Research




When granular materials (like sand) deform, strain is often localized to sliding planes called shear zones.
We found a new effect for shear zones that are created in layered granular materials. When two materials with different frictional properties are layered on top of each other, shear zones are refracted at the interface[1,2]. The phenomenon is in complete analogy with the refraction of light. The angle of refraction follows Snell's law from geometric optics.
The effect of refraction is tested by discrete element simulations based on the algorithm of Contact Dynamics. We analyzed slow shear flow of 100000 spherical grains confined in a cylindrical drum. The cylinder is cut in two along the axis and each half slides along the axis in opposite directions which leads to the formation of a shear zone. The simulations confirmed the phenomenon and also the law of refraction[2].

A recent model of shear zones can account for the effect refraction. According to this model, shear zones are optimal in the sense that their shapes correspond to the least possible rate of energy dissipation[3]. This approach was first applied for a modified Couette geometry to describe the open and closed shapes of shear zones.



Within the framework of this model the effect of refraction can be understood as follows: the selection principle of minimum dissipation, when applied at material interfaces, has exactly the form of Fermat's principle of optics[2]. Only, in case of shear zones, the effective friction coefficient plays the role of the index of refraction. Based on the same selection principles the same laws can be derived for the angle of refraction. Thus Snell's law turns out to be valid also for shear zones in granular media.





[1]



A little light reading;
pdf
Nature Physics, 3, 76 (2007)

[2]



Refraction of shear zones in granular materials,
pdf
Phys. Rev. Letters, 98 , 018301 (2007),

[3]


Shear band formation in granular media as a variational problem,
pdf
Phys. Rev. Lett., 92, 214301 (2004).