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Spontaneous shear localization in a model brittle solid

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Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)

Abstract

Fracture in brittle materials exhibits common features on scales ranging from nano-indented glass to faults in the earth's crust, and an improved understanding of brittle failure is crucial to a wide range of disciplines. To date, the most studied statistical models of brittle materials have been so-called random fuse models (1). They consist of networks of springs which fail when stretched past some threshold. Such models are well-suited to studies of tensile fracture, but miss essential physics in the shear fracture that occurs in compressed materials or along earthquake faults. The reason is that they do not include the excluded volume interactions along the damaged regions or faults. These repulsive interactions carry significant shear stress in the damaged solid and prevent opposing faces of a damaged interface from interpenetrating. To account for these effects, we modify a 2D amorphous Lennard-Jones (LJ) model. LJ bonds that form during deformation are assigned a reduced interaction strength relative to initial bonds; this accounts for loss of cohesion via damage (in roughly the same spirit as the fuse models) while maintaining hard-core repulsive interactions to prevent interpenetration of opposing sides of damaged surfaces. The LJ particles may be thought of as representing a few atoms in a glass or large regions of intact rock in the earth's crust. We will compare and contrast the global mechanical response, damage statistics, spatio-temporal patterning, etc. of this modified LJ model which exhibits brittle behavior (spontaneous shear localization onto a geometrically complex primary fault system) with a standard LJ system which responds in a ductile way (localized strain bursts on short times, but homogenous strain over long times). (1) MJ Alava, PKVV Nukala , and S Zapperi. Advances in physics 55 (3):349 2006.

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