Breakdown of elasticity theory for jammed hard-particle packings: Conical nonlinear constitutive theory

S. Torquato, A. Donev, F. H. Stillinger

Research output: Contribution to journalArticlepeer-review


Hard-particle packings have provided a rich source of outstanding theoretical problems and served as useful starting points to model the structure of granular media, liquids, living cells, glasses, and random media. The nature of "jammed" hard-particle packings is a current subject of keen interest. We demonstrate that the response of jammed hard-particle packings to global deformations cannot be described by linear elasticity (even for small particle displacements) but involves a "conical" nonlinear constitutive theory. It is the singular nature of the hard-particle potential that leads to the breakdown of linear elasticity. Interestingly, a nonlinear theory arises because the feasible particle displacements (leading to unjamming) depend critically on the local spatial arrangement of the particles, implying a directionality in the feasible strains that is absent in particle systems with soft potentials. Mathematically, the set of feasible strains has a conical structure, i.e., components of the imposed strain tensor generally obey linear inequalities. The nature of the nonlinear behavior is illustrated by analyzing several specific packings. Finally, we examine the conditions under which a packing can be considered to "incompressible" in the traditional sense.

Original languageEnglish (US)
Pages (from-to)7143-7153
Number of pages11
JournalInternational Journal of Solids and Structures
Issue number25
StatePublished - Dec 2003

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


Dive into the research topics of 'Breakdown of elasticity theory for jammed hard-particle packings: Conical nonlinear constitutive theory'. Together they form a unique fingerprint.

Cite this