Influence of Irreversible Contacts on the Stiffness of Dense Polydisperse Packings

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

*Corresponding author for this work

    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).
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    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.",
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    author = "H. Smit and R. Kievitsbosch and V. Magnanimo and S. Luding and K. Taghizadeh",
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    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

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    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.

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    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.

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    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