GEOL599: Strain localization

Fall 2009

Times: Mon 9 – 10am; Wed, 8 – 10am, Location: ZHS200

Instructor: Profs. Thorsten Becker and Yehuda Ben-Zion

Becker contact: ZHS269; (213)740-8365; twb -at-

Ben-Zion contact: ZSH109; (213)740-06734; benzion -at-


When materials deform to large strain, they typically enter a non-linear regime where deformation becomes progressively concentrated in narrow zones of shear that can lead to catastrophic failure or ductile deformation. Such behavior is observed at micro-scales during laboratory deformation experiments of metals or rocks, in natural samples such as rock thin sections, at meso-scales of exposed geological fault and fold structures, and at the macro-scale at the boundaries between lithospheric plates. It is clear that complex thermo-mechanical interactions of heterogeneous media govern this process, yet many aspects of the expression of strain localization are poorly understood.

Important issues related to strain localization include structural design in engineering, the mechanics of earthquakes and fault systems, and the operation of plate tectonics on Earth and other planets. The complex nature of this subject matter is reflected in the study of phenomena such as damage across several natural science disciplines, and we intend to make new connections between fields and also try to connect localization and damage processes at the short, elastic (e.g. earthquake) and long, viscous (e.g. plate boundary formation and maintenance) timescales.

The class targets graduate students from all Earth science fields, applied math, and engineering and will include reading and in-class discussion of the recent literature and classic papers. We will have lectures from members of the faculty and outside speakers, student presentations, and students are expected to work on a term paper. The latter can be a research project (preferred), or an in depth review of a subject area. The grade will be based 50% on the final project, 40% on student presentations and homework projects, and 10% on student participation.

Link to PDF files for selected reading

Link to lecture material including slides

Monday 9 – 10am

Wednesday 8-10am

Week 1: 08/24

Organizational meeting

Introduction (TWB)

Aydin and Johnson (1978); Ramsay (1980); Rutter et al. (2001), Bercovici (2003)

Week 2: 08/31

Basic concepts I (YBZ)

Basic concepts II (YBZ)

Week 3: 09/07

Labor day

Observations: brittle crust I (YBZ)

Ben-Zion and Sammis (2003), Chester et al., 2005; Rockwell and Ben-Zion (2007)

Week 4: 09/14



Week 5: 09/21

Observations: brittle crust II (YBZ)

Rheology I: viscous macro (TWB)


Tackley (2000a)

Week 6: 09/28

Rheology II viscous micro (Platt)


Kohlstedt et al. (1995), Hirth and Kohlstedt (2003), Warren and Hirth (2006)

Rheology III: friction and fracture (YBZ)


Ben-Zion (2003, sections 4 and 5)

Week 7: 10/05

Viscous flow models (TWB)

Student presentations

Braun et al. (1999), Hobbs et al. (1990)

Week 8: 10/12

Student presentations

Precigout and Gueydan (2009)

Student presentations

Montesi and Zuber (2002)

Montesi & Hirth (2003), Burlini & Bruhn (2005)


Regenauer-Lieb and Yuen (2003), Vissers et al. (1995), Regenauer-Lieb et al. (2006)

Week 9: 10/19

Elastic Damage I (Sammis)

Ashby and Sammis (1990)

Elastic Damage II (YBZ)

Ben-Zion (2008, sections 6)

Lyakhovsky et al. (1997), Sammis and Ben-Zion (2008)

Week 10: 10/26

Elastic damage III

Student presentations

Lyakhovsky & Ben-Zion (2009); Finzi et al. (2009); Hamiel et al., (2009); Lyakhovsky et al. (2009).

Viscous Damage I (TWB) Introduction

Bercovici et al. (2001), Bercovici and Ricard (2003, 2005), Ricard and Bercovici (2009)

Week 11: 11/02

Discussion session

Viscous damage II – Shear zones

Student presentation

Landuyt & Bercovici (2009)

Week 12: 11/09

Implementation of strain localization in mantle convection models

Student presentations

Bercovici & Karato (2003), Tackley (2000a), Gurnis et al. (2000)


Student presentations

Moresi & Solomatov (1998), Tackley (2000b, 2000c), Auth et al. (2002), Landuyt & Bercovici (2008)

Week 13: 11/16

Viscous shear zones in nature and lab (Davis)

Work on term paper

Week 14: 11/23

Work on term paper


Week 15: 11/30:

Work on term paper

Work on term paper

Week 16: 12/07:

Presentations of term papers

Presentations of term paper


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Auth, C., Bercovici, D., and Christensen, U. R.: Two-dimensional convection with a self-lubricating, simple-damage rheology. Geophys. J. Int., 154, 783-800, 2003.

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Ben-Zion, Y., Collective Behavior of Earthquakes and Faults: Continuum-Discrete Transitions, Evolutionary Changes and Corresponding Dynamic Regimes, Rev. Geophysics, 46, doi:10.1029/2008rg000260, 2008.

Ben-Zion, Y. and C. G. Sammis, Characterization of Fault Zones, Pure Appl. Geophys., 160, 677-715, 2003.

Bercovici, D.: A source-sink model of the generation of plate-tectonics from non-Newtonian mantle flow. J. Geophys. Res., 100, 2013, 1995a.

Bercovici, D.: On the purpose of toroidal motion in a convecting mantle, Geophys. Res. Lett., 22, 3107, 1995b.

Bercovici, D. and Ricard, Y. and Schubert, G.: A two-phase model for compaction and damage. 3. Applications to shear localization and plate boundary formation, J. Geophys. Res., 106, 8925, 2001.

Bercovici, D.: Mantle dynamics, Past, Present and Future: An Overview, in Treatise on Geophyiscs, vol. 7, Mantle Dynamics, D. Bercovici editor; G. Schubert, editor in chief, Elsevier, New York; Ch. 1, p. 1-30, 2007.

Bercovici, D., The generation of plate tectonics from mantle convection, Earth Planet. Sci. Lett., 205, 107, 2003.

Braun, J., Chery, J., Poliakov, A., Mainprice, D., Vauchez, A., Tomassi, A., and Daignieres, M.: Parameterization of strain localization in the ductile regime due to grain size reduction: A case study for olivine, J. Geophys. Res., 104, 25167, 1999.

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Burlini, L. and Bruhn, D.: High-strain zones: laboratory perspectives on strain softening during ductile deformation. High-strain Zones: Structure and Physical Properties, Geol. Soc. Lond. Spec. Pub., 245, p. 1-24, 2005.

Chester, J. S., F. M. Chester, and A. K. Kronenberg (2005), Fracture surface energy of the Punchbowl fault, San Andreas system, Nature, 437, 133-136.

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Hirth, G. and Kohlstedt, D. L., Rheology of the Upper Mantle and the Mantle Wedge: A View From the Experimentalists, In: Inside the Subduction Factory, Eiler, J. (ed), Geophys. Monograph, 138, p. 83-105, 2004.

Hobbs, B. E., Ord, A., and Teyssier, C.: Earthquakes in the ductile regime? Pure App. Geophys., 124, 309, 1986.

Hobbs, B. E., Muhlhaus, H.-B., and Ord, A.: Instability, softening and localization of deformation. Geol. Soc. London Spec. Pub., 54, p. 143-165, 1990.

Hudson, J. A. (1980), Overall properties of a cracked solid. Cambridge Phil. Soc., Math. Proc. 88, 371, 1980.

Jin, D., Karato, S.-i., and Obata, M.: Mechanisms of shear localization in the continental lithosphere: inference from the deformation microstructure of peridotites from the Ivrea zone, northwestern Italy. J. Struct. Geol., 20, 195, 1998.

Kachanov, M.: Effective elastic properties of cracked solids: Critical review of some basic concepts, Appl. Mech. Rev. 45, 304, 1992.

Kameyama, M., Yuen, D. A., Fujimoto, H.: The interaction of viscous heating with grain-size dependent rheology in the formation of localized slip zones. Geophys. Res. Lett., 24, 2523, 1997.

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Landuyt, W. and D. Bercovici, Formation and structure of lithospheric shear zones with two-phase damage, Phys. Earth Planet. Int., 175, 115, 2009.

Landuyt, W., D. Bercovici and Y. Ricard, Plate generation and two-phase damage theory in a model of mantle convection, Geophys. J. Int. 174, 1065, 2008.

Lyakhovsky, V., Ben-Zion, Y. & Agnon, A.: Distributed damage, faulting, and friction, J. Geophys. Res., 102, 27635-27649, 1997.

Lyakhovsky, V., Ben-Zion, Y., and Agnon, A.: Earthquake cycle, fault zones and seismicity patterns in a rheologically layered lithosphere. J. Geophys. Res., 106, 4103-4120, 2001.

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Montési, L. and Zuber, M.: A unified description of localization for application to large-scale tectonics, J. Geophys. Res., 107, 2045, doi:10.1029/2001JB000465, 2002.

Montési, L.: A constitutive model for layer development in shear zones near the brittle-ductile transition. Geophys. Res. Lett., 34, L08307, doi:10.1029/2007GL029250, 2007.

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Poirier, J. P.: Shear localization and shear instability in materials in the ductile field. J. Struct. Geol., 2, 135, 1980.

Precigout et al. Strain localisation in the subcontinental mantle — a ductile alternative to the brittle mantle. Tectonophysics, 445, 318-336, 2007.

Raimbourg, H., Toyoshima, T., Harima, Y. and Kimura, G.: Grain-size reduction mechanisms and rheological consequences in high-temperature gabbro mylonites of Hidaka, Japan. Earth Planet. Sci. Lett., 267, 637, 2008.

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Regenauer-Lieb, K., Yuen, D. A., and Branlund, J.: The initiation of subduction; criticality by addition of water? Science, 294, 578, 2001.

Regenauer-Lieb, K., and D. A. Yuen: Modeling shear zones in geological and planetary sciences: solid-and fluid-thermal–mechanical approaches, Earth-Sci. Rev., 63, 295, 2003.

Regenauer-Lieb, K., Weinberg, R. F., and Rosenbaum, G.: The effect of energy feedbacks on continental strength. Nature, 442, 67, 2006.

Ricard, Y. and Bercovici, D.: A continuum theory of grain size evolution and damage, J. Geophys. Res., 114, B01204, 10.1029/2007JB005491, 2009.

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Rockwell, T. K., and Y. Ben-Zion: High localization of primary slip zones in large earthquakes from paleoseismic trenches: Observations and implications for earthquake physics, J. Geophys. Res., 112, B10304, doi:10.1029/2006JB004764, 2007.

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Sammis, C. G., and Y. Ben-Zion, Mechanics of grain-size reduction in fault zones, J. Geophys. Res., 113, B02306, doi:10.1029/2006JB004892, 2008.

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Disability notice

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