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Fracture & Renormalization Group: Understanding Stress Distribution in Objects

Explore how fracture occurs at lower stress levels, probability of system survival, extreme value statistics, universal forms of survival distributions, fuse networks, and computational survival probabilities. Investigate finite size effects on stress distribution.

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Fracture & Renormalization Group: Understanding Stress Distribution in Objects

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  1. Fracture and the Renormalization Group Bryan Daniels with AshivniShekhawat, StefanosPapanikolaou, PhaniNukala, Mikko Alava, Stefano Zapperi, Jim Sethna

  2. Larger objects fracture at lower stress stress s • A small weak spot will form a crack that breaks the whole system • Thus the probability of surviving S(s) = the probability of not having any weak spots L s 2L S2L(s) = SL(s) 4

  3. Extreme value statistics • As you recall from homework exercise N.8, extreme value statistics lead to a universal form (Gumbel, Weibull, or Frechet) • So a large brittle object should have a survival distribution S(s) with a universal form

  4. Fuse networks I • Fuse networks provide a simplified model for fracture • Stress s ↔ Current I • Does the survival probability depend on L in the expected way?

  5. Computational survival probabilities 1 S2L(s) ≠ SL(s) 4 survival prob. S(s) 0 stress s

  6. What’s wrong? • Some sort of finite size effect • Could be: • Boundary effects • Incorrect intuition about critical crack formation • Effect of crack spanning an edge

  7. Fracture and the Renormalization Group Bryan Daniels, AshivniShekhawat, StefanosPapanikolaou, Jim Sethna

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