
Micro-macro methods: states and transitions from particles to continuum
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First goal is an overview/review on states and transitions – and second, how to transfer from particles to continuum. Granular matter can behave both solid- or fluid-like, including all the various transitions between these states. In order to understand the fundamental micro-mechanics one can use particle simulation methods. To bridge the gap between the scales, so-called micro-macro transition methods are necessary, which translate particle positions, velocities and forces into density-, stress-, and strain-fields. These macroscopic quantities must be compatible with the conservation equations for mass and momentum of continuum theory. Furthermore, some additional non-classical fields might be needed to describe the micro- structure or the statistical fluctuations, e.g., the fabric or the kinetic energy, before one can reach the ultimate goal of understanding and solving application problems.