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Modelling Avalanches in Martensites

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Avalanches in Functional Materials and Geophysics

Part of the book series: Understanding Complex Systems ((UCS))

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.

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Notes

  1. 1.

    A snap-spring in elastic materials can be viewed as the analogue of a spin in magnetic materials.

  2. 2.

    Meaning that the boundaries of the neighbourhood do not belong to the neighbourhood itself.

  3. 3.

    Typical states have magnetisation m that can be represented by an exponentially large number of microscopic spin configurations, \(\mathbf {s}\).

  4. 4.

    See [76] for an explicit calculation of the spin-spin correlation function near the OD transition.

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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.

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  1. Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, Aberdeen, UK

    Francisco J. Perez-Reche

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  1. Francisco J. Perez-Reche
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Correspondence to Francisco J. Perez-Reche .

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Editors and Affiliations

  1. Department of Earth Sciences, University of Cambridge , Cambridge, United Kingdom

    Ekhard K.H. Salje

  2. Theoretical Division, Los Alamos National Laboratory, Los Alamos, USA

    Avadh Saxena

  3. Estructura i Constitutents de la Matèria, Universitat de Barcelona, Barcelona, Spain

    Antoni Planes

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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

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