COMPLAS 2023

A data-driven framework for breakage mechanics in granular media

  • Ulloa, Jacinto (California Institute of Technology)
  • Gorgogianni, Anna (California Institute of Technology)
  • Karapiperis, Konstantinos (ETH Zurich)
  • Ortiz, Michael (California Institute of Technology)
  • Andrade, Jose (California Institute of Technology)

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Particle breakage and the resulting changes in grain-size distribution (GSD) strongly modulate the mechanics of granular media. This problem raises modeling challenges related to the characterization of evolving microstructure and its effect on the mechanical state of the material. The first approach to modeling breakage in continuum mechanics was proposed by Einav [1] using an internal state variable that tracks the evolution of GSD. This model is, by now, well established and has been extended to plasticity and other material behaviors. These extensions rely on certain phenomenological functions and parameters, inevitably introducing epistemic uncertainty. An approach to overcome this limitation of constitutive models, in general, was proposed by Kirchdoerfer and Ortiz [2] using data-driven computing. Therein, kinematic constraints and mechanical balance are enforced as in classical continuum mechanics, but the material behavior is extracted directly from empirical data (from physical experiments or lower-scale simulations) rather than from a constitutive model. This approach was recently adopted by Karapiperis et al. [3] in the context of granular materials using the level-set discrete element method (LS-DEM) for high-fidelity data acquisition. However, materials with strongly evolving microstructures, as in the case of particle breakage, were not considered. In this presentation, we develop a model-free data-driven framework for breakage mechanics in granular media. The proposed framework extracts the mechanical response and the evolution of GSD directly from data furnished by experiments and LS-DEM simulations of granular comminution. To this end, data set representations that take the state of breakage into account are established. The framework may be viewed as an extension of the data-driven methodology to materials with evolving microstructure, providing a novel counterpart to constitutive breakage mechanics. [1] I. Einav. Breakage mechanics—Part I: Theory. Journal of the Mechanics and Physics of Solids (2007a) 6:1274–1297. [2] T. Kirchdoerfer and M. Ortiz. Data-driven computational mechanics. Computer Methods in Applied Mechanics and Engineering (2016) 304:81–101. [3] K. Karapiperis, L. Stainier, M. Ortiz, and J.E. Andrade. Data-driven multiscale modeling in mechanics. Journal of the Mechanics and Physics of Solids (2021) 147:104239.