Abstract
Solids subject to continuous changes of temperature or mechanical load often exhibit discontinuous avalanche-like responses. For instance, avalanche dynamics have been observed during plastic deformation , fracture, domain switching in ferroic materials or martensitic transformations. The statistical analysis of avalanches reveals a very complex scenario with a distinctive lack of characteristic scales. Much effort has been devoted in the last decades to understand the origin and ubiquity of scale-free behaviour in solids and many other systems. This chapter reviews some efforts to understand the characteristics of avalanches in martensites through mathematical modelling.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
A snap-spring in elastic materials can be viewed as the analogue of a spin in magnetic materials.
- 2.
Meaning that the boundaries of the neighbourhood do not belong to the neighbourhood itself.
- 3.
Typical states have magnetisation m that can be represented by an exponentially large number of microscopic spin configurations, \(\mathbf {s}\).
- 4.
See [76] for an explicit calculation of the spin-spin correlation function near the OD transition.
References
D.M. Dimiduk, C. Woodward, R. Lesar, M.D. Uchic, Scale-free intermittent flow in crystal plasticity. Science (New York) vol. 312, pp. 1188–1190. (2006). ISSN: 0036-8075
M.C. Miguel, A. Vespignani, S. Zapperi, J. Weiss, J.R. Grasso, Intermittent dislocation flow in viscoplastic deformation. Nature 410, 667–671 (2001)
A. Petri, G. Paparo, A. Vespignani, A. Alippi, M. Costantini, Experimental evidence for critical dynamics in microfracturing processes. Phys. Rev. Lett. 73, 3423–3426 (1994). ISSN: 0031-9007
J. Baró et al., Statistical similarity between the compression of a porous material and earthquakes. Phys. Rev. Lett. 110(8), 088702 (2013). doi:10.1103/PhysRevLett.110.088702
G. Bertotti, I.D. Mayergoyz, G. Durin, S. Zapperi, The Science of Hysteresis (Elsevier, Amsterdam, 2006), pp. 181–267. doi:10.1016/B978-012480874-4/50014-2. http://www.sciencedirect.com/science/article/pii/B9780124808744500142
E.K. Salje, K.A. Dahmen, Crackling Noise in Disordered Materials. Annu. Rev. Condens. Matter Phys. 5, 233–254 (2014). ISSN: 1947–5454
E. Vives et al., Distributions of avalanches in martensitic transformations. Phys. Rev. Lett. 72, 1694–1697 (1994). ISSN: 0031-9007
F.-J. Pérez-Reche, B. Tadić, L. Mañosa, A. Planes, E. Vives, Driving rate effects in Avalanche-mediated first-order phase transitions. Phys. Rev. Lett. 93, 195701 (2004). ISSN: 0031-9007
U. Chandni, A. Ghosh, H.S. Vijaya, S. Mohan, Criticality of Tuning in Athermal Phase Transitions. Phys. Rev. Lett. 102, 25701 (2009)
M. Carmen Gallardo et al., Avalanche criticality in the martensitic transition of \(\rm Cu\mathit{_{67.64}\rm Zn}_{16.71}\rm Al_{15.65}\) shape-memory alloy: A calorimetric and acoustic emission study. Phys. Rev. B 81, 174102 (2010). ISSN: 1098-0121
X. Balandraud, N. Barrera, P. Biscari, M. Grédiac, G. Zanzotto, Strain intermittency in shape-memory alloys. Phys. Rev. B 91, 174111 (2015)
Y. Ben-Zion, Collective behavior of earthquakes and faults: Continuumdiscrete transitions, progressive evolutionary changes, and different dynamic regimes. Rev. Geophys. 46, RG4006 (2008). ISSN: 8755-1209
D. Sornette, Why Stock Markets Crash (Princeton University Press, Princeton, 2003)
R.V. Solé, S.C. Manrubia, M. Benton, P. Bak, Self-similarity of extinction statistics in the fossil record. Nature 388, 764–767 (1997). ISSN: 0028-0836
C.J. Rhodes, H.J. Jensen, R.M. Anderson, On the critical behaviour of simple epidemics. Proceedings. Biological sciences. R. Soc. 264, 1639–1646 (1997). ISSN: 0962-8452
D. Plenz (ed.), Criticality in Neural Systems (Wiley, New York, 2014). doi:10.1002/9783527651009. http://onlinelibrary.wiley.com/book/10.1002/9783527651009. ISBN: 9783527651009
F. Ginelli et al., Intermittent collective dynamics emerge from conflicting imperatives in sheep herds, in Proceedings of the National Academy of Sciences, 12729–12734 (2015). ISSN: 0027-8424
M.E.J. Newman, Power laws, Pareto distributions and Zipf’s law. Contemp. Phys. 46, 323–351 (2004)
L. Gil, D. Sornette, Landau-Ginzburg theory of self-organized criticality. Phys. Rev. Lett. 76, 3991–3994 (1996)
H.L.D. de S Cavalcante, M. Oriá, D. Sornette, E. Ott, D.J. Gauthier, Predictability and suppression of extreme events in a chaotic system. Phys. Rev. Lett. 111, 198701 (2013)
H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, New York, 1983)
N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, Reading, MA, 1992)
J. Cardy, Scaling and Renormalization in Statistical Physics (Cambridge University Press, Cambridge, 1996)
P. Bak, How Nature Works: the science of self-organized criticality (Oxford University Press, Oxford, 1997)
J.P. Sethna, K.A. Dahmen, C.R. Myers, Crackling noise. Nature 410, 242–250 (2001). ISSN: 0028-0836
D.S. Fisher, Collective transport in random media: from superconductors to earthquakes. Phys. Rep. 301, 113–150 (1998). ISSN: 03701573
F.-J. Pérez-Reche, L. Truskinovsky, G. Zanzotto, Training-Induced Criticality in Martensites. Phys. Rev. Lett. 99, 075501 (2007). ISSN: 0031-9007
F.J. Pérez-Reche, C. Triguero, L. Truskinovsky, G. Zanzotto, Origin of scale-free intermittency in structural first-order phase transitions. arXiv:1606.00607 (2016)
K. Otsuka, C.M. Wayman (eds.), Shape Memory Materials (Cambridge University Press, Cambridge, 1998)
L. Mañosa, A. Planes, M. Acet, Advanced materials for solid-state refrigeration. J. Mat. Chem. A 1, 4925 (2013). ISSN: 2050-7488
J, Christian, The theory of transformations in metals and alloys, pp. 1102–1113 (Elsevier, Amsterdam, 2012). doi:10.1016/B978-008044019-4/50031-3. http://www.sciencedirect.com/science/article/pii/B9780080440194500313. ISBN: 9780080440194
G. Bertotti, I.D. Mayergoyz, J. Ortin, A. Planes, A, L. Delaey, The Science of Hysteresis, pp. 467–553 (Elsevier, Amsterdam, 2006). doi:10.1016/B978-012480874-4/50023-3. http://www.sciencedirect.com/science/article/pii/B9780124808744500233. ISBN: 9780124808744
L. Carrillo, L. Mañosa, J. Ortín, A. Planes, E. Vives, Experimental Evidence for Universality of Acoustic Emission Avalanche Distributions during Structural Transitions. Phys. Rev. Lett. 81, 1889–1892 (1998)
J. Baró, E. Vives, Analysis of power-law exponents by maximum-likelihood maps. Phys. Rev. E 85, 066121 (2012)
L. Carrillo, J. Ortín, Avalanches in the growth of stress-induced martensites. Phys. Rev. B 56, 11508 (1997). ISSN: 0163–1829
R.J. Harrison, E.K.H. Salje, The noise of the needle: Avalanches of a single progressing needle domain in LaAlO[sub\(_3\)]. Appl. Phys. Lett. 97, 021907 (2010). ISSN: 00036951
R. J. Harrison, E.K.H. Salje, Ferroic switching, avalanches, and the Larkin length: Needle domains in LaAlO3. Appl. Phys. Lett. 99, 1077–3118 (2011). ISSN: 0003-6951
E.K.H. Salje, X. Ding, Z. Zhao, T. Lookman, A. Saxena, Thermally activated avalanches: Jamming and the progression of needle domains. Phys. Rev. B 83, 104109 (2011)
X. Ding et al., Dynamically strained ferroelastics: Statistical behavior in elastic and plastic regimes. Phys. Rev. B 87, 094109 (2013)
E. Vives, J. Goicoechea, J. Ortín, A. Planes, Universality in models for disorder-induced phase transitions. Phys. Rev. E 52, R5–R8 (1995). ISSN: 1063-651X
J. Goicoechea, J.A. Ortín, Random field 3-State spin model to simulate hysteresis and avalanches in martensitic transformations. J. Phys. IV 5, C2-71–C2-76 (1995)
S.R. Shenoy, T. Lookman, Strain pseudospins with power-law interactions: Glassy textures of a cooled coupled-map lattice. Phys. Rev. B 78, 144103 (2008)
R. Vasseur, T. Lookman, Effects of disorder in ferroelastics: A spin model for strain glass. Phys. Rev. B 81, 094107 (2010)
D. Sherrington, in Disorder and Strain-Induced Complexity in Functional Materials, ed. by T. Kakeshita, T. Fukuda, A. Saxena, A. Planes (Springer, Heidelberg, 2012), pp. 177–199. doi:10.1007/978-3-642-20943-7-10. ISBN: 978-3-642-20943-7
B. Cerruti, E. Vives, Random-field Potts model with dipolarlike interactions:hysteresis, avalanches, and microstructure. Phys. Rev. B 77, 064114 (2008). ISSN: 1098-0121
H. Ji et al., M.O. Robbins, Percolative, self-affine, and faceted domain growth in random three-dimensional magnets. Phys. Rev. B 46, 14519 (1992). ISSN: 0163-1829
J.P. Sethna et al., Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations. Phys. Rev. Lett 70, 12 (1993). ISSN: 0031-9007
F.J. Pérez-Reche et al., Kinetics of martensitic transitions in Cu-Al-Mn under thermal cycling: Analysis at multiple length scales. Phys. Rev. B 69, 064101 (2004). ISSN: 1098-0121
F.J. Pérez-Reche, E. Vives, L. Mañosa, A. Planes, Acoustic emission studyof martensitic transition kinetics in Cu-based shape-memory alloys. J. Phys. IV 112, 597–600 (2003)
G. Krauss, Fine structure of austenite produced by the reverse martensitic transformation. Acta Metall. 11, 499–509 (1963). ISSN: 00016160
J. Pons, F. Lovey, E. Cesari, Electron microscopy study of dislocations associated with thermal cycling in a CuZnAl shape memory alloy. Acta Metallurgica et Materialia 38, 2733–2740 (1990). ISSN: 09567151
T. Simon, A. Kröger, C. Somsen, A. Dlouhy, G. Eggeler, n the multiplication of dislocations during martensitic transformations in NiTi shape memory alloys. Acta Materialia 58, 1850–1860 (2010). ISSN: 13596454
D.M. Norfleet et al., Transformation-induced plasticity during pseudoelastic deformation in Ni-Ti microcrystals. Acta Materialia 57, 3549–3561 (2009). ISSN: 1359-6454
F.J. Pérez-Reche, L. Truskinovsky, G. Zanzotto, Martensitic transformations: from continuum mechanics to spin models and automata. Contin. Mech. Thermodyn. 21, 17–26 (2009). ISSN: 0935-1175
F.J. Pérez-Reche, L. Truskinovsky, G. Zanzotto, Driving-induced crossover: From classical criticality to self-organized criticality. Phys. Rev. Lett. 101, 230601 (2008). ISSN: 00319007
J.L. Ericksen, Some phase transitions in crystals. Arch. Ration. Mech. Anal. 73, 99–124 (1980). ISSN: 0003-9527
I. Folkins, Functions of two-dimensional Bravais lattices. J. Math. Phys. 32, 1965 (1991). ISSN: 00222488
M. Pitteri, G. Zanzotto, Continuum Models for Phase Transitions and Twinning in Crystals (Chapman & Hall/CRC, Boca Raton, 2003)
S. Conti, G. Zanzotto, A variational model for reconstructive phase transformations in crystals, and their relation to dislocations and plasticity. Arch. Ration. Mech. Anal. 173, 69–88 (2004)
K. Bhattacharya, Microestructure of Martensite: Why it Forms and How it Gives Rise to the Shape-Memory Effect (Oxford University Press, Oxford, 2003)
K. Bhattacharya, S. Conti, G. Zanzotto, J. Zimmer, Crystal symmetry and the reversibility of martensitic transformations. Nature (London) 428, 55–59 (2004)
G. Bertotti, I.D. Mayergoyz, J.P. Sethna, K.A. Dahmen, O. Perkovic, The Science of Hysteresis (Elsevier, Amsterdam, 2006), pp. 107–179. doi:10.1016/B978-012480874-4/50013-0. http://www.sciencedirect.com/science/article/pii/B9780124808744500130. ISBN: 9780124808744
B. Koiller, M.O. Robbins, Morphology transitions in three-dimensional domain growth with Gaussian random fields. Phys. Rev. B 62, 5771–5778 (2000). ISSN: 0163-1829
E. Kierlik, P.A. Monson, M.L. Rosinberg, L. Sarkisov, G. Tarjus, Capillary vcondensation in disordered porous materials: hysteresis versus equilibrium behavior. Phys. Rev. Lett. 87, 055701 (2001). ISSN: 0031-9007
T.P. Handford, F.J. Pérez-Reche, S.N. Taraskin, Capillary condensation in one-dimensional irregular confinement. Phys. Rev. E 88, 012139 (2013)
Q. Michard, J.P. Bouchaud, Theory of collective opinion shifts: From smooth trends to abrupt swings. Europ. Phys. J. B 47, 151–159 (2005). ISSN: 14346028
J.S. Urbach, R.C. Madison, J.T. Markert, Interface depinning, Self- organized criticality, and the Barkhausen effect. Phys. Rev. Lett. 75, 276–279 (1995). ISSN: 0031-9007
F.J. Pérez-Reche, E. Vives, Spanning avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics: Field dependence and geometrical properties. Phys. Rev. B 70, 214422 (2004). ISSN: 1098-0121
M. C. Kuntz, J.P. Sethna, Noise in disordered systems: The power spectrum and dynamic exponents in avalanche models. Phys. Rev. B 62, 11699–11708 (2000). ISSN: 01631829
J.H. Carpenter, K.A. Dahmen, A.C. Mills, M.B. Weissman, Historyinduced critical bahavior in disordered systems. Phys. Rev. B 72, 052410 (2005)
R. Dickman, M.A. Muñoz, A. Vespignani, S. Zapperi, Paths to Self- Organized Criticality. Braz. J. Phys. 30, 27 (2000)
M. Alava, Scaling in self-organized criticality from interface depinning. J. Phys.: Condens. Matter 14, 2353–2360 (2002)
K. Dahmen, J.P. Sethna, Hysteresis, avalanches, and disorder-induced critical scaling: A renormalization-group approach. Phys. Rev. B 53, 14872 (1996). ISSN: 0163-1829
O. Perković, K.A. Dahmen, J. P. Sethna, Disorder-induced critical phenomena in hysteresis: Numerical scaling in three and higher dimensions. Phys. Rev. B 59, 6106–6119 (1999). ISSN: 0163-1829
S. Sabhapandit, P. Shukla, D. Dhar, Distribution of Avalanche sizes in the hysteretic response of random field ising model on a Bethe lattice at zero temperature. J. Stat. Phys. 98, 103–129 (1999). ISSN: 00224715
T.P. Handford, F.-J. Perez-Reche, S.N. Taraskin, Exact spinspin correlation function for the zero-temperature random-field ising model. J. Stat. Mech.: Theor. Exp. 2012, P01001 (2012)
T.P. Handford, F.J. Pérez-Reche, S.N. Taraskin, Mechanisms of evolution of avalanches in regular graphs. Phys. Rev. E 87, 062122 (2013)
T.P. Handford, F.J. Pérez-Reche, S.N. Taraskin, Zero-temperature random-field Ising model on a bilayered Bethe lattice. Phys. Rev. E 88, 022117 (2013)
I. Balog, M. Tissier, G. Tarjus, Same universality class for the critical behavior in and out of equilibrium in a quenched random field. Phys. Rev. B 89, 104201 (2014). ISSN: 10980121
F.J. Pérez-Reche, E. Vives, Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics. Phys. Rev. B 67, 134421 (2003)
I. Müller, P. Villaggio, A model for an elastic-plastic body. Arch. Rat. Mech. Anal. 65, 25–46 (1977)
I, Müller, A model for a body with shape-memory. Arch. Ration. Mech. Anal. 70 (1979). doi:10.1007/BF00276382. http://link.springer.com/10.1007/BF00276382. ISSN: 0003-9527
B. Fedelich, G. Zanzotto, Hysteresis in discrete systems of possibly interacting elements with a double-well energy. J. Nonlinear Sci. 2, 319–342 (1992)
G. Puglisi, L. Truskinovsky, Mechanics of a discrete chain with bi-stable elements. J. Mech. Phys. Solids 48, 1–27 (2000)
L. Truskinovsky, A. Vainchtein, About the origin of the nucleation peak in transformational plasticity. J. Mech. Phys. Solids 52, 1421–1446 (2004)
G.Puglisi, Hysteresis in multi-stable lattices with non-local interactions. J. Mech. Phys. Solids 54, 2060–2088 (2006). ISSN: 00225096
E.K.H. Salje, Phase transitions in ferroelastic and co-elastic crystals (Cambridge University Press, Cambridge, 1993)
E.K.H. Salje, Ferroelastic Materials. Annu. Rev. Mater. Res. 42, 265–283 (2012)
A.E. Jacobs, Solitons of the square-rectangular martensitic-transformation. Phys. Rev. B 31, 5984–5989 (1985). ISSN: 1550-235X
S. Shenoy, T. Lookman, A. Saxena, A. Bishop, Martensitic textures: Multiscale consequences of elastic compatibility. Phys. Rev. B 60, R12537–R12541 (1999). ISSN: 0163-1829
T. Lookman, S.R. Shenoy, K.O. Rasmussen, A.R. Saxena, A. Bishop, Ferroelastic dynamics and strain compatibility. Phys. Rev. B 67, 024114 (2002). ISSN: 0163-1829
R. Ahluwalia, G. Ananthakrishna, Power-law statistics for Avalanches in a martensitic transformation. Phys. Rev. Lett. 86, 4076–4079 (2001)
P. Lloveras, T. Castán, M. Porta, A. Planes, A. Saxena, Influence of elastic anisotropy on structural nanoscale textures. Phys. Rev. Lett. 100, 165707 (2008)
M. Pitteri, Reconciliation of local and global symmetries of crystals. J. Elast. 14, 175–190 (1984)
J.M. Ball, R.D. James, Proposed experimental tests of a theory of fine microstructure and the two-well problem. Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 338, 389–450 (1992). ISSN: 1364-503X
P. Tolédano, V. Dmitriev, Reconstructive Phase Transitions (World Scientific, Singapore, 1996)
D.M. Hatch, T. Lookman, A. Saxena, H.T. Stokes, Systematics of groupnonsubgroup transitions: Square to triangle transition. Phys. Rev. B 64, 060104 (2001). ISSN: 0163-1829
V. Dmitriev, S. Rochal, Y. Gufan, P. Toledano, Definition of a transcendental order parameter for reconstructive phase transitions. Phys. Rev. Lett. 60, 1958–1961 (1988). ISSN: 1079-7114
S. Shenoy, T. Lookman, A. Saxena, in Magnetism and Structure in Functional Materials, ed. by A. Planes, L. Mañosa, A. Saxena (Springer, Berlin, 2005). doi:10.1007/3-540-31631-2
O.U. Salman, L. Truskinovsky, Minimal Integer Automaton behind Crystal Plasticity. Phys. Rev. Lett. 106, 175503 (2011)
O.U. Salman, L. Truskinovsky, On the critical nature of plastic flow: One and two dimensional models. Int. J. Eng. Sci. 59, 219–254 (2012). ISSN: 00207225
D. Rodney, A. Tanguy, D. Vandembrouc, Modeling the mechanics of amorphous solids at different length scale and time scale. Modell. Simul. Mater. Sci. Eng. 19, 083001 (2011). ISSN: 0965-0393
M. Braun, Compatibility conditions for discrete elastic structures. Rendiconti del Seminario Matematico 58, 37–48. ISSN: 0373-1243
X. Balandraud, G. Zanzotto, Stressed microstructures in thermally induced M9R-M18R martensites. J. Mech. Phys. Solids 55, 194–224 (2007). ISSN: 00225096
T. Kakeshita, T. Fukuda, A. Saxena, A. Planes (eds.), Disorder and Strain-Induced Complexity in Functional Materials (Springer, Berlin, 2012). doi:10.1007/978-3-642-20943-7. ISBN: 978-3-642- 20943-7
S. Kartha, T. Castán, J. Krumhansl, J. Sethna, Spin-glass nature of tweed precursors in martensitic transformations. Phys. Rev. Lett. 67, 3630–3633 (1991). ISSN: 1079-7114
S. Kartha, J.A. Krumhansl, J.P. Sethna, L.K. Wickham, Disorder-driven pretransitional tweed pattern in martensitic transformations. Phys. Rev. B 52, 803–822 (1995)
D. Wang, Y. Wang, Z. Zhang, X. Ren, Modeling abnormal strain states in ferroelastic systems: the role of point defects. Phys. Rev. Lett. 105, 205702 (2010). ISSN: 1079-7114
D. Sherrington, A simple spin glass perspective on martensitic shape-memory alloys. J. Phys. Condens. Matter 20, 304213 (2008)
R. Gröger, T. Lookman, A. Saxena, Defect-induced incompatibility of elastic strains: dislocations within the Landau theory of martensitic phase transformations. Phys. Rev. B 78, 184101 (2008)
R. Gröger, T. Lookman, A. Saxena, Incompatibility of strains and its application to mesoscopic studies of plasticity. Phys. Rev. B 82, 144104 (2010). ISSN: 1098-0121
F.J. Pérez-Reche, E. Vives, L. Mañosa, A. Planes, Athermal character of structural phase transitions. Phys. Rev. Lett. 87, 195701 (2001). ISSN: 0031- 9007
D. Wang et al., Superelasticity of slim hysteresis over a wide temperature range by nanodomains of martensite. Acta Materialia 66, 349–359 (2014). ISSN: 13596454
E. Bonnot et al., Hysteresis in a system driven by either generalized force or displacement variables: Martensitic phase transition in single-crystalline Cu-Zn-Al. Phys. Rev. B 76, 064105 (2007). ISSN: 10980121
X. Illa, M.-L. Rosinberg, E. Vives, Influence of the driving mechanism on the response of systems with athermal dynamics: The example of the random-field Ising model. Phys. Rev. B 74, 224403 (2006). ISSN: 1098-0121
X. Illa, M.-L. Rosinberg, P. Shukla, E. Vives, Magnetization-driven random-field Ising model at T \(=\) 0. Phys. Rev. B 74, 224404 (2006). ISSN: 1098-0121
F. J. Pérez-Reche, M.L. Rosinberg, G. Tarjus, Numerical approach to metastable states in the zero-temperature random-field Ising model. Phys. Rev. B 77, 064422 (2008). ISSN: 10980121
M.L. Rosinberg, G. Tarjus, F.J. Pérez-Reche, The \(T = 0\) random-field Ising model on a Bethe lattice with large coordination number: hysteresisand metastable states. J. Stat. Mech.: Theor. Exp. 2009, P03003 (2009)
S. Nandi, G. Biroli, G.Tarjus, Spinodals with Disorder: from Avalanches in Random Magnets to Glassy Dynamics. Phys. Rev. Lett. 116, 145701 (2016)
E. Vives, D. Soto-Parra, L. Mañosa, R. Romero, A. Planes, Drivinginduced crossover in the avalanche criticality of martensitic transitions. Phys. Rev. B 80, 180101 (2009). ISSN: 1098-0121
E. Vives, D. Soto-Parra, L. Mañosa, R. Romero, A. Planes, Imaging the dynamics of martensitic transitions using acoustic emission. Phys. Rev. B 84, 060101 (2011). ISSN: 1098-0121
K. G. Wilson, The renormalization group and critical phenomena. Rev. Mod. Phys. 55, 583–600 (1983). ISSN: 00346861
M. Müller, M. Wyart, Marginal Stability in Structural, Spin, and Electron Glasses. Ann. Rev. Condens. Matter Phys. 6, 177–200 (2015)
Acknowledgments
The author is grateful to Lev Truskinovsky and Giovanni Zanzotto for an enlightening collaboration on the topics covered in this chapter. The author is also grateful for insightful discussions and/or collaboration with a number of researchers including Eduard Vives, Antoni Planes, Lluís Mañosa, Jordi Ortín, Carles Triguero, Eckhard Salje, Sergei Taraskin, Stefano Zapperi, Turab Lookman and Avadh Saxena.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Perez-Reche, F.J. (2017). Modelling Avalanches in Martensites. In: Salje, E., Saxena, A., Planes, A. (eds) Avalanches in Functional Materials and Geophysics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-45612-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-45612-6_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-45610-2
Online ISBN: 978-3-319-45612-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)