Representing stochastic damage evolution in disordered media as a jump Markov process using the fiber bundle model

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The damage evolution in quasi-brittle materials is inherently stochastic due to the presence of strong disorder in the form of heterogeneities, voids, and microcracks. The final macroscopic failure is foreshadowed by accumulation of a significant amount of distributed damage that results in precursory events observed as avalanches in experiments and simulations. Simulations on spring lattice models of disordered media have been widely used to understand the collective nature of the quasi-brittle material failure process. In this study, we use the jump Markov process to model stochastic damage evolution, which is informed by the avalanche size distributions for a given material. The jump Markov process is defined based on the probability distributions of the jump sizes, the wait-time between consecutive jumps, and the failure strength. The fiber bundle model is used as an example to obtain the required inputs and test the viability of the proposed approach. The stochasticity and size-dependence of the damage evolution process is inherently captured through the inputs provided for the jump Markov process. The avalanche and strength distributions are used to describe the effect of microscopic information present in the form of disorder, on the macroscopic damage evolution behavior.

Original languageEnglish (US)
Pages (from-to)146-160
Number of pages15
JournalInternational Journal of Damage Mechanics
Issue number1
StatePublished - Jan 1 2017


  • Disordered media
  • Markov process
  • avalanches
  • fiber bundle model
  • size-effect

ASJC Scopus subject areas

  • Computational Mechanics
  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering


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