Particle fragmentation based on strain energy field
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ORIGINAL PAPER
Particle fragmentation based on strain energy field Yupeng Jiang1 · Fernando Alonso‑Marroquín1 · Hans J Herrmann2 · Peter Mora3 Received: 28 February 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We propose a method for the simulation of particle fragmentation based on the calculation of the strain energy field inside the particle. The topography of strain energy is calculated in terms of internal stress using the principles of damage and fracture mechanics. Numerical calculation of the energy field’s ridges is used to determine the breakage criterion as well as the shape of the post-breakage fragments. This method provides a physical-based understanding of the breakage effect in granular material. Keywords Particle breakage · Fragmenting model · Strain energy field · Granular material
1 Introduction The mechanical properties of granular materials are fully governed by its discrete components and the contact forces. Breakage of a single particle, ranged from coarse sand (4–2 mm) to boulders ( ≈ 300 mm), could be caused by the strong compressive loading exerted by its surrounding environment. Breakage is affected by particle shape [1, 2], the number of particles [3–5], and the distribution of contact forces [1, 6]. In granular materials, particle breakage is commonly observed, which has a major effect on the mechanical properties, such as density [6], and compressibility [7]. As a collective response to particle breakage, the particle size distribution (PSD) [3–7] and normal compression line (NCL) [4–7] are adopted as indicators of the breakage effect. Their relations with the state variables have been studied through experiments [1–5, 7], which provides a solid foundation for understanding particle breakage. However, because of the difficulties of direct laboratory measurements, the relation between a single breakage event and the change of macroscale mechanics is still poorly understood. * Yupeng Jiang [email protected] 1
School of Civil Engineering, The University of Sydney, Sydney, NSW, Australia
2
PMMH, ESPCI, 17 quai St. Bernard, 75005 Paris, France
3
College of Petroleum Engineering and Geosciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
The particle replacement paradigm of the discrete element method (DEM), i.e. replacing the particle by its fragments when it reaches a breakage criterion, is used in many numerical models [8–14]. The existing methods possess high computational efficiency and the ability to reproduce PSD and NCL that agree well with experimental results [8]. Generally, two major attributes must be considered when developing a particle replacement model: a proper breakage criterion and a realistic approach for the determination of the geometry of post-breakage particles. The existing breakage criteria are based on the averaged stress tensor. Particle breakage happens if the maximum principle stress or invariants of the stress tensor, or a linear combination of them, reaches a critical
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