Structural evolution of granular systems: theory
Clara C. Wanjura, Paula A. Gago, Takashi Matsushima, Raphaël Blumenfeld
Abstract
Abstract A general theory is developed for the evolution of the cell order (CO) distribution in planar granular systems. Dynamic equations are constructed and solved in closed form for several examples: systems under compression; dilation of very dense systems; and the general approach to steady state. We find that all the steady states are stable and that they satisfy a detailed balance-like condition when the CO $$\,\le 6$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mspace/> <mml:mo>≤</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:math> . Illustrative numerical solutions of the evolution are shown. Our theoretical results are validated against an extensive simulation of a sheared system. The formalism can be readily extended to other structural characteristics, paving the way to a general theory of structural organisation of granular systems. Graphic abstract