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The purpose of this paper is to develop a discrete element (DE) and multiscale modeling methodology to represent granular media at their particle scale as they interface solid deformable bodies, such as soil‐tool, tire, penetrometer, pile, etc., interfaces.

A three‐dimensional ellipsoidal discrete element method (DEM) is developed to more physically represent particle shape in granular media while retaining the efficiency of smooth contact interface conditions for computation. DE coupling to finite element (FE) facets is presented to demonstrate initially the development of overlapping bridging scale methods for concurrent multiscale modeling of granular media.

A closed‐form solution of ellipsoidal particle contact resolution and stiffness is presented and demonstrated for two particle, and many particle contact simulations, during gravity deposition, and quasi‐static oedometer, triaxial compression, and pile penetration. The DE‐FE facet coupling demonstrates the potential to alleviate artificial boundary effects in the shear deformation region between DEM granular media and deformable solid bodies.

The research is being extended to couple more robustly the ellipsoidal DEM code and a higher order continuum FE code via overlapping bridging scale methods, in order to remove dependence of penetration/shear resistance on the boundary placement for DE simulation.

When concurrent multiscale computational modeling of interface conditions between deformable solid bodies and granular materials reaches maturity, modelers will be able to simulate the mechanical behavior accounting for physical particle sizes and flow in the interface region, and thus design their tool, tire, penetrometer, or pile accordingly.

A closed‐form solution for ellipsoidal particle contact is demonstrated in this paper, and the ability to couple DE to FE facets.

Granular lubrication is a new lubrication method and can be used in extreme working conditions; however, the obstacle of force transmission characteristics needs to be urgently solved to fully understand the mechanical and bearing mechanisms of granular lubrication.

A flat sliding friction cell is developed to study the force transmission behaviors of granules under shearing. Granular material, sliding velocity, granule size and granule humidity are considered in these experiments. The measured normal and shear force, which is transmitted from the bottom friction pair to the top friction pair via the granular lubrication medium, reveals the influence of these controlling parameters on the force transmission characteristics of granules.

Experimental results show that a low sliding velocity, a large granule size and a low granular humidity increase the measured normal force and shear force. Besides, a comparison experiment with other typical lubrication styles is also carried out. The force transmission under granular lubrication is mainly dependent on the force transmission path, which is closely related to the deconstruction and reconstruction of the force chains in the granule assembly.

These findings reveal the force transmission mechanism of granular lubrication and can also offer the helpful reference for the design of the new granular lubrication bearing.

A numerical analysis of the micromechanical behaviour of a granular material is described using a new program MASOM based on Cundall's discrete element method. In the analysis the individual grains which make up the material are taken to be deformable 2D polygons of arbitrary size and shape. Contact forces between the grains are calculated according to Mindlin's solution for frictional contact between elastic bodies. The material in each grain is taken to be linear elastic but limited by the fracture strength of the material. Fracture is permitted along any one of a number of candidate fracture planes if an associated compressive load tending to split the gain reaches a critical level. Fragments of fractured grains are carried until they become too small to track using the explicit time integration algorithm used to advance the solution. The MASOM program is able to consider a number of different classes of elements and different types of contact between the various classes. Thus, in addition to the granular material the program can also model containers and loading devices. The program is used to simulate uniaxial and triaxial compression tests for geological materials. The results are shown to give results for stress‐strain and stress difference versus pressure which are in qualitative agreement with test data. The numerical results reveal a very complex micromechanical behaviour in granular materials, including highly variable and rather unstable load paths and a very inhomogeneous load distribution within a representative sample of the material. A video of the response of a typical frictional material to applied loads shows an interesting localized effect near sample boundaries involving crowding together of grains which cannot be observed using conventional static field plots.

This paper aims to present a novel scheme for imposing periodic boundary conditions with downscaled macroscopic strain measures of gradient Cosserat continuum on the representative volume element (RVE) of discrete particle assembly in the frame of the second-order computational homogenization methods for granular materials.

The proposed scheme is based on the generalized Hill’s lemma of gradient Cosserat continuum and the incremental non-linear constitutive relation condensed to the peripheral particles of the RVE of discrete particle assembly. The generalized Hill’s lemma conducts to downscale the macroscopic strain or stress measures and to impose the periodic boundary conditions on the RVE boundary so that the Hill-Mandel energy equivalence condition is ensured. Because of the incremental non-linear constitutive relation condensed to the peripheral particles of the RVE, the periodic boundary displacement and traction constraints together with the downscaled macroscopic strains and strain gradients, micro-rotations and curvatures are imposed in the point-wise sense without the need of introducing the Lagrange multipliers for enforcing the periodic boundary displacement and traction constraints in a weak sense.

Numerical results demonstrate that the applicability and effectiveness of the proposed scheme in imposing the periodic boundary conditions on the RVE. The results of the RVE subjected to the periodic boundary conditions together with the displacement boundary conditions in the second-order computational homogenization for granular materials provide the desired estimations, which lie between the upper and the lower bounds provided by the displacement and the traction boundary conditions imposed on the RVE respectively.

Each grain in the particulate system under consideration is assumed to be rigid and circular.

The proposed scheme for imposing periodic boundary conditions on the RVE can be adopted solely for estimating the effective mechanical properties of granular materials and/or integrated into the frame of the second-order computational homogenization method with a nested finite element method-discrete element method solution procedure for granular materials. It will tend to provide, at least theoretically, more reasonable results for effective material properties and solutions of a macroscopic boundary value problem simulated by the computational homogenization method.

This paper presents a novel scheme for imposing periodic boundary conditions with downscaled macroscopic strain measures of gradient Cosserat continuum on the RVE of discrete particle assembly for granular materials without need of introducing Lagrange multipliers for enforcing periodic boundary conditions in a weak (integration) sense.

A microstructural finite element model (MFEM) for granular material considering the microstructure of material is presentented. In the MFEM method, a volume of large number of particles is represented by an element consisting of a few nodal points. The stiffness matrix of the element is then formulated based on the contact stiffness and the packing arrangement of the particles. The method can be easily applied in the framework of finite element technique to solve boundary value problems in practical situations. Applicability of the model is evaluated by comparing the results of MFEM model with that from DEM model.

Shear-induced strain localization in granular materials has been a hot topic under intensive research during the last four decades. However, the micromechanical process and mechanisms underlying the initiation and development of shear bands are still not fully understood. The purpose of this paper is to eliminate this deficiency.

The paper carries out several two-dimensional distinct element method simulations to examine various global and local micromechanical quantities particular the energy dissipation and local stress and strain invariants with a special emphasis on the initiation and propagation of shear bands. Moreover, the effects of various influential variables including initial void ratio, confining stress, inter-particle friction coefficient, rolling resistance coefficient, specimen slenderness and strain rate on the pattern, scope and degree of shear bands are investigated.

Novel findings of the relationship between sliding and rolling dissipation band and shear band are achieved, indicating a plastic dissipation nature for the shear band. The high inter-particle sliding or rolling resistance, relative small initial void ratio, relative low confining stress and high strain rate facilitate the formation of shear band. In addition, the specimen slenderness affects the pattern of shear band.

In this paper, a comprehensive and deep investigation on shear band formation linked with localization of energy dissipation and strain invariants was presented. The new findings on particle scale during shear band formation helps to develop robust micromechanics-based constitutive models in the future.

To simulate the dynamic feature of bulk granular material (such as agricultural products) during sudden braking of a truck by applying discrete element method.

The bulk granular material was modeled by the discrete element approach, in which the spherical elements were used to represent the granular particles; the interaction between two in‐adhesive particles was modeled by Hertz for normal interaction, and by Mindlin and Deresiewicz for tangential interaction; the interaction between two particles with adhesion was modeled by the JKR theory for normal interaction, and by Thornton's theory for the tangential interaction. Different initial conditions (braking speeds/accelerations) were considered. The dynamic system was numerically solved by the central difference based explicit time integration, and the dynamic impact forces were recorded to further analysis.

The computation predicted that the resultant dynamic force acting upon the front wall behaves in four stages, i.e. increasing, plateau, sharp increasing and drop with damped fluctuation. It was observed that, the shorter the breaking time is, the faster the force reaches its peak, and the greater the peak value is. The phenomenon was in good agreement with physical principals and common knowledge.

It is an application of the discrete element method and, therefore, no important contribution is made to advance the methodology.

The proposed modeling approach may serve as a useful tool for advanced design of trucks.

This paper is the first to apply the advanced discrete element method to the problem concerned.

Liquefaction phenomenon and its catastrophic nature can be analysed as a particular material behaviour of granular media under certain loading paths. Proposes a definition of liquefaction and its modelling by constitutive relations. Discusses this modelling in relation to the questions of stability and uniqueness. Considers the signs of three scalar quantities: the work of second order, the determinant of the symmetric part of the tangent constitutive tensor and the determinant of the tensor itself. Concludes that the liquefaction path is situated inside a potentially unstable domain and that in some cases this path reaches some states of loss of uniqueness, which are essentially bifurcation points.

The purpose of this paper is to extend complex-shaped discrete element method simulations from a few thousand particles to millions of particles by using parallel computing on department of defense (DoD) supercomputers and to study the mechanical response of particle assemblies composed of a large number of particles in engineering practice and laboratory tests.

Parallel algorithm is designed and implemented with advanced features such as link-block, border layer and migration layer, adaptive compute gridding technique and message passing interface (MPI) transmission of C++ objects and pointers, for high performance optimization; performance analyses are conducted across five orders of magnitude of simulation scale on multiple DoD supercomputers; and three full-scale simulations of sand pluviation, constrained collapse and particle shape effect are carried out to study mechanical response of particle assemblies.

The parallel algorithm and implementation exhibit high speedup and excellent scalability, communication time is a decreasing function of the number of compute nodes and optimal computational granularity for each simulation scale is given. Nearly 50 per cent of wall clock time is spent on rebound phenomenon at the top of particle assembly in dynamic simulation of sand gravitational pluviation. Numerous particles are necessary to capture the pattern and shape of particle assembly in collapse tests; preliminary comparison between sphere assembly and ellipsoid assembly indicates a significant influence of particle shape on kinematic, kinetic and static behavior of particle assemblies.

The high-performance parallel code enables the simulation of a wide range of dynamic and static laboratory and field tests in engineering applications that involve a large number of granular and geotechnical material grains, such as sand pluviation process, buried explosion in various soils, earth penetrator interaction with soil, influence of grain size, shape and gradation on packing density and shear strength and mechanical behavior under different gravity environments such as on the Moon and Mars.

In this paper, a new homogenization technique for the determination of dynamic and kinematic quantities of representative elementary volumes (REVs) in granular assemblies is presented. Based on the definition of volume averages, expressions for macroscopic stress, couple stress, strain and curvature tensors are derived for an arbitrary REV. Discrete element model simulations of two different test set‐ups including cohesionless and cohesive granular assemblies are used as a validation of the proposed homogenization technique. A non‐symmetric macroscopic stress tensor, as well as couple stresses are obtained following the proposed procedure, even if a single particle is described as a standard continuum on the microscopic scale.