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Large-scale numerical simulation using the discrete element method (DEM) contributes to improving our understanding of granular flow dynamics involved in many industrial processes and geophysical flows. In industry, it leads to an enhanced design and an overall optimization of the corresponding equipment and process. Most of the DEM simulations in the literature have been performed using spherical particles. A limited number of studies dealt with non-spherical particles, even less with non-convex particles. Even convex bodies do not always represent the real shape of certain particles. In fact, more complex-shaped particles are found in many industrial applications, for example, catalytic pellets in chemical reactors or crushed glass debris in recycling processes. In Grains3D-Part I (Wachs et al. in Powder Technol 224:374–389, 2012), we addressed the problem of convex shape in granular simulations, while in Grains3D-Part II (Rakotonirina and Wachs in Powder Technol 324:18–35, 2018), we suggested a simple though efficient parallel strategy to compute systems with up to a few hundreds of millions of particles. The aim of the present study is to extend even further the modelling capabilities of Grains3D towards non-convex shapes, as a tool to examine the flow dynamics of granular media made of non-convex particles. Our strategy is based on decomposing a non-convex-shaped particle into a set of convex bodies, called elementary components. We call our method glued or clumped convex method, as an extension of the popular glued sphere method. Essentially, a non-convex particle is constructed as a cluster of convex particles, called elementary components. At the level of these elementary components of a glued convex particle, we employ the same contact detection strategy based on a Gilbert–Johnson–Keerthi algorithm and a linked-cell spatial sorting that accelerates the resolution of the contact, that we introduced in [39]. Our glued convex model is implemented as a

Granular flows are omnipresent in nature and industrial processes, but their rheological properties such as apparent friction and packing fraction are still elusive when inertial, cohesive and viscous interactions occur between particles in addition to frictional and elastic forces. Here we report on extensive particle dynamics simulations of such complex flows for a model granular system composed of perfectly rigid particles. We show that, when the apparent friction and packing fraction are normalized by their cohesion-dependent quasistatic values, they are governed by a single dimensionless number that, by virtue of stress additivity, accounts for all interactions. We also find that this dimensionless parameter, as a generalized inertial number, describes the texture variables such as the bond network connectivity and anisotropy. Encompassing various stress sources, this unified framework considerably simplifies and extends the modeling scope for granular dynamics, with potential applications to powder technology and natural flows. Granular materials are abundant in nature, but we haven't fully understood their rheological properties as complex interactions between particles are involved. Here, Vo et al. show that granular flows can be described by a generalized dimensionless number based on stress additivity.

Granular flows are omnipresent in nature and industrial processes, but their rheological properties such as apparent friction and packing fraction are still elusive when inertial, cohesive and viscous interactions occur between particles in addition to frictional and elastic forces. Here we report on extensive particle dynamics simulations of such complex flows for a model granular system composed of perfectly rigid particles. We show that, when the apparent friction and packing fraction are normalized by their cohesion-dependent quasistatic values, they are governed by a single dimensionless number that, by virtue of stress additivity, accounts for all interactions. We also find that this dimensionless parameter, as a generalized inertial number, describes the texture variables such as the bond network connectivity and anisotropy. Encompassing various stress sources, this unified framework considerably simplifies and extends the modeling scope for granular dynamics, with potential applications to powder technology and natural flows. Granular materials are abundant in nature, but we haven't fully understood their rheological properties as complex interactions between particles are involved. Here, Vo et al. show that granular flows can be described by a generalized dimensionless number based on stress additivity.

We use particle dynamics simulations to investigate the evolution of a wet agglomerate inside homogeneous shear flows of dry particles. The agglomerate is modeled by introducing approximate analytical expressions of capillary and viscous forces between particles in addition to frictional contacts. During shear flow, the agglomerate may elongate, break, or be eroded by loss of its capillary bonds and primary particles. By systematically varying the shear rate and surface tension of the binding liquid, we characterize the rates of these dispersion modes. All the rates increase with increasing inertial number of the flow and decreasing cohesion index of the agglomerate. We show that the data points for each mode collapse on a master curve for a dimensionless scaling parameter that combines the inertial number and the cohesion index. The erosion rate vanishes below a cutoff value of the scaling parameter. This leads to a power-law borderline between the vanishing erosion states and erosion states in the phase space defined by the inertial number and the cohesion index.

We use particle dynamics simulations to investigate the evolution of a wet agglomerate inside homogeneous shear flows of dry particles. The agglomerate is modeled by introducing approximate analytical expressions of capillary and viscous forces between particles in addition to frictional contacts. During shear flow, the agglomerate may elongate, break, or be eroded by loss of its capillary bonds and primary particles. By systematically varying the shear rate and surface tension of the binding liquid, we characterize the rates of these dispersion modes. All the rates increase with increasing inertial number of the flow and decreasing cohesion index of the agglomerate. We show that the data points for each mode collapse on a master curve for a dimensionless scaling parameter that combines the inertial number and the cohesion index. The erosion rate vanishes below a cutoff value of the scaling parameter. This leads to a power-law borderline between the vanishing erosion states and erosion states in the phase space defined by the inertial number and the cohesion index.

Granular flows are omnipresent in nature and industrial processes, but their rheological properties such as apparent friction and packing fraction are still elusive when inertial, cohesive and viscous interactions occur between particles in addition to frictional and elastic forces. Here we report on extensive particle dynamics simulations of such complex flows for a model granular system composed of perfectly rigid particles. We show that, when the apparent friction and packing fraction are normalized by their cohesion-dependent quasistatic values, they are governed by a single dimensionless number that, by virtue of stress additivity, accounts for all interactions. We also find that this dimensionless parameter, as a generalized inertial number, describes the texture variables such as the bond network connectivity and anisotropy. Encompassing various stress sources, this unified framework considerably simplifies and extends the modeling scope for granular dynamics, with potential applications to powder technology and natural flows. Granular materials are abundant in nature, but we haven't fully understood their rheological properties as complex interactions between particles are involved. Here, Vo et al. show that granular flows can be described by a generalized dimensionless number based on stress additivity.

We use particle dynamics simulations to investigate the evolution of a wet agglomerate inside homogeneous shear flows of dry particles. The agglomerate is modeled by introducing approximate analytical expressions of capillary and viscous forces between particles in addition to frictional contacts. During shear flow, the agglomerate may elongate, break, or be eroded by loss of its capillary bonds and primary particles. By systematically varying the shear rate and surface tension of the binding liquid, we characterize the rates of these dispersion modes. All the rates increase with increasing inertial number of the flow and decreasing cohesion index of the agglomerate. We show that the data points for each mode collapse on a master curve for a dimensionless scaling parameter that combines the inertial number and the cohesion index. The erosion rate vanishes below a cutoff value of the scaling parameter. This leads to a power-law borderline between the vanishing erosion states and erosion states in the phase space defined by the inertial number and the cohesion index.

Granular flows are omnipresent in nature and industrial processes, but their rheological properties such as apparent friction and packing fraction are still elusive when inertial, cohesive and viscous interactions occur between particles in addition to frictional and elastic forces. Here we report on extensive particle dynamics simulations of such complex flows for a model granular system composed of perfectly rigid particles. We show that, when the apparent friction and packing fraction are normalized by their cohesion-dependent quasistatic values, they are governed by a single dimensionless number that, by virtue of stress additivity, accounts for all interactions. We also find that this dimensionless parameter, as a generalized inertial number, describes the texture variables such as the bond network connectivity and anisotropy. Encompassing various stress sources, this unified framework considerably simplifies and extends the modeling scope for granular dynamics, with potential applications to powder technology and natural flows. Granular materials are abundant in nature, but we haven't fully understood their rheological properties as complex interactions between particles are involved. Here, Vo et al. show that granular flows can be described by a generalized dimensionless number based on stress additivity.

In order to get insight into the wet agglomeration process, we numerically investigate the growth of a single granule inside a dense flow of an initially homogeneous distribution of wet and dry particles. The simulations are performed by means of the discrete element method and the binding liquid is assumed to be transported by the wet particles, which interact via capillary and viscous force laws. The granule size is found to be an exponential function of time, reflecting the conservation of the amount of liquid and the decrease of the number of available wet particles inside the flow during agglomeration. We analyze this behavior in terms of the accretion and erosion rates of wet particles for a range of different values of material parameters such as mean particle size, size polydispersity, friction coefficient and liquid viscosity. In particular, we propose a phase diagram of the granule growth as a function of the mean primary particle diameter and particle size span, which separates the parametric domain in which the granule grows from the domain in which the granule does not survive.

Roots provide basic functions to plants such as water and nutrient uptake and anchoring in soil. The growth and development of root systems contribute to colonizing the surrounding soil and optimizing the access to resources. It is generally known that the variability of plant root architecture results from the combination of genetic, physiological, and environmental factors, in particular soil mechanical resistance. However, this last factor has never been investigated at the soil grain scale for roots. In this paper, we are interested in the effect of the disordered texture of granular soils on the evolution of forces experienced by the root cap during its growth. We introduce a numerical model in which the root is modeled as a flexible self-elongating tube that probes a soil composed of solid particles. By means of extensive simulations, we show that the forces exerted on the root cap reflect interparticle force chains. Our simulations also show that the mean force declines exponentially with root flexibility, the highest force corresponding to the soil hardness. Furthermore, we find that this functional dependence is characterized by a single dimensionless parameter that combines granular structure and root bending stiffness. This finding will be useful to further address the biological issues of mechanosensing and thigmomorphogenesis in plant roots.

In order to get insight into the wet agglomeration process, we numerically investigate the growth of a single granule inside a dense flow of an initially homogeneous distribution of wet and dry particles. The simulations are performed by means of the discrete element method and the binding liquid is assumed to be transported by the wet particles, which interact via capillary and viscous force laws. The granule size is found to be an exponential function of time, reflecting the conservation of the amount of liquid and the decrease of the number of available wet particles inside the flow during agglomeration. We analyze this behavior in terms of the accretion and erosion rates of wet particles for a range of different values of material parameters such as mean particle size, size polydispersity, friction coefficient and liquid viscosity. In particular, we propose a phase diagram of the granule growth as a function of the mean primary particle diameter and particle size span, which separates the parametric domain in which the granule grows from the domain in which the granule does not survive.

In order to get insight into the wet agglomeration process, we numerically investigate the growth of a single granule inside a dense flow of an initially homogeneous distribution of wet and dry particles. The simulations are performed by means of the discrete element method and the binding liquid is assumed to be transported by the wet particles, which interact via capillary and viscous force laws. The granule size is found to be an exponential function of time, reflecting the conservation of the amount of liquid and the decrease of the number of available wet particles inside the flow during agglomeration. We analyze this behavior in terms of the accretion and erosion rates of wet particles for a range of different values of material parameters such as mean particle size, size polydispersity, friction coefficient and liquid viscosity. In particular, we propose a phase diagram of the granule growth as a function of the mean primary particle diameter and particle size span, which separates the parametric domain in which the granule grows from the domain in which the granule does not survive.

Roots provide basic functions to plants such as water and nutrient uptake and anchoring in soil. The growth and development of root systems contribute to colonizing the surrounding soil and optimizing the access to resources. It is generally known that the variability of plant root architecture results from the combination of genetic, physiological, and environmental factors, in particular soil mechanical resistance. However, this last factor has never been investigated at the soil grain scale for roots. In this paper, we are interested in the effect of the disordered texture of granular soils on the evolution of forces experienced by the root cap during its growth. We introduce a numerical model in which the root is modeled as a flexible self-elongating tube that probes a soil composed of solid particles. By means of extensive simulations, we show that the forces exerted on the root cap reflect interparticle force chains. Our simulations also show that the mean force declines exponentially with root flexibility, the highest force corresponding to the soil hardness. Furthermore, we find that this functional dependence is characterized by a single dimensionless parameter that combines granular structure and root bending stiffness. This finding will be useful to further address the biological issues of mechanosensing and thigmomorphogenesis in plant roots.

We present here a numerical study dedicated to the fluidization of a submerged granular medium induced by a localized fluid injection. To this end, a two-dimensional (2D) model is used, coupling the lattice Boltzmann method (LBM) with the discrete element method (DEM) for a relevant description of fluid-grains interaction. An extensive investigation has been carried out to analyze the respective influences of the different parameters of our configuration, both geometrical (bed height, grain diameter, injection width) and physical (fluid viscosity, buoyancy). Compared to previous experimental works, the same qualitative features are recovered as regards the general phenomenology including transitory phase, stationary states, and hysteretic behavior. We also present quantitative findings about transient fluidization, for which several dimensionless quantities and scaling laws are proposed, and about the influence of the injection width, from localized to homogeneous fluidization. Finally, the impact of the present 2D geometry is discussed, by comparison to the real three-dimensional (3D) experiments, as well as the crucial role of the prevailing hydrodynamic regime within the expanding cavity, quantified through a cavity Reynolds number, that can presumably explain some substantial differences observed regarding upward expansion process of the fluidized zone when the fluid viscosity is changed.

We investigate the mechanical behavior of wet granular agglomerates composed of spherical particles by means of molecular dynamics simulations. The capillary cohesion force is modeled as an attraction force at the contact between two particles and expressed as an explicit function of the gap and volume of the liquid bridge. We are interested in the effect of the friction coefficient between primary particles. The agglomerates are subjected to diametrical compression tests. We find that the deformation is ductile involving particle rearrangements. However, a well-defined stress peak is observed and the peak stress is used as a measure of the compressive strength of the agglomerate. The strength increases with friction coefficient but levels off at friction coefficients above 0.4. Furthermore, the compressive strength is an increasing function of particle size span.

We present a novel root observation apparatus capable of measuring the mechanical evolution of both the root network and the surrounding granular medium. The apparatus consists of 11 parallel growth frames, two of them being shearable, where the roots grow inside a photo-elastic or glass granular medium sandwiched between two pieces of glass. An automated system waters the plant and image each frame periodically in white light and between crossed polarisers. This makes it possible to follow (i) the root tips and (ii) the grain displacements as well as (iii) their inner pressure. We show how a root networks evolve in a granular medium and how it can mechanically stabilize it. This constitutes a model experiment to move forward in the understanding of the complex interaction between root growth and surrounding soil mechanical evolution.

We use molecular dynamics simulations to investigate the effects of root bending stiffness and packing fraction on the path followed by a growing root in 2D packings of grains representing a soil. The root is modeled as a chain of elements that can grow in length and change their direction depending on the forces exerted by soil grains. We show that the root shape is mainly controlled by the bending stiffness of its apex. At low stiffness, the root randomly explores the pore space whereas at sufficiently high stiffness, of the order of soil hardness multiplied by mean grain size, the root follows a straight path across the soil. Between these two limits, the root shape can be characterized by the standard deviation of its re-directions at the scale of soil grains. We find that this shape parameter varies as a power-law function of the normalized bending stiffness.

We investigate the mechanical behavior of wet granular agglomerates composed of spherical particles by means of molecular dynamics simulations. The capillary cohesion force is modeled as an attraction force at the contact between two particles and expressed as an explicit function of the gap and volume of the liquid bridge. We are interested in the effect of the friction coefficient between primary particles. The agglomerates are subjected to diametrical compression tests. We find that the deformation is ductile involving particle rearrangements. However, a well-defined stress peak is observed and the peak stress is used as a measure of the compressive strength of the agglomerate. The strength increases with friction coefficient but levels off at friction coefficients above 0.4. Furthermore, the compressive strength is an increasing function of particle size span.

We investigate the mechanical behavior of wet granular agglomerates composed of spherical particles by means of molecular dynamics simulations. The capillary cohesion force is modeled as an attraction force at the contact between two particles and expressed as an explicit function of the gap and volume of the liquid bridge. We are interested in the effect of the friction coefficient between primary particles. The agglomerates are subjected to diametrical compression tests. We find that the deformation is ductile involving particle rearrangements. However, a well-defined stress peak is observed and the peak stress is used as a measure of the compressive strength of the agglomerate. The strength increases with friction coefficient but levels off at friction coefficients above 0.4. Furthermore, the compressive strength is an increasing function of particle size span.

We use molecular dynamics simulations to investigate the effects of root bending stiffness and packing fraction on the path followed by a growing root in 2D packings of grains representing a soil. The root is modeled as a chain of elements that can grow in length and change their direction depending on the forces exerted by soil grains. We show that the root shape is mainly controlled by the bending stiffness of its apex. At low stiffness, the root randomly explores the pore space whereas at sufficiently high stiffness, of the order of soil hardness multiplied by mean grain size, the root follows a straight path across the soil. Between these two limits, the root shape can be characterized by the standard deviation of its re-directions at the scale of soil grains. We find that this shape parameter varies as a power-law function of the normalized bending stiffness.

We present a novel root observation apparatus capable of measuring the mechanical evolution of both the root network and the surrounding granular medium. The apparatus consists of 11 parallel growth frames, two of them being shearable, where the roots grow inside a photo-elastic or glass granular medium sandwiched between two pieces of glass. An automated system waters the plant and image each frame periodically in white light and between crossed polarisers. This makes it possible to follow (i) the root tips and (ii) the grain displacements as well as (iii) their inner pressure. We show how a root networks evolve in a granular medium and how it can mechanically stabilize it. This constitutes a model experiment to move forward in the understanding of the complex interaction between root growth and surrounding soil mechanical evolution.

We investigate by means of Contact Dynamics simulations the transient dynamics of a 2D granular pile set into motion by applying shear velocity during a short time interval to all particles. The spreading dynamics is directly controlled by the input energy whereas in recent studies of column collapse the dynamics scales with the initial potential energy of the column. As in column collapse, we observe a power-law dependence of the runout distance with respect to the input energy with nontrivial exponents. This suggests that the power-law behavior is a generic feature of granular dynamics, and the values of the exponents reflect the distribution of kinetic energy inside the material. We observe two regimes with different values of the exponents: the low-energy regime reflects the destabilization of the pile by the impact with a runout time independent of the input energy whereas the high-energy regime is governed by the input energy. We show that the evolution of the pile in the high-energy regime can be described by a characteristic decay time and the available energy after the pile is destabilized.

We investigate by means of Contact Dynamics simulations the transient dynamics of a 2D granular pile set into motion by applying shear velocity during a short time interval to all particles. The spreading dynamics is directly controlled by the input energy whereas in recent studies of column collapse the dynamics scales with the initial potential energy of the column. As in column collapse, we observe a power-law dependence of the runout distance with respect to the input energy with nontrivial exponents. This suggests that the power-law behavior is a generic feature of granular dynamics, and the values of the exponents reflect the distribution of kinetic energy inside the material. We observe two regimes with different values of the exponents: the low-energy regime reflects the destabilization of the pile by the impact with a runout time independent of the input energy whereas the high-energy regime is governed by the input energy. We show that the evolution of the pile in the high-energy regime can be described by a characteristic decay time and the available energy after the pile is destabilized.

We investigate by means of Contact Dynamics simulations the transient dynamics of a 2D granular pile set into motion by applying shear velocity during a short time interval to all particles. The spreading dynamics is directly controlled by the input energy whereas in recent studies of column collapse the dynamics scales with the initial potential energy of the column. As in column collapse, we observe a power-law dependence of the runout distance with respect to the input energy with nontrivial exponents. This suggests that the power-law behavior is a generic feature of granular dynamics, and the values of the exponents reflect the distribution of kinetic energy inside the material. We observe two regimes with different values of the exponents: the low-energy regime reflects the destabilization of the pile by the impact with a runout time independent of the input energy whereas the high-energy regime is governed by the input energy. We show that the evolution of the pile in the high-energy regime can be described by a characteristic decay time and the available energy after the pile is destabilized.

Beyond a given threshold, an upward fluid flow at constant flowrate, injected through a small size section, is able to generate a fluidization along a vertical chimney over the entire height of a granular assembly. Fluidization is first initiated in the immediate vicinity of the injection hole and then the fluidized zone grows gradually until reaching the upper surface of the granular packing. In this work, we present numerical results on the kinetics of chimney fluidization in an immersed granular bed produced with two-dimensional simulations coupling the Discrete Element and Lattice Boltzmann Methods (DEM-LBM). A parametric study is carried out with 11 different sets of physical parameters and analyzed based on spatio-temporal diagrams. Then a dimensional analysis allows finding general scaling laws for both threshold and growth rate of the fluidized zone by use of two dimensionless numbers, namely Reynolds and Archimedes numbers, while quite simple empirical relationships can also be proposed.

The elementary mechanisms driving the ubiquitous surface erosion of cohesive geomaterials can be analysed from a micromechanical perspective combining well-known numerical techniques. Here, a coupled model combining the Discrete Element and Lattice Boltzmann methods (DEM-LBM) provides an insight into the solid-fluid interaction during the transient erosion caused by a vertical fluid jet impinging on the surface of a granular assembly. The brittle cementation providing cohesion between the solid grains is described here by means of a simple bond model with a single-parameter yield surface. The initial topology of the surface erosion tends to mimic the profile of fluid velocity directly above the soil surface. We find that both the rate of erosion and the magnitude of eroded mass depend directly on the micromechanical strength of the single solid bonds.