Cristian F. Moukarzel

ISOSTATIC PHASE TRANSITION AND INSTABILITY IN STIFF GRANULAR MATERIALS

Structural rigidity concepts are used to understand the origin of instabilities in granular aggregates. It is first demonstrated that the contact network of a noncohesive granular aggregate becomes exactly isostatic when

A vectorizable random lattice

I\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}k\ensuremath{\epsilon}/{f}_{l}\ensuremath{\gg}1

Stressed backbone and elasticity of random central-force systems.

, where

Floppy modes and the free energy: Rigidity and connectivity percolation on Bethe lattices

k

Shortest paths on systems with power-law distributed long-range connections

is the stiffness,

Failure of three‐dimensional random composites

\ensuremath{\epsilon}

Phase transition in liquid drop fragmentation

is the typical interparticle gap, and

Sliding blocks with random friction and absorbing random walks

{f}_{L}

Numerical complex zeros of the random energy model

is the typical stress induced by loads. Thus random packings of stiff particles are typically isostatic. Furthermore isostaticity is responsible for the anomalously large susceptibility to perturbation observed in granular aggregates. The load-stress response function of granular piles is critical (power-law distributed) in the isostatic limit, which means that slight overloads will produce internal rearrangements.

Static response in disk packings

We describe a family of random lattices in which the connectivity is determined by the Voronoi construction while the vectorizability is not lost. We can continuously vary the degree of randomness so in a certain limit a regular lattice is recovered. Several statistical properties of the cells and bonds of these lattices are measured. We also study anisotropy effects on the numerical solution of the Laplace equation for varying degrees of randomness.