# Crack To Blue Eye Macro Full ((EXCLUSIVE))

in the second example, we consider the flow path of the crack in a two-dimensional layered structure containing heterogeneous quasibrittle granular materials such as concrete, as shown in fig. 2. the material was compacted, which entailed an initial sliding of the particles followed by a compaction of the contact force. through the compaction process, the disordered force chains slowly ordered and became more compact, until there was no apparent preferred orientation of the contact force. the work of unwin and greenwoods study, in which they showed that compaction can lead to anisotropic material properties, provided a basis for the expectation of localized anisotropic failure. once the force chains established, they appeared to be resistant to further shearing in the direction of force, just as we observed in our quasi-brittle granular material. this behavior is in contrast to our intuition, which expects a plastic response to further shearing of the force chains. interestingly, the crack paths perpendicular to the plane of shear were also observed, which may have been induced by heterogeneities in the material properties, such as the strength of the force chains.

## Crack To Blue Eye Macro Full

on the basis of these results, we anticipate that the critical point at which the energetic bottleneck dominates failure as a path of least resistance and the softening point at which the pre-peak softening rate becomes zero to be the early indicators of failure. however, the greater the energetic potential available in the system to support the tensile force chains, the higher the fracture risk. therefore, there is a trade-off between the amount of strain energy a system can store and the number of bonds that can be broken without exceeding the maximum energy release rate. the failure risk is defined as the probability of exceeding the maximum energy release rate while using a particular set of bonds, thus being the counterpart of the post-peak softening rate. these concepts are illustrated in fig. 11, where mathcal c is the crack path, mathcal f_e is the set of bonds that are able to support fracture (beyond the failure cascade) and be broken, and mathcal f_f is the set of bonds that store strain energy. the failure risk is the probability that bonds from mathcal f_e are available to support the system-spanning tensile force chains and thus are broken. the set of bonds from mathcal f_e and mathcal f_f that are broken collectively form the set of bonds that support the final crack path. the failure risk is therefore the probability of breaking the bonds from mathcal f_e and the probability that the bonds from mathcal f_e are available to break. thus the failure risk (red-blue interface) in d2 (fig. 11, bottom panel) is greater than in d1 (fig. 11, top panel) because the set of bonds that are able to support fracture (beyond the failure cascade) is larger in d2, leading to a higher probability of exceeding the maximum energy release rate and thus a higher failure risk. this analysis provides a conceptual framework that elucidates the reason behind the observed differences in crack paths from the three loading conditions. this is discussed in the next section.