A mathematical model of particle-particle interaction for discrete element based modeling of deformation and fracture of heterogeneous elastic-plastic materials

S. G. Psakhie, E. V. Shilko, A. S. Grigoriev, S. V. Astafurov, A. V. Dimaki, A. Yu Smolin

Research output: Contribution to journalArticle

46 Citations (Scopus)

Abstract

An approach to implementation of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of discrete element method (DEM) is proposed. The approach is based on constructing many-body forces of element-element interaction within the formalism of simply deformable element approximation of generalized concept of DEM. Implementation of the approach is shown by the example of the movable cellular automaton method, which integrates the possibilities of DEM and cellular automaton methods. For correct modeling of inelastic deformation and failure of heterogeneous materials the dilatational non-associated model of plastic flow is implemented within the formalism of DEM. The examples are presented which illustrate correctness of the developed mathematical formalism and its usefulness in analysis of various problems in mechanics of discontinua.

Original languageEnglish
Pages (from-to)96-115
Number of pages20
JournalEngineering Fracture Mechanics
Volume130
DOIs
Publication statusPublished - 1 Nov 2014

Fingerprint

Particle interactions
Finite difference method
Mathematical models
Plastics
Cellular automata
Plastic flow
Plasticity
Elasticity
Mechanics

Keywords

  • Cracks
  • Discrete element method
  • Fracture criteria
  • Many-body interaction
  • Movable cellular automata
  • Two-invariant plasticity model

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

A mathematical model of particle-particle interaction for discrete element based modeling of deformation and fracture of heterogeneous elastic-plastic materials. / Psakhie, S. G.; Shilko, E. V.; Grigoriev, A. S.; Astafurov, S. V.; Dimaki, A. V.; Smolin, A. Yu.

In: Engineering Fracture Mechanics, Vol. 130, 01.11.2014, p. 96-115.

Research output: Contribution to journalArticle

Psakhie, S. G. ; Shilko, E. V. ; Grigoriev, A. S. ; Astafurov, S. V. ; Dimaki, A. V. ; Smolin, A. Yu. / A mathematical model of particle-particle interaction for discrete element based modeling of deformation and fracture of heterogeneous elastic-plastic materials. In: Engineering Fracture Mechanics. 2014 ; Vol. 130. pp. 96-115.
@article{04815078be2d4a889d6c49f329b22f43,
title = "A mathematical model of particle-particle interaction for discrete element based modeling of deformation and fracture of heterogeneous elastic-plastic materials",
abstract = "An approach to implementation of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of discrete element method (DEM) is proposed. The approach is based on constructing many-body forces of element-element interaction within the formalism of simply deformable element approximation of generalized concept of DEM. Implementation of the approach is shown by the example of the movable cellular automaton method, which integrates the possibilities of DEM and cellular automaton methods. For correct modeling of inelastic deformation and failure of heterogeneous materials the dilatational non-associated model of plastic flow is implemented within the formalism of DEM. The examples are presented which illustrate correctness of the developed mathematical formalism and its usefulness in analysis of various problems in mechanics of discontinua.",
keywords = "Cracks, Discrete element method, Fracture criteria, Many-body interaction, Movable cellular automata, Two-invariant plasticity model",
author = "Psakhie, {S. G.} and Shilko, {E. V.} and Grigoriev, {A. S.} and Astafurov, {S. V.} and Dimaki, {A. V.} and Smolin, {A. Yu}",
year = "2014",
month = "11",
day = "1",
doi = "10.1016/j.engfracmech.2014.04.034",
language = "English",
volume = "130",
pages = "96--115",
journal = "Engineering Fracture Mechanics",
issn = "0013-7944",
publisher = "Elsevier BV",

}

TY - JOUR

T1 - A mathematical model of particle-particle interaction for discrete element based modeling of deformation and fracture of heterogeneous elastic-plastic materials

AU - Psakhie, S. G.

AU - Shilko, E. V.

AU - Grigoriev, A. S.

AU - Astafurov, S. V.

AU - Dimaki, A. V.

AU - Smolin, A. Yu

PY - 2014/11/1

Y1 - 2014/11/1

N2 - An approach to implementation of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of discrete element method (DEM) is proposed. The approach is based on constructing many-body forces of element-element interaction within the formalism of simply deformable element approximation of generalized concept of DEM. Implementation of the approach is shown by the example of the movable cellular automaton method, which integrates the possibilities of DEM and cellular automaton methods. For correct modeling of inelastic deformation and failure of heterogeneous materials the dilatational non-associated model of plastic flow is implemented within the formalism of DEM. The examples are presented which illustrate correctness of the developed mathematical formalism and its usefulness in analysis of various problems in mechanics of discontinua.

AB - An approach to implementation of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of discrete element method (DEM) is proposed. The approach is based on constructing many-body forces of element-element interaction within the formalism of simply deformable element approximation of generalized concept of DEM. Implementation of the approach is shown by the example of the movable cellular automaton method, which integrates the possibilities of DEM and cellular automaton methods. For correct modeling of inelastic deformation and failure of heterogeneous materials the dilatational non-associated model of plastic flow is implemented within the formalism of DEM. The examples are presented which illustrate correctness of the developed mathematical formalism and its usefulness in analysis of various problems in mechanics of discontinua.

KW - Cracks

KW - Discrete element method

KW - Fracture criteria

KW - Many-body interaction

KW - Movable cellular automata

KW - Two-invariant plasticity model

UR - http://www.scopus.com/inward/record.url?scp=84908226265&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84908226265&partnerID=8YFLogxK

U2 - 10.1016/j.engfracmech.2014.04.034

DO - 10.1016/j.engfracmech.2014.04.034

M3 - Article

AN - SCOPUS:84908226265

VL - 130

SP - 96

EP - 115

JO - Engineering Fracture Mechanics

JF - Engineering Fracture Mechanics

SN - 0013-7944

ER -