Stress response function from Voronoi tessellation of static granular layers
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ORIGINAL PAPER
Stress response function from Voronoi tessellation of static granular layers Eduardo Célio Boaventura1 · Fernando Andrade Ducha2 · A. P. F. Atman3 Received: 27 January 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Graphical abstract
Keywords Granular material · Computational geometry · Stress response function · Voronoi tessellation · Micromechanics
1 Introduction * Eduardo Célio Boaventura [email protected] Extended author information available on the last page of the article
Granular materials are complex systems that pose challenges for a predictive theoretical description [1, 2]. Nevertheless, some approaches, such as the stress response function [3, 4]
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provides a useful resource for studying stress propagation in granular assemblies and plastic deformation (see [5] and other related articles in the Special Issue), in particular for testing and validating models [6–10]. A particularly important aspect is that the distribution of forces and stresses in static granular piles is strongly dependent on the history of sample preparation [11]. Granular piles formed by dropping grains from a point source (hopper) typically generate a spatial stress profile at their bottom that exhibits a central “dip” directly below the apex of the pile [12, 13]. Granular piles formed instead by using a sieve, analogous to a “rainfall” of grains, generate a stress profile with a central hump [14]. Furthermore, ordered stackings of particles (composed of monodispersed grains) exhibit double peak stress profiles, while disordered assemblies (with polydispersed grains) exhibit single peak profiles [15, 16]. The Stress Response Function (SRF) [3, 17–19] consists of measuring the stress profile in response to a small overload force applied to a single grain of a layer. By varying the contact force network due to overloading, it is possible to obtain the stress components [20], and to calculate the difference between stress profiles before and after overloading. SRF is typically calculated at the bottom of granular piles [21
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