Current work focuses on fundamental aspects of fracture in disordered systems. A brittle material is modeled using a stochastic beam lattice, i.e, a lattice where each individual beam is assumed linearly elastic up to the breaking threshold - the thresholds having previously been assigned randomly according to some statistical distribution.
   Imagine a lattice of beams which is stretched in one direction until it begins to break apart. The first beam to break will cause neighbouring beams to experience an increased load. For very low disorders, when all thresholds are approximately equal, the next beam to break will be one these lateral neighbours, creating a situation where the crack propagates from the initial damage point in a direction perpendicular to the line of force, thus taking the shortest possible path to break the lattice apart.
   Introducing disorder in the breaking thresholds, material strength is no longer uniformly distributed throughout the lattice, and consequently the crack will not necessarily develop from the point of initial damage. Instead, during crack development microcracks and voids form wherever the stress concentration most exceeds the local strength. Towards the end of the fracture process some of these merge into a macroscopic crack which eventually traverses the width of the lattice and thus breaks it apart. In this situation we have a highly correlated process in which the quenched disorder and the non-uniform stress distribution combine to determine where the next break should occur, while, simultaneously, the stress distribution itself continually changes as the damage spreads.
   The force-displacement characteristic i.e., the elastic response of the system as a function of external displacement when being strained, is highly dependent on the disorder. Also of interest is the dependence on system size of various breaking characteristics, such as the maximum force and displacement needed to trigger catastrofic breakdown, the number of beams broken, and so on.
   We also study burst dynamics of fracture processes. As already remarked, stretching the beam lattice causes beams to break according to where the stress distribution most exceeds the local strength. The number of beams which break during a finite increment in the displacement, however, will vary. Sometimes the breaking of a single beam will trigger an avalanche, or burst, of broken beams. The relative occurrence of such bursts with respect to the number of broken beams involved has an asymptotic scaling behaviour, and we study how this is affected by disorder.
   The use of different threshold distributions enables us to study not only how disorder affects quantities of the fracture process, but also properties of the fractured material itself, such as the surface roughness. Fracture surfaces are found to be self-affine, i.e., the topology of the surface is statistically invariant with respect to the scale of observation. This means that the statistical properties of the surface at one length scale may be recovered by carrying out an anisotropic scale transformation at another length scale. Objects which obey the same scaling transformation in all directions, on the other hand, are termed self-similar. Self-similarity and self-affinity are both symmetry properties of a system, and much of the physics which characterizes such complex, or fractal, systems can be obtained from their scaling behaviour and critical exponents.
   An aspect of fracture which is of the utmost technological importance is buckling. Using the model outlined above, we can study how various quantities of the fracture process in a disordered material (and the resulting fractured surface) is affected by allowing out-of-plane components to modify the fracture process.

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