2008/02/19 by R. C. Hidalgo, K. Kovacs, K. Kovács +4 · 31 citations
Materials Science · Mathematics · Physics and Astronomy · #Bundle #Condensed matter physics #Critical exponent #Critical point (mathematics) #Cutoff #Exponent #Fiber bundle #Material Dynamics and Properties #Materials science #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Phase transition #Physics #Power law #Quantum mechanics #Renormalization group #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Transition point #Universality (dynamical systems) #cond-mat.stat-mech
paper · pdf · doi:10.1209/0295-5075/81/54005
published in Europhysics Letters (EPL) 81(5), 54005 (Institute of Physics)
arxiv created 2008/02/19 · openalex publication_date 2008/02/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the effect of strong heterogeneities on the fracture of disordered materials using a fiber bundle model. The bundle is composed of two subsets of fibers, i.e. a fraction 0⩽α⩽1 of fibers is unbreakable, while the remaining 1−α fraction is characterized by a distribution of breaking thresholds. Assuming global load sharing, we show analytically that there exists a critical fraction of the components α c which separates two qualitatively different regimes of the system: below α c the burst size distribution is a power law with the usual exponent τ=5/2, while above α c the exponent switches to a lower value τ=9/4 and a cutoff function occurs with a diverging characteristic size. Analyzing the macroscopic response of the system we demonstrate that the transition is conditioned to disorder distributions where the constitutive curve has a single maximum and an inflexion point defining a novel universality class of breakdown phenomena.