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

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

Research output: Contribution to journalArticle

Abstract

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
Volume40
Issue number25
DOIs
StatePublished - Dec 2003

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Elasticity Theory
Packing
Breakdown
Elasticity
elastic properties
breakdown
Linear Elasticity
Tensors
Granular Media
Random Media
Particle System
Cells
Glass
Linear Inequalities
Arrangement
Tensor
Liquids
Liquid
tensors
Cell

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials

Cite this

Breakdown of elasticity theory for jammed hard-particle packings : Conical nonlinear constitutive theory. / Torquato, S.; Donev, Aleksandar; Stillinger, F. H.

In: International Journal of Solids and Structures, Vol. 40, No. 25, 12.2003, p. 7143-7153.

Research output: Contribution to journalArticle

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