Title Page -- Contents -- Foreword -- Preface -- Chapter 1. Some General Points about SMAs -- 1.1. Introduction -- 1.2. Why are SMAs of interest for industry? -- 1.3. Crystallographic theory of martensitic transformation -- 1.4. Content of this book -- 1.4.1. State of the art in the domain and main publications -- 1.4.2. Content of this book -- Chapter 2. The World of Shape-memory Alloys -- 2.1. Introduction and general points -- 2.2. Basic metallurgy of SMAs, by Michel Morin -- 2.2.1. Copper-based shape-memory alloys -- 2.2.2. Cu-Zn-Al -- 2.2.3. Cu-Al-Ni -- 2.2.4. Cu-Al-Be -- 2.2.5. The phenomena of aging, stabilization and fatigue -- 2.2.6. Methods for copper-based SMA elaboration -- 2.2.7. Ti-Ni-based alloys -- 2.2.8. Ti-Ni alloy -- 2.2.9. Ti-Ni-X alloys -- 2.2.10. Elaboration -- 2.2.11. Shaping -- 2.2.12. Final heat treatments -- 2.2.13. Table comparing the physical and mechanical properties -- 2.2.14. Biocompatibility of SMAs -- 2.3. Measurements of phase transformation temperatures -- 2.4. Self-accommodating martensite and stress-induced martensite -- 2.5. Fatigue resistance -- 2.5.1. Causes of degradation of the properties -- 2.5.2. Fatigue of a Cu-Al-Be monocrystal -- 2.5.3. Results -- 2.6. Functional properties of SMAs -- 2.6.1. The pseudo-elastic effect -- 2.6.2. One-way shape-memory effect -- 2.6.3. Recovery stress -- 2.6.4. Double shape-memory effect: training -- 2.7. Use of NiTi for secondary batteries -- 2.8. Use of SMAs in the domain of civil engineering -- Chapter 3. Martensitic Transformation -- 3.1. Overview of continuum mechanics -- 3.1.1. Main notations for vectors -- 3.2. Main notations for matrices -- 3.3. Additional notations and reminders -- 3.3.1. Unit matrices -- 3.3.2. Rotation matrix -- 3.3.3. Symmetric matrices -- 3.3.4. Positive definite symmetric matrices -- 3.3.5. Polar decomposition -- 3.4. Kinematic description.

3.4.1. Strain gradient -- 3.4.2. Dilatation and strain tensors -- 3.4.3. Transformation of an element of volume or surface (see Figure 3.2) -- 3.5. Kinematic compatibility -- 3.6. Continuous theory of crystalline solids -- 3.6.1. Bravais lattices -- 3.6.2. Deformation of lattices and symmetry -- 3.6.3. Link between lattices and the continuous medium: Cauchy-Born hypothesis -- 3.6.4. Energy density in crystalline solids -- 3.7. Martensitic transformation -- 3.7.1. Introduction -- 3.7.2. Martensitic transformation: Bain matrix or transformation matrix -- 3.8. Equation governing the interface between two martensite variants Mi/Mj or the "twinning equation" -- 3.8.1. Cubic --> quadratic transformation -- 3.8.2. Cubic --> orthorhombic transformation -- 3.9. Origin of the microstructure -- 3.9.1. Simplified one-dimensional case -- 3.9.2. Simplified two-dimensional case -- 3.9.3. Three-dimensional case -- 3.10. Special microstructures -- 3.10.1. Austenite-martensite interface -- 3.10.2. Phenomenological theory of martensite -- 3.10.3. Crystallographic theory of martensite -- 3.11. From the scale of the crystalline lattice to the mesoscopic and then the macroscopic scale -- 3.11.1. Approach at the level of the crystalline lattice -- 3.11.2. Microscopic approach -- 3.11.3. Mesoscopic approach -- 3.11.4. Macroscopic approach -- 3.12. Linear geometric theory -- 3.12.1. Linearized kinematics -- 3.12.2. Linear geometric theory for phase transformation -- 3.12.3. Some microstructures and comparison -- 3.13. Chapter conclusion -- Chapter 4. Thermodynamic Framework for the Modeling of Solid Materials -- 4.1. Introduction -- 4.2. Conservation laws -- 4.2.1. Concept of a material system -- 4.2.2. Concept of a particulate derivative -- 4.2.3. Mass balance Lagrange variables -- 4.2.4. Motion balance equation -- 4.2.5. Energy balance: first law of thermodynamics.

4.2.6. Variation of entropy: second law of thermodynamics -- 4.3. Constitutive laws -- 4.3.1. Clausius-Duhem inequality -- Chapter 5. Use of the "CTM" to Model SMAs -- 5.1. Introduction -- 5.2. Process of reorientation of the martensite variants in a monocrystal -- 5.2.1. Internal variable model of the thermomechanical behavior of an SMA monocrystal -- 5.2.2. Experimental procedure and results obtained -- 5.2.3. Modeling of the experiments -- 5.2.4. Conclusion -- 5.3. Process of creation of martensite variants in a monocrystal: pseudoelastic behavior -- 5.3.1. Modeling the pseudoelastic behav -- 5.3.2. Traction curves -- 5.4. Prediction of the surfaces for the austenite --> martensite phase transformation -- 5.4.1. Case of a monocrystal -- 5.4.2. Case of a polycrystal -- Chapter 6. Phenomenological and Statistical Approaches for SMAs -- 6.1. Introduction -- 6.2. Preisach models -- 6.3. First-order phase transitions and Falk's model -- 6.3.1. Falk's model -- 6.3.2. Extension of Falk's model -- 6.3.3. Description of hysteresis loops -- 6.3.4. Phase domains with moving boundaries -- 6.3.5. Properties of the model and validation -- 6.4. Constitutive framework of the homogenized energy model -- 6.4.1. One-dimensional mesoscopic model -- 6.4.2. Thermal change -- 6.4.3. Macroscopic model -- 6.4.4. Performance of the model and material characterization -- 6.5. Conclusion -- Chapter 7. Macroscopic Models with Internal Variables -- 7.1. Introduction -- 7.2. RL model -- 7.2.1. Reversible R model -- 7.2.2. RL model with a hysteresis loop -- 7.2.3. Extension to reversible phase transformation: austenite ==>.R phase for NiTi -- 7.2.4. Multiaxial isothermal behavior -- 7.3. Anisothermal expansion -- 7.3.1. Kinetics of phase transformation or reorientation -- 7.3.2. Criticism of the RL approach -- 7.4. Internal variable model inspired by micromechanics.

7.4.1. Introduction -- 7.4.2. Chemisky et al.'s model -- 7.4.3. Kelly and Bhattacharya's model -- 7.4.4. Internal variable model taking account of initiation, reorientation and saturation [KEL 12, SAD 07, KEL 08] -- 7.4.5. Certain constraints on simulation and modeling -- 7.4.6. Certain ingredients of the model -- 7.4.7. Traction and compression for an isotropic material -- 7.4.8. Pure shearing of an isotropic material -- 7.4.9. Examination of the parameters for a uniaxial extension combined with shearing -- 7.4.10. Digital implantation -- 7.5. Elastohysteresis model: formalism and digital implantation -- 7.5.1. Experimentally-observed behaviors for shearing and traction/compression -- 7.5.2. Elasto-hysteresis model -- 7.5.3. Illustrations -- 7.6. Conclusion -- Chapter 8. Design of SMA Elements: Case Studies -- 8.1. Introduction -- 8.2. "Strength of materials"-type calculations for beams subject to flexion or torsion -- 8.2.1. Beam with a rectangular cross-section, subject to pure flexion: theoretical study -- 8.2.2. Experimental and theoretical validation [REJ 02] -- 8.2.3. Solving pure torsion problem: relation between the twisting torque C and the unitary angle of torsion α -- 8.3. Elements of calculations for SMA actuators -- 8.3.1. Stress/position diagram: temperature parameterization -- 8.3.2. Work provided depending on the nature of the loading -- 8.3.3. Torsion of a cylindrical wire -- 8.3.4. Flexion of a beam -- 8.3.5. Comparison of the different modes of loading -- 8.3.6. A few remarks about the duration of heating and cooling of SMAs -- 8.4. Case studies -- 8.4.1. Study of the flexion of a prismatic bar subjected to a point force -- 8.4.2. Slender tube subject to twisting torques -- 8.4.3. Study of a "parallel" hybrid structure -- 8.4.4. Study of a "series" hybrid structure -- 8.4.5. Design of an application: breakage of a mechanical link.

Chapter 9. Behavior of Magnetic SMAs -- 9.1. Introduction -- 9.2. Some models of the thermo-magneto-mechanical behavior of MSMAs -- 9.2.1. O'Handley and Murray et al.'s model -- 9.2.2. Micromagnetism -- 9.2.3. Likhachev and Ullakko's model -- 9.2.4. Original approaches -- 9.2.5. Overlaps between these approaches -- 9.3. Crystallography of Ni-Mn-Ga -- 9.3.1. The different phases and variants -- 9.3.2. Rearrangement and transformation -- 9.3.3. Calculations of microstructures -- 9.4. Model of the magneto-thermo-mechanical behavior of a monocrystal of magnetic shape-memory alloy -- 9.4.1. Expression of the Gibbs free energy associated with magneto-thermo-mechanical loading -- 9.4.2. Choice of the representative elementary volume -- 9.4.3. Expression of chemical energy -- 9.4.4. Expression of thermal energy -- 9.4.5. Expression of mechanical energy -- 9.4.6. Expression of magnetic energy -- 9.4.7. General expression of the free energy -- 9.4.8. Clausius-Duhem inequality -- 9.4.9. Kinetics of phase transformation or reorientation -- 9.4.10. Heat balance equation -- 9.4.11. Identification of the parameters -- 9.4.12. Application: creation of a "push/pull" actuator -- 9.5. Conclusion -- Chapter 10. Fracture Mechanics of SMAs -- 10.1. Introduction -- 10.2. The elastic stress field around a crack tip -- 10.2.1. Basic modes of fracture and stress intensity factors -- 10.2.2. Complex potential method for plane elasticity (the Kolosov-Muskhelishvili formulae) -- 10.2.3. Westergaard stress functions method -- 10.2.4. Solutions by the Westergaard function method -- 10.3. Prediction of the phase transformation surfaces around the crack tip (no curvature at the crack tip) [LEX 11] -- 10.3.1. Mode I -- 10.3.2. Mode II -- 10.3.3. Mode III -- 10.3.4. Mixed Mode I + II: analytical prediction of the transformation surfaces.

10.4. Prediction of the phase transformation surfaces around the crack tip (curvature ρ at the crack tip).