Interacting damage models mapped onto Ising and percolation models

Details Interacting damage models mapped onto Ising and percolation models Interacting damage models mapped onto Ising and percolation models

2004-03-17

arxiv.org/abs/cond-mat/0403412v1

Physics

Condensed Matter

Statistical Mechanics

16 pages, 3 figures

Scientific paper

10.1103/PhysRevE.71.046127

We introduce a class of damage models on regular lattices with isotropic interactions, as e.g. quasistatic fiber bundles. The system starts intact with a surface-energy threshold required to break any cell sampled from an uncorrelated quenched-disorder distribution. The evolution of this heterogeneous system is ruled by Griffith's principle which states that a cell breaks when the release in elastic energy in the system exceeds the surface-energy barrier necessary to break the cell. By direct integration over all possible realizations of the quenched disorder, we obtain the probability distribution of each damage configuration at any level of the imposed external deformation. We demonstrate an isomorphism between the distributions so obtained and standard generalized Ising models, in which the coupling constants and effective temperature in the Ising model are functions of the nature of the quenched-disorder distribution and the extent of accumulated damage. In particular, we show that damage models with global load sharing are isomorphic to standard percolation theory, that damage models with local load sharing rule are isomorphic to the standard Ising model, and draw consequences thereof for the universality class and behavior of the autocorrelation length of the breakdown transitions corresponding to these models. We also treat damage models having more general power-law interactions, and classify the breakdown process as a function of the power-law interaction exponent. Last, we also show that the probability distribution over configurations is a maximum of Shannon's entropy under some specific constraints related to the energetic balance of the fracture process, which firmly relates this type of quenched-disorder based damage model to standard statistical mechanics.

Affiliated with

Also associated with

No associations

Rating

Interacting damage models mapped onto Ising and percolation models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Interacting damage models mapped onto Ising and percolation models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Interacting damage models mapped onto Ising and percolation models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-151697