Microscopic origin of macroscopic strength in granular media: Friction
Alex Jerves (California Institute of Techno), Jose Andrade (Caltech), Sergio Torres ()
Multiscale Mechanics of Particulate Media
Mon 2:40 - 4:00
Sayles 105
In the last decade, micro-scale physics has become a fundamental object of study in the attempt of developing a comprehensive theory in granular mechanics, capable of furnishing a more physics-based framework in the field. Furthermore, understanding (from the micro mechanical point of view) the evolution and physical meaning of experimental results (macro-scale) promises to give a deeper insight into the behavior of these complex materials. The present work introduces an analytical treatment of the relations between micro and macro mechanical behaviors in granular materials undergoing quasi-static loading. Thus, this attempts to contribute in the quest for a broader understanding of the relation among scales without the need to rely on particular cases or specific experimental data, which have been used to illustrate the existence and main features of chain forces and macro-mechanics (e.g., photo-elasticity in 2D discs, phenomenological constitutive laws). In particular, we derive explicit theoretical expressions that allow us to compute principal stresses and directions, mobilized and peak friction angles, as well as, dilatancy directly from micro-scale parameters (e.g., contact forces, branch vectors, and inter-particle friction coefficients) for arrays of two-dimensional arbitrary shape particles. Hence, physical-geometrical properties and mechanisms like distribution of forces, buckling, maximum strength, and directional strength are studied in a general fashion from the micro-scale point of view.