicsA/Solids, 17, 789-806, 1998.Suquet P., Local and global aspect in the mathematical theory of plasticity, Plastcitytoday: modeling, Methods and aopplications. Elsevier, London, 279-310, 1985.Tanaka K., A thermomechanical sketch of shape-memory effect: one dimensionaltensile behavior, Res. Mechanica, 18, 251-263, 1986.Tanaka K., Hayashi T., Itoh Y., Tobushi H., Analysis of thermomechanical behaviorof shape-memory alloys, Mechanics of Materials, 13, 207-215, 1992.Tanaka K., Kobayashi S., Soto Y., Thermomechanics of transformationpseudoelasticity and shape-memory effect in alloys, Internation Journal ofPlasticity, 2, 59-72, 1986.170
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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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RRRRRRRR*( f )2 2 2Xd, X= I+ hΔ ζ
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If equation (6.42) is considered as
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7 3D-1D Constitutive Model with 1D
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*∂f6 3σ9 3 2 2 T Ml− hϑ+mz β
Page 125 and 126: ⎡⎤⎢1 0 0 ⎥⎢⎥1ε t= ϑ
Page 127 and 128: (7.21)σ3 1.5R=− βc( T − Mf)+2
Page 129 and 130: It is interesting to evaluate how m
Page 131 and 132: It can be noted that equations (7.3
Page 133 and 134: The inelastic step is solved by the
Page 135 and 136: For brevity, only the saturated pha
Page 137 and 138: Fig. 7.2. Timoshenko’s beam theor
Page 139 and 140: NNNv1v2v3N θ1= ξξ ( − 1)21= ξ
Page 141 and 142: to analyze the two-dimensional elem
Page 143 and 144: 300 N . A regular mesh characterize
Page 145 and 146: 8.1.1.3 Superelastic and Shape-Memo
Page 147 and 148: 200180T=285 K160140120Force [N]1008
Page 149 and 150: 8.1.2 Comparison between 3D and 3D-
Page 151 and 152: PhLFig. 8.7: Geometry and boundary
Page 153 and 154: 250200150100Axial force [N]500-50-1
Page 155 and 156: 908070Bending moment [Nmm]605040302
Page 157 and 158: The arch is subjected to tension-co
Page 159 and 160: 10864Axial force [N]20-2-4-6-8beam
Page 161 and 162: Some parameters characterizing the
Page 163 and 164: 9876Applied load [N]54321Numerical
Page 165 and 166: The proposed constitutive models se
Page 167 and 168: REFERENCESAdler P.H., Yu W., Pelton
Page 169 and 170: Auricchio F., Taylor R., A return-m
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: Raniecki B., Lexcellent Ch., Thermo
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