Localization

= Localization =

Localization, or more precisely "strain localization", describes a process by which a material or other mechanical system deforms in response to an applied shear stress. In a system that exhibits localization the system shears along a very narrow region rather than accommodating the stress uniformly throughout. This behavior can be observed in metallic glasses (shear bands), amorphous polymeric systems (shear bands that induce anisotropy in the material), complex fluids and granular media. The relationship to earthquakes arises from two questions:


 * 1) Slip during fault rupture is often accommodated in the ultracataclasite layer, a region of highly broken up rock in the foliated gouge zone. Although this layer is centimeters in width the actula rupture surface is only millimeters in width. Can our understanding of strain localization in materials systems help us understand the localization during earthquake rupture?
 * 2) The fault system itself undergoes a process of damage that leads the maturing of faults and the evolution of fault networks. This leads to extremely straight faults, although it is important to note that even small roughnesses can lead to high residual stresses. Can this process of damage be related to the kinds of events that lead up to shear band formation in materials?

Particular thanks to Jim Rice for his excellent talk during the conference regarding the earthquake physics of faulting. For more references see slides and audio from his talk at: http://online.kitp.ucsb.edu/online/earthq_c05/rice/

For a detailed of particular instances of localization in materials systems see the Localization (more...) page.

Additional references:


 * An early paper trying to relate the predicitions of constitutive theory to the onset of localization: L. Anand and W. A. Spitzig, "Initiation of Localized Shear Bands in Plane Strain," J. Mech. Phys. Solids 28, 113-128 (1980). [|Link]



References by Falk on molecular dynamics simulations of localization in metallic glass analogs:


 * Y. Shi and M.L. Falk, "Strain localization and percolation of stable structure in amorphous solids," Physical Review Letters **95**, 095502 (2005) http://link.aip.org/link/?PRL/95/095502
 * Y. Shi and M.L. Falk, "Structural transformation and localization during simulated nanoindentation of a noncrystalline metal film," Applied Physics Letters **86**, 011914 (2005). http://link.aip.org/link/?APL/86/011914

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