Influence of Irreversible Contacts on the Stiffness of Dense Polydisperse Packings

H. Smit, R. Kievitsbosch, V. Magnanimo, S. Luding, K. Taghizadeh

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

Abstract

Modelling granular materials can help us to understand their behaviour on the microscopic scale, and to obtain macroscopic continuum relations by a micro-macro transition approach. In this paper, the Discrete Element Method (DEM) is used to investigate the influence of the irreversibility at the contact level on the macroscopic behaviour of granular packings in the context of an elasto-plastic cohesive contact model. From the microscopic contact characteristics the effective stiffness parameters are determined at different volume fractions. The conventional way to calculate the stiffness of a packing is to apply compression or shear strain to the entire system and measure the stress response. The results show that the stiffness of the packings increases with the volume fraction as expected. Surprisingly, the samples experience multiple regimes depending on the applied strain and the hysteretic contact model. In the limit of elastic regime at very small strain, all contacts have equal unloading (reversible) stiffness k 2 . As the strain increases, the contacts transit to the loading stiffness branch and the macroscopic stiffness show a second plateau, where the microstructure of the packing does not change but the contact forces do due to the (irreversible) transition from the unloading to the loading branch and the corresponding reduction in stiffness by k 1 ∕k 2 . Only for much larger strain particles start to rearrange and the overall behaviour becomes plastic.

Original languageEnglish
Title of host publicationMicro to MACRO Mathematical Modelling in Soil Mechanics
EditorsPasquale Giovine, Paolo Maria Mariano, Giuseppe Mortara
PublisherSpringer International Publishing AG
Pages327-336
Number of pages10
ISBN (Electronic)978-3-319-99474-1
ISBN (Print)978-3-319-99473-4
DOIs
Publication statusPublished - 25 Jan 2019

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Fingerprint

Packing
Stiffness
Contact
Volume Fraction
Branch
Discrete Element Method
Large Strain
Irreversibility
Contact Force
Granular Materials
Elasto-plastic
Influence
Microstructure
Plastics
Continuum
Compression
Entire
Calculate
Modeling
Model

Keywords

  • Discrete element method
  • Elasto-plastic contact model
  • Small-strain stiffness

Cite this

Smit, H., Kievitsbosch, R., Magnanimo, V., Luding, S., & Taghizadeh, K. (2019). Influence of Irreversible Contacts on the Stiffness of Dense Polydisperse Packings. In P. Giovine, P. M. Mariano, & G. Mortara (Eds.), Micro to MACRO Mathematical Modelling in Soil Mechanics (pp. 327-336). (Trends in Mathematics). Springer International Publishing AG. https://doi.org/10.1007/978-3-319-99474-1_33
Smit, H. ; Kievitsbosch, R. ; Magnanimo, V. ; Luding, S. ; Taghizadeh, K. / Influence of Irreversible Contacts on the Stiffness of Dense Polydisperse Packings. Micro to MACRO Mathematical Modelling in Soil Mechanics. editor / Pasquale Giovine ; Paolo Maria Mariano ; Giuseppe Mortara. Springer International Publishing AG, 2019. pp. 327-336 (Trends in Mathematics).
@inbook{aa7b20b792f64784b37e73eeff66955c,
title = "Influence of Irreversible Contacts on the Stiffness of Dense Polydisperse Packings",
abstract = "Modelling granular materials can help us to understand their behaviour on the microscopic scale, and to obtain macroscopic continuum relations by a micro-macro transition approach. In this paper, the Discrete Element Method (DEM) is used to investigate the influence of the irreversibility at the contact level on the macroscopic behaviour of granular packings in the context of an elasto-plastic cohesive contact model. From the microscopic contact characteristics the effective stiffness parameters are determined at different volume fractions. The conventional way to calculate the stiffness of a packing is to apply compression or shear strain to the entire system and measure the stress response. The results show that the stiffness of the packings increases with the volume fraction as expected. Surprisingly, the samples experience multiple regimes depending on the applied strain and the hysteretic contact model. In the limit of elastic regime at very small strain, all contacts have equal unloading (reversible) stiffness k 2 . As the strain increases, the contacts transit to the loading stiffness branch and the macroscopic stiffness show a second plateau, where the microstructure of the packing does not change but the contact forces do due to the (irreversible) transition from the unloading to the loading branch and the corresponding reduction in stiffness by k 1 ∕k 2 . Only for much larger strain particles start to rearrange and the overall behaviour becomes plastic.",
keywords = "Discrete element method, Elasto-plastic contact model, Small-strain stiffness",
author = "H. Smit and R. Kievitsbosch and V. Magnanimo and S. Luding and K. Taghizadeh",
year = "2019",
month = "1",
day = "25",
doi = "10.1007/978-3-319-99474-1_33",
language = "English",
isbn = "978-3-319-99473-4",
series = "Trends in Mathematics",
publisher = "Springer International Publishing AG",
pages = "327--336",
editor = "Pasquale Giovine and Mariano, {Paolo Maria} and Giuseppe Mortara",
booktitle = "Micro to MACRO Mathematical Modelling in Soil Mechanics",
address = "Switzerland",

}

Smit, H, Kievitsbosch, R, Magnanimo, V, Luding, S & Taghizadeh, K 2019, Influence of Irreversible Contacts on the Stiffness of Dense Polydisperse Packings. in P Giovine, PM Mariano & G Mortara (eds), Micro to MACRO Mathematical Modelling in Soil Mechanics. Trends in Mathematics, Springer International Publishing AG, pp. 327-336. https://doi.org/10.1007/978-3-319-99474-1_33

Influence of Irreversible Contacts on the Stiffness of Dense Polydisperse Packings. / Smit, H.; Kievitsbosch, R.; Magnanimo, V.; Luding, S.; Taghizadeh, K.

Micro to MACRO Mathematical Modelling in Soil Mechanics. ed. / Pasquale Giovine; Paolo Maria Mariano; Giuseppe Mortara. Springer International Publishing AG, 2019. p. 327-336 (Trends in Mathematics).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

TY - CHAP

T1 - Influence of Irreversible Contacts on the Stiffness of Dense Polydisperse Packings

AU - Smit, H.

AU - Kievitsbosch, R.

AU - Magnanimo, V.

AU - Luding, S.

AU - Taghizadeh, K.

PY - 2019/1/25

Y1 - 2019/1/25

N2 - Modelling granular materials can help us to understand their behaviour on the microscopic scale, and to obtain macroscopic continuum relations by a micro-macro transition approach. In this paper, the Discrete Element Method (DEM) is used to investigate the influence of the irreversibility at the contact level on the macroscopic behaviour of granular packings in the context of an elasto-plastic cohesive contact model. From the microscopic contact characteristics the effective stiffness parameters are determined at different volume fractions. The conventional way to calculate the stiffness of a packing is to apply compression or shear strain to the entire system and measure the stress response. The results show that the stiffness of the packings increases with the volume fraction as expected. Surprisingly, the samples experience multiple regimes depending on the applied strain and the hysteretic contact model. In the limit of elastic regime at very small strain, all contacts have equal unloading (reversible) stiffness k 2 . As the strain increases, the contacts transit to the loading stiffness branch and the macroscopic stiffness show a second plateau, where the microstructure of the packing does not change but the contact forces do due to the (irreversible) transition from the unloading to the loading branch and the corresponding reduction in stiffness by k 1 ∕k 2 . Only for much larger strain particles start to rearrange and the overall behaviour becomes plastic.

AB - Modelling granular materials can help us to understand their behaviour on the microscopic scale, and to obtain macroscopic continuum relations by a micro-macro transition approach. In this paper, the Discrete Element Method (DEM) is used to investigate the influence of the irreversibility at the contact level on the macroscopic behaviour of granular packings in the context of an elasto-plastic cohesive contact model. From the microscopic contact characteristics the effective stiffness parameters are determined at different volume fractions. The conventional way to calculate the stiffness of a packing is to apply compression or shear strain to the entire system and measure the stress response. The results show that the stiffness of the packings increases with the volume fraction as expected. Surprisingly, the samples experience multiple regimes depending on the applied strain and the hysteretic contact model. In the limit of elastic regime at very small strain, all contacts have equal unloading (reversible) stiffness k 2 . As the strain increases, the contacts transit to the loading stiffness branch and the macroscopic stiffness show a second plateau, where the microstructure of the packing does not change but the contact forces do due to the (irreversible) transition from the unloading to the loading branch and the corresponding reduction in stiffness by k 1 ∕k 2 . Only for much larger strain particles start to rearrange and the overall behaviour becomes plastic.

KW - Discrete element method

KW - Elasto-plastic contact model

KW - Small-strain stiffness

UR - http://www.scopus.com/inward/record.url?scp=85064604030&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-99474-1_33

DO - 10.1007/978-3-319-99474-1_33

M3 - Chapter

SN - 978-3-319-99473-4

T3 - Trends in Mathematics

SP - 327

EP - 336

BT - Micro to MACRO Mathematical Modelling in Soil Mechanics

A2 - Giovine, Pasquale

A2 - Mariano, Paolo Maria

A2 - Mortara, Giuseppe

PB - Springer International Publishing AG

ER -

Smit H, Kievitsbosch R, Magnanimo V, Luding S, Taghizadeh K. Influence of Irreversible Contacts on the Stiffness of Dense Polydisperse Packings. In Giovine P, Mariano PM, Mortara G, editors, Micro to MACRO Mathematical Modelling in Soil Mechanics. Springer International Publishing AG. 2019. p. 327-336. (Trends in Mathematics). https://doi.org/10.1007/978-3-319-99474-1_33