Maximum entropy methods in the mechanics of quasi-static deformation of granular materials

N. P. Kruyt, L. Rothenburg

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

4 Citations (Scopus)

Abstract

In statistical physics of dilute gases maximum entropy methods are widely used for theoretical predictions of macroscopic quantities in terms of microscopic quantities. In this study an analogous approach to the mechanics of quasi-static deformation of granular materials is proposed. The reasoning is presented that leads to the definition of an entropy that is appropriate to quasi-static deformation of granular materials. This entropy is formulated in terms of contact quantities, since contacts constitute the relevant microscopic level for granular materials that consist of semi-rigid particles. The proposed maximum entropy approach is then applied to two cases. The first case deals with the probability density functions of contact forces in a two-dimensional assembly with frictional contacts under prescribed hydrostatic stress. The second case deals with the elastic behaviour of two-dimensional assemblies of non-rotating particles with bonded contacts. For both cases the probability density functions of contact forces are determined from the proposed maximum entropy method, under the constraints appropriate to the case. These constraints form the macroscopic information available about the system. With the probability density functions for contact forces thus determined, theoretical predictions of macroscopic quantities can be made. These theoretical predictions are then compared with results obtained from two-dimensional Discrete Element simulations and from experiments.

Original languageEnglish
Title of host publicationASME 2002 International Mechanical Engineering Congress and Exposition
PublisherAmerican Society of Mechanical Engineers (ASME)
Pages329-336
Number of pages8
ISBN (Print)0791836401, 9780791836408
DOIs
Publication statusPublished - 2002
EventASME 2002 International Mechanical Engineering Congress and Exposition - New Orleans, United States
Duration: 17 Nov 200222 Nov 2002

Conference

ConferenceASME 2002 International Mechanical Engineering Congress and Exposition
CountryUnited States
CityNew Orleans
Period17/11/0222/11/02

Keywords

  • Granular materials
  • Maximum entropy method
  • Micromechanics
  • Probability density function

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