A hybrid approach for modeling of breakable granular materials using combined finite-discrete element method

It is well known that particle breakage plays a critical role in the mechanical behavior of granular materials and has been a topic subject to intensive studies. This paper presents a three dimensional fracture model in the context of combined finite-discrete element method (FDEM) to simulate the breakage of irregular shaped granular materials, e.g., sands, gravels, and rockfills. In this method, each particle is discretized into a finite element mesh. The potential fracture paths are represented by pre-inserted non-thickness cohesive interface elements with a progressive damage model. The Mohr–Coulomb model with tension cut-off is employed as the damage initiation criterion to rupture the predominant failure mode at the particle scale. The particle breakage modeling using combined FDEM is validated by the qualitative agreement between the results of simulated single particle crushing tests and those obtained from laboratory tests and prior DEM simulations. A comprehensive numerical triaxial tests are carried out on both the unbreakable and breakable particle assemblies with varied confining pressure and particle crushability. The simulated stress–strain–dilation responses of breakable granular assembly are qualitatively in good agreement with the experimental observations. The effects of particle breakage on the compressibility, shear strength, volumetric response of the fairly dense breakable granular assembly are thoroughly investigated through a variety of mechanism demonstrations and micromechanical analysis. This paper also reports the energy input and dissipation behavior and its relation to the mechanical response.     

A stochastic multiscale algorithm for modeling complex granular materials

Modeling of granular materials in which the grains have irregular shapes and surface is a long-standing problem that has been studied for decades. Almost all the current models either represent the grains as particles with geometrically-regular shapes or attempt to infer some low-order statistical properties of the materials in order to describe granular media. We use an approach to modeling of granular materials that utilizes a two- or three-dimensional image of the material’s morphology. It reconstructs realizations of the image based on a Markov process, and uses a multiscale approach and graph-theoretical concepts to refine the realizations and make them free of artefacts. The method is applied to several complex 2D and 3D examples of granular materials. Various morphological properties of the models are computed and are compared with those of the original images; very good agreement is found for all the cases. Furthermore, the computational cost of the method is very low and, therefore, the method can generate large-size models for complex granular materials.     

Two-scale random field model for quasi-brittle materials

A new idea of two-scale random field is presented by taking the mechanical behaviors of quasi-brittle materials as an example. In this way, the random fluctuation of material damage at the micro-meso-scale and the spatial correlation of mechanical properties at the macro-scale are both well described by the random distribution of fracture strain. Moreover, it is proved that by introducing a transform matrix, the mesoscopic random fields can be described by a two-scale random field. Based on this, a two-step numerical implementation of the two-scale random field is proposed, and the mechanical behaviors of quasi-brittle materials can be analyzed by incorporating the probability density evolution theory. Finally, an experimental example is presented to demonstrate the capability of the proposed model. Ideal agreements are achieved against the experimental results. Particularly, the randomness of material properties at both scales can be well reproduced.     

DEM modeling of shear bands in crushable and irregularly shaped granular materials

A method of modeling convex or concave polygonal particles is proposed. DEM simulations of shear banding in crushable and irregularly shaped granular materials are presented in this work. Numerical biaxial tests are conducted on an identical particle assembly with varied particle crushability. The particle crushing is synchronized with the development of macroscopic stress, and the evolution of particle size distribution can be characterized by fractal dimension. The shear banding pattern is sensitive to particle crushability, where one shear band is clearly visible in the uncrushable assembly and X-shaped shear bands are evident in the crushable assembly. There are fewer branches of strong force chains and weak confinement inside the shear bands, which cause the particles inside the shear bands to become vulnerable to breakage. The small fragments with larger rotation magnitudes inside the shear bands form ball-bearing to promote the formation of shear bands. While there are extensive particle breakages occurring, the ball-bearing mechanism will lubricate whole assembly. With the increase of particle crushability the shear band formation is suppressed and the shear resistance of the assembly is reduced. The porosity inside the shear bands are related to the particle crushability.     

An approach to micro-macro modeling of heterogeneous materials

 A micro-macro strategy suitable for modeling the mechanical response of heterogeneous materials at large deformations and non-linear history dependent material behaviour is presented. When using this micro-macro approach within the context of finite element implementation there is no need to specify the homogenized constitutive behaviour at the macroscopic integration points. Instead, this behaviour is determined through the detailed modeling of the microstructure. The performance of the method is illustrated by the simulation of pure bending of porous aluminum. The influence of the spatial distribution of heterogeneities on the overall macroscopic behaviour is discussed by comparing the results of micro-macro modeling for regular and random structures. Received 9 July 2000     

A novel approach to examining double-shearing type models for granular materials

A novel method, designated as the Rotation of Principal Axes Method (RPAM), capable of examining the double-shearing type kinematic models for granular materials is presented herein. A planar velocity field, which is proposed to represent a continuous rotation of principal strain rate axes, is applied to each model to analyse the rotation of principal stress axes. The proposed approach was proven to show main features of the double-shearing model, the double-sliding free-rotating model, and the revised double-shearing model, in a simple way interesting to geo-researchers. Furthermore, the RPAM was efficient in investigating the choice of a Cosserat rotation rate in kinematic theories and determining a key model parameter in the revised double-shearing model.     

Mixtures of granular materials

Balance laws are given for a mixture of granular materials of a type described by Goodman and Cowin. Constitutive equations are given for the case of two dry granular constituents, and consequences of the entropy principle are found.     

Creep of granular materials

This paper examines the creep of brittle granular materials subjected to one-dimensional compression. One-dimensional creep tests were performed on aggregates of brittle pasta and compared with the behaviour of sand at much higher stress levels. It was found that for both materials, creep strain is proportional to the logarithm of time. One possible mechanism for creep is particle crushing. However, it is usually difficult to measure changes in the particle size distribution during creep because the fines produced are so small, and the mass of fines is too small to measure accurately unless creep is permitted for a very long time. However, for pasta, the particle fragments produced are large, and it is found that particle crushing does occur during creep for 24 hours. This is consistent with the proposition that the behaviour of all brittle granular materials is essentially the same. A micro mechanical argument is then summarised which predicts that creep strain should be proportional to log time.     

Stresses in granular materials

When circularly polarised light is passed through a granular material under boundary stresses patterns—‘light stripes’—are seen in the resulting images which have been traditionally associated with the directions of major principal stresses in the equivalent continuum. In this paper the passage of polarised light through a single spherical particle under stress is studied experimentally and analytically. The effect of placing the particle within a layer of particles, a layer of thickness 2–3 particles, and within a mass of particles is investigated experimentally. The appearance of light stripes is a visual reinforcement of effects seen at the particle level provided the level of stresses in individual particles is low. The implications for quantitative photoelastic interpretation of granular media are discussed.     

Modeling soft granular materials

Soft-grain materials such as clays and other colloidal pastes share the common feature of being composed of grains that can undergo large deformations without rupture. For the simulation of such materials, we present two alternative methods: (1) an implicit formulation of the material point method (MPM), in which each grain is discretized as a collection of material points, and (2) the bonded particle model (BPM), in which each soft grain is modeled as an aggregate of rigid particles using the contact dynamics method. In the MPM, a linear elastic behavior is used for the grains. In order to allow the aggregates in the BPM to deform without breaking, we use long-range center-to-center attraction forces between the primary particles belonging to each grain together with steric repulsion at their contact points. We show that these interactions lead to a plastic behavior of the grains. Using both methods, we analyze the uniaxial compaction of 2D soft granular packings. This process is nonlinear and involves both grain rearrangements and large deformations. High packing fractions beyond the jamming state are reached as a result of grain shape change for both methods. We discuss the stress-strain and volume change behavior as well as the evolution of the connectivity of the grains. Similar textures are observed at large deformations although the BPM requires higher stress than the MPM to reach the same level of packing fraction.     

Prediction of damage-growth based fatigue life of polycrystalline materials using a microstructural modeling approach

A new finite element-based mesoscale model is developed to simulate the localization of deformation and the growth of microstructurally short fatigue cracks in crystalline materials by considering the anisotropic behavior of the individual grains. The inelastic hysteresis energy is used as a criterion to predict the fatigue crack initiation and propagation. This criterion in conjunction with continuum damage modeling provides a strong tool for studying the behavior of materials under cyclic loading at the level of the microstructure. The model predictions are validated against an austenitic stainless steel alloy experimental data. The results show that a combined microstructural and continuum damage modeling approach is able to express the overall fatigue behavior of crystalline materials at the macroscale based on the microstructural features. It correctly predicts the crack initiation on slip bands and at inclusions in low-cycle and high-cycle fatigue, respectively, in agreement with experimental observations reported in the literature.     

Asymptotic behaviour of granular materials

The concept of the asymptotic behaviour of particulate materials is described, including its enhancement by considering asymptotic states in extension. A 3D discrete element model with elastic spherical particles and the granulometry of a real sand is set up. The numerical sample is stretched from different initial states, and the influence of the strain rate direction on the final state is studied within the stress ratio, void ratio and mean stress space. Asymptotic behaviour is clearly observed, although the grains remain intact (no grain crushing is considered). The extension asymptotic states were observed, and the notion of a normal extension line is introduced. The extension asymptotic states coincide with the peak states observed in the shear tests with constant stress path direction in dense samples.     

Gravitational flow of granular materials

The free flow of granular materials through an orifice in a horizontal bottom has been investigated. An equation is proposed for calculating the mass flow rate.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 15, No. 5, pp. 870–874, November, 1968.     

Discrete element modeling of first shear strain gradient effects on mechanical behaviors in granular materials

Granular Matter - We introduce an improved version of a computational algorithm that “clones”/generates an arbitrary number of new digital grains from a sample of real digitalized...     

Numerical study and multi-objective optimization of flexible screening process of flip-flow screen: A DEM-FEM approach

Vibrating flip-flow screens are widely used in deep screening processes. However, in-depth studies on flexible screening processes and the optimization of their operating parameters are limited. This study combines the discrete element method (DEM) and finite element method (FEM) to establish a coupled DEM–FEM model for simulating flexible screening processes. The reliability of the model was experimentally verified. Single-factor and central composite experiments were conducted to analyze the effects of y-direction amplitude, relative amplitude, installation angle, and frequency on particle speed, screening efficiency, and sieve plate stress. Finally, multi-objective optimization was implemented. The results revealed the dynamic response of the amplitude and stress on the flexible screen surface under the impact of materials. Moreover, a mathematical fitting model was derived to describe the relationship between the evaluation index and vibration parameters. Accordingly, a foundation for effectively improving the performance and reliability of flexible screening was established.     

Mixing of granular materials in a half-filled rotating drum

The process of avalanche mixing of two fractions of granular material in a half-filled rotating drum is described accurately and it is shown that under these conditions, the fractions do not generally undergo complete mixing. Pis’ma Zh. Tekh. Fiz. 23, 43–48 (February 12, 1997)     

Membrane separations: a materials science approach

An overview of the benefits and limitations of different types of industrial separation membranes is presented. Their properties strongly influence the choice of methods of manufacture. The choice of membrane composition is also influenced by their role in the total filtration plant, especially by methods of cleaning and flow optimisation. The discussion has been limited to liquid filtration systems and concentrates on microfiltration.     

Evaluation of a physical length scale for granular materials

Classical continuum mechanics considers the interaction of microstructural units of the material through stresses and displacements of material points. Therefore, conventional continuum mechanics approaches can not incorporate any intrinsic material length scale. However in reality interaction of grains may include rotations and the corresponding couple stresses as well, and real materials have a number of important length scales (e.g., grains, particles, fibers, etc.). An equation for determining the length scale is proposed. The proposed length scale equations include the effect of plastic deformation (microrotation), the effect of normal stress and contact area. The proposed length scale is implemented into elastic–elastoplastic Cosserat formulation. The effect of length scale on the finite element simulation and yield surface was evaluated by using the proposed length scale equation. The importance of length scale on the constitutive modeling of granular materials is analyzed in numerical simulations.