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Stress response function from Voronoi tessellation of static granular layers

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Abstract

A new technique to obtain the stress response function of static granular layers from the geometric properties of the corresponding Voronoi tessellations is presented. We measured the vertex displacements of the Voronoi polygons due to the application of a vertical force located on the surface of the layer. A protocol to obtain the stress response function is proposed by establishing a gauge between the geometric measurements and the contact forces, which allows to calculate the stress components indirectly. We show that the Voronoi tessellation response function—VTRF—exhibits the elastic characteristics of additivity, reversibility and linearity as the stress response function. Thus, we applied this protocol to calculate the stress response profiles of two different preparations and to compare them with the results obtained from microscopic measurements, that is, the stress response calculated using contact forces.

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Acknowledgements

We are indebted to Prof. Luis Pugnaloni for the helpful suggestions in his referee report which improved considerably this work. E.C.B. wish to acknowledge the support given by CEFET-MG and A.P.F. Atman thanks FAPEMIG Brazilian funding agency and CNPq Research Grant 308792/2018-1.

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Authors and Affiliations

  1. Department of Physics and Graduate Program in Mathematical and Computational Modeling (PPGMMC) - Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG)., Av. Amazonas, 7675 - Nova Gameleira, Belo Horizonte, MG, 30510-000, Brazil

    Eduardo Célio Boaventura

  2. Graduate Program in Mathematical and Computational Modeling - CEFET-MG, Belo Horizonte, Brazil

    Fernando Andrade Ducha

  3. Department of Physics (CEFET-MG) and National Institute of Science and Technology for Complex Systems INCT-SC, Belo Horizonte, Brazil

    A. P. F. Atman

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  1. Eduardo Célio Boaventura
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Correspondence to Eduardo Célio Boaventura.

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Boaventura, E.C., Ducha, F.A. & Atman, A.P.F. Stress response function from Voronoi tessellation of static granular layers. Granular Matter 22, 61 (2020). https://doi.org/10.1007/s10035-020-01026-w

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