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Fracture and the Renormalization Group

Fracture and the Renormalization Group. Bryan Daniels with Ashivni Shekhawat , Stefanos Papanikolaou , Phani Nukala , Mikko Alava, Stefano Zapperi , Jim Sethna. Larger objects fracture at lower stress. stress s. A small weak spot will form a crack that breaks the whole system

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Fracture and the Renormalization Group

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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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