
Influence of contact friction and particle shape on rotational dissipation
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Discrete particles interact with each other through frictional contacts. Any change of properties at grain level [1], the micro scale, affects the response of the material on the macro scale. It has been shown that contact friction and particle shape are factors that influence the rotational behaviour of the material [2, 3]. 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 contact stress. Following the approach by Goldhirsch [4] and Weinhart [5, 6], and using a smoothening function, we develop a D2C method to transform particle properties related to rotation like discrete angular velocity, angular momentum, tangential forces, and contact torque to non-classical micropolar fields like relative rotation, curvature, skew-symmetric stress, and couple stress. In classic continuum mechanics, the work-conjugate pair of symmetric stress and strain rate causes plastic dissipation. The aforementioned micropolar fields can be sorted in work-conjugates as well, leading to two additional dissipation mechanisms related to rotational behaviour. Bulk shear causes rotations on the micro-scale which translates to the micropolar macroscopic fields. On the example of a DEM simulation of a Cartesian (planar) split-bottom shear cell, we can understand the effect of microscopic parameters between spherical particles via a parameter study. Hereby, rolling friction has the strongest effect on the non-classical micropolar fields such as skew-symmetric stress or relative rotation. This is indicating that the shape of particles plays a significant role for those phenomena. We thus systematically study the influence of particle shape on rotation related macroscopic quantities. They are appearing in the area of failure (i.e., permanent plastic flow) where the shear band emerges. their magnitude, position and width are similar. Future applications can be the formulation of constitutive equations with the additional aspect of rotation/micropolar fields and their effect on dissipation in plastic deformation/flow situations.