Abstract
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, 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.
Highlights
A Renormalization Group Procedure for Fiber Bundle ModelsSpecialty section: This article was submitted to Interdisciplinary Physics, a section of the journal Frontiers in Physics
In an age where computer modeling of fracture and material breakdown is reaching a stage where the systems one may study span from the atomistic level to the continuum level in a single go [1, 2], one may wonder what is the use of simplified models
We have in this paper introduced a renormalization group for the equal load sharing fiber bundle model based on formulating the fiber bundle in the context of damage mechanics
Summary
Specialty section: This article was submitted to Interdisciplinary Physics, a section of the journal Frontiers in Physics. 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. 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, 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
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