Modeling Failure, Fatigue and Fragmentation

Abstract

Failure of heterogeneous due to fatigue and subsequent fragmentation are ideally modelled by stochastic networks made of beams, springs or similar elements.  Fibre models are the simplest description for failure. They are based on the probability distribution of broken fibres. The load redistribution after a fibre yields can be global or local and the first case can often be solved analytically. We will present an interpolation between these the local and the global case and apply it to experimental situations like the compression of granular packings. Introducing viscoelastic fibres allows to describe the creep of wood. It is even possible to deal analytically with a gradual degradation of fibres and consider damage as well as healing. In this way Basquin's law of fatigue can be reproduced giving good agreement with measurements of asphalt samples in Brazil tests. The histograms of bursts and waiting times reveal universal laws that are independent  on the material. The fragmentation of solids is important in industry and geoscience. Using a combination of Discrete Element Method and beam networks it becomes possible to simulate the cracking and detachments of fragments in diverse geometries. We studied impacts against walls, particle-particle collisions, explosions of bulk objects and of shells, milling and crushing under cyclic load. Besides purely brittle failure under traction or bending we also studied plasticity under compression or under shear. We find the existence of a critical energy below above which no fragment having a size of the order of the original sample survives. This critical point is dominated by power laws in the fragment size distribution and a divergence of the ratio between the second largest and the largest fragment. This exponent depends among others on the dimension of the object. We also study the distribution of velocities and directions of the fragments and the dependence of their shape on the material. Later question is of relevance for space debris. The numerical results are compared to experiments.

Brief Bio

Born on January 1st, 1954 in La Habana, Cuba, and raised in Bogotá, he studied physics in Göttingen and Cologne where he made his PhD in 1981. After spending one year as post-doc in the USA he became collaborator at the Service de Physique Théorique in Saclay. He became member of section 02 of the CNRS and is today Directeur de Recherche 1ère Cl. en mise à disponibilité. In 1990 he was head of the many-body group at HLRZ of KFA Jülich for four years. Then he was director of the PMMH of ESPCI, Paris for six years, where he also filled a chair. In 1996, he was named full professor and director of the Institute of Computer Physics at the University of Stuttgart. He is a Guggenheim Fellow (1986), member of the Brazilian Academy of Science, Max-Planck prize recipient (2002) and won the 2005 Gentner-Kastler prize. He is managing editor of International Journal of Modern Physics C and of Granular Matter and member of several editorial boards and committees including the Forschungskommission of ETH. He has co-authored over 500 publications and co-edited 15 books.

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