Discrete to Continuum Upscaling for Rotational Particle Information

  • Winkelmann, Max (University of Edinburgh)
  • Magnanimo, Vanessa (University of Twente)
  • Luding, Stefan (University of Twente)
  • Papanicolopulos, Stefanos-Aldo (University of Edinburgh)

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Through discrete-to-continuum (D2C) upscaling methods, the discrete particle data such as particle mass, particle velocity and contact force can be mapped on continuous fields like density, velocity, and stress. However the rotational particle information is usually neglected, even though the rotation of particles has a significant influence on the behaviour of the whole bulk, such as in shear bands. Using micropolar theory on continuum scale – where rotational degrees of freedom are added to the micrstructure of a continuum – allows describing those aspects of granular materials. Following the approach by Goldhirsch [1] and Weinhart [2], and using a smoothening function, we are developing a new D2C method to transform the rotational particle properties like angular velocity, angular momentum, and contact torque to non-classical micropolar fields like curvature, skew-symmetric stress, and couple stress. Measuring those quantities in an experiment is a difficult challenge [3]. One possibility is the triaxial test in micro-computed tomography. It is limited to the kinematic quantities, but can give insights into the influence of shape. This talk will introduce micropolar theory and motivate the need for a new D2C method by presenting a parameter study on the contact laws. The discrete data obtained from a Discrete Element Simulation was upscaled towards continuum fields and the influence of sliding, rolling and torsion friction on micropolar fields was investigated. First application examples are a chute flow over a rough inclined plane and a Cartesian shear cell. Based on rolling resistance, the influence of shape will be motivated and shown on the example of a triaxial test in micro-computed tomography. Future large scale industrial application might be a silo discharge, as well as the application to non-spherical particles.