35 research outputs found
Modes of failures in disordered solids
The two principal ingredients determining the failure modes of disordered
solids are the level of heterogeneity and the length scale of the region
affected in the solid following a local failure. While the latter facilitates
damage nucleation, the former leads to diffused damage, the two extreme failure
modes. In this study, using the random fiber bundle model as a prototype for
disorder solids, we classify every failure modes that are the results of
interplay between these two effects. We obtain scaling criteria for the
different modes and propose a general phase diagram that provides a framework
for understanding previous theoretical and experimental attempts of
interpolation between these modes.Comment: 10 pages, 13 figure
A Renormalization Group Procedure for Fiber Bundle Models
We introduce two versions of a renormalization group scheme for the equal
load sharing fiber bundle model. The renormalization group is based on
formulating the fiber bundle model in the language of damage mechanics. A
central concept is the work performed on the fiber bundle to produce a given
damage. The renormalization group conserves this work. In the first version of
the renormalization group, we take advantage of ordering the strength of the
individual fibers. This procedure, which is the simpler one, gives EXACT
results -but cannot be generalized to other fiber bundle models such as the
local load sharing one. The second renormalization group scheme based on the
physical location of the individual fibers may be generalized to other fiber
bundle models.Comment: 9 pages, 12 figure