Stick-slip behaviour of model granular materials in drained triaxial compression

Drained triaxial axisymmetric compression tests are performed on water-saturated short cylindrical samples of nearly monodisperse glass beads, initially assembled in a loose state by a moist tamping technique. Both deviator stress $q$ and volumetric strain $\epsilon _v$ , measured as functions of axial strain $\epsilon _a$ , for different strain rates, are affected by stick-slip events of very large amplitude, while the classical behavior of loose, contractant granular assemblies, approaching the critical state for large $\epsilon _a$ , corresponds to the upper envelop of the stress-strain behaviour. Those events consist in $(i)$ a very fast (slip) part in which a drop of $q$ coincides with a jump of $\epsilon _v$ (contraction), while loss of control of $\epsilon _a$ and generation of pore pressure signal a dynamic collapse of the material structure triggered by an instability; and then $(ii)$ a quasi-static (stick) part in which the sample regains its strength and, over a short strain interval, behaves similarly to a denser system that dilates before reaching its critical state. A unique stress-dilatancy relation applies to all stick-slip events. Apparent internal friction angles and effects of strain rate and confining pressure are discussed, and it is argued that stick-slip instabilities originate in physico-chemical aging phenomena coupled to contact mechanics.     

Mechanical relation for porous metal foams under complex loads of triaxial tension and compression

The mechanical relation of isotropic three-dimensional reticulated porous metal foams with stochastic pores is investigated under complex loads of triaxial tension and compression. From the simplified structural model, the mathematical relationship between three nominal main stresses and porosity has been derived for this class of porous materials at failure under the above-mentioned complex loads, covering three loading conditions of biaxial tension with monoaxial compression, of biaxial compression with monoaxial tension, and of triaxial compression. Through the relevant expression from the deduction, the criterion of strength design can be further obtained for these porous materials under these multiaxial complex loadings.     

Failure of cemented granular materials under simple compression: experiments and numerical simulations

We investigate the strength and failure properties of a model cemented granular material under simple compressive deformation. The particles are lightweight expanded clay aggregate beads coated by a controlled volume fraction of silicone. The beads are mixed with a joint seal paste (the matrix) and molded to obtain dense cemented granular samples of cylindrical shape. Several samples are prepared for different volume fractions of the matrix, controlling the porosity, and silicone coating upon which depends the effective particle–matrix adhesion. Interestingly, the compressive strength is found to be an affine function of the product of the matrix volume fraction and effective particle–matrix adhesion. On the other hand, it is shown that particle damage occurs beyond a critical value of the contact debonding energy. The experiments suggest three regimes of crack propagation corresponding to no particle damage, particle abrasion and particle fragmentation, respectively, depending on the matrix volume fraction and effective particle–matrix adhesion. We also use a sub-particle lattice discretization method to simulate cemented granular materials in two dimensions. The numerical results for crack regimes and the compressive strength are in excellent agreement with the experiments.     

Structure and mechanical properties of Cu-Al alloys under pulsed compression

The familiar competition between the mechanisms of plastic deformation and twining when specimens are subjected to shock-wave compression is illustrated on alloys of the Cu-Al system with different stacking-fault energies.Translated from Problemy Prochnosti, No. 7, pp. 44–48, July, 1992.     

Triaxial behavior of granular material under complex loading path by a new numerical true triaxial engine

A new numerical true triaxial engine based on discrete element method accounting for rolling resistance contact is developed. By this engine, we have simulated mechanical behavior of granular materials under complex stress loading path in this study. Stress-strain responses of a kind of typical granular sand under several stress loading path in meridian and deviatoric stress space are provided. The results show that the three dimensional effects like the intermediate principal stress play an important role in the modeling processes. Theoretical analysis in strength characteristic implies the strength criteria with three parameters such as unified strength criterion and van Eekelen strength criterion are capable of describing cohesionless granular material behaviors in three dimensional stress states. Moreover, the case study for Chende sand further demonstrates the numerical true triaxial engine, is a potential tool. As compared to conventional triaxial compression test, this new developed apparatus could be widely used to “measure” elastic-plastic behavior in three dimensional stress space for finite element analysis in geotechnical problems.     

Identification of the influential parts in a complex mechanical product from a reliability perspective using complex network theory

Due to the difference in the numbers and strengths of physical relationships among parts, complex mechanical products (CMPs) have community structure characteristics. There are often some influential parts in the community. Failures of these influential parts spread rapidly along the physical relationships between parts in the community, which seriously affects the reliability of a product. Therefore, identifying the influential parts in the community and adopting targeted measures can effectively improve the reliability and service life of a product. However, identifying the influential parts within each community in a collection of parts with complex relationships is very difficult. Thus, from the perspective of reliability, a method for identifying the influential parts of a CMP based on complex network theory is proposed and used to identify the influential parts in each community of products. First, weighted complex network (WCN) theory is employed to construct a CMP into a WCN model. Second, the complex network community detection method is employed to detect the community structure of the WCN model. Third, a modified LocalRank algorithm is employed to identify the influential nodes in each community, ie, the influential parts in each community of a CMP. Fourth, a modified susceptible-infectious-recovered (SIR) model is employed to evaluate the impacts of the influential parts. An analysis of a company's DC drill planetary gearbox shows that the proposed method is accurate and effective.     

A phenomenological law for complex granular materials from Mohr-Coulomb theory

Manipulating powders still entails some clumsy and risky operations even now in the middle of the fourth industrial revolution. This is because there is a lack of well-understood theory about granular matter due to its ravelled complexity. However, granular matter is the second most handled material by man after water and is thus ubiquitous in daily life and industry only after water. Since the eighteenth century, mechanical and chemical engineers have been striving to manage the many difficulties of grain handling, most of which are related to flow problems. Many continuum models for dense granular flow have been proposed. Herein, we investigated Mohr–Coulomb failure analysis as it has been the cornerstone of stress distribution studies in industrial applications for decades. This research gathers over 130 granular materials from several industrial sectors, as varied as cement and flour, including raw materials, food, pharmaceuticals, and cosmetics. A phenomenological law derived from the yield locus and governed exclusively by one dimensionless number from adhesive interactions has been found. Surprisingly, and in contrast to the common perception, flow in the quasi-static regime is actually independent of the friction, the packing fraction and any other grains/bulk intrinsic properties. The simplicity and accuracy of the model are remarkable in light of the complex constitutive properties of granular matter.     

Effective properties of cemented granular materials

An analytical model is developed to describe the effective elastic properties of a cemented granular material that is modeled as a random packing of identical spheres. The elastic moduli of grains may differ from those of cement. The effective bulk and shear moduli of the packing are calculated from geometrical parameters (the average number of contacts per sphere and porosity), and from the normal and tangential stiffnesses of a two-grain combination. The latter are found by solving the problems of normal and tangential deformation of two elastic spherical grains cemented at their contact. A thin cement layer is approximated by an elastic foundation, and the grain-cement interaction problems are reduced to linear integral equations. The solution reveals a peculiar distribution pattern of normal and shear stresses at the cemented grain contacts: the stresses are maximum at the center of the contact region when the cement is soft relative to the grain, and are maximum at the periphery of the contact region when the cement is stiff. Stress distribution shape gradually varies between these two extremes as the cement's stiffness increases. The solution shows that it is mainly the amount of cement that influences the effective elastic properties of cemented granular materials. The radius of the cement layer affects the stiffness of a granular assembly much more strongly than the stiffness of the cement does. This theoretical model is supported by experimental results.     

Discrete element analysis for shear band modes of granular materials in triaxial tests

The discrete element method (DEM) is adopted to simulate the triaxial tests of granular materials in this study. In the DEM simulations, two different membrane-forming methods are used to generate triaxial samples. One method is to pack the internal particles first, then to generate the enclosed membrane; the other is to generate the internal particles and the enclosed membrane together. A definition of the effective strain, which combines microscopic numerical results with macroscopic expression in three-dimensional space, is presented to describe the macroscopic deformation process of granular materials. With these two membrane generation methods, the effective strain distributions in longitudinal section and transverse section of the triaxial sample are described to investigate the progressive failure and the evolution of the shear bands in granular materials. Two typical shear band failure modes in triaxial tests are observed in the DEM simulations with different membrane-forming methods. One is a single shear band like a scraper bowl, and the other is an axial symmetric shear band like two hoppers stacking as the shape of rotational “X” in triaxial sample. The characteristics of the shear bands during the failure processes are discussed in detail based on the DEM simulations.     

Critical state behaviour of granular materials from isotropic and rebounded paths: DEM simulations

This paper presents the results of numerical simulations using the three-dimensional discrete element method (DEM) on the critical state behaviour of isotropically compressed and rebounded assemblies of granular materials. Drained and undrained (constant volume) numerical simulations were carried out. From these numerical simulations of drained and undrained tests, it has been shown that the steady state is same as the critical state. Critical state for both isotropically compressed and rebounded assemblies form unique curved line that can be approximated by a bilinear line as proposed by Been et al. [Géotechnique 41(3): 365–381, 1991]. Further more, evolution of the internal variables such as average coordination number and induced anisotropy coefficients during shear deformation has been studied.     

Influence of relative density on granular materials behavior: DEM simulations of triaxial tests

The rheological behavior of non-cohesive soils results from the arrangement and complex geometry of the grains. Numerical models based on discrete element modeling provides an opportunity to understand these phenomena while considering the discrete elements with a similar shape to that of the grains the soil is composed of. However, dealing with realistic shapes would lead to a prohibitive calculation cost. In a macroscopic modeling approach, simplification of the discrete elements’ shape can be done as long as the model can predict experimental results. Since the intrinsic non-convex geometry property of real grains seems to play a major role on the response of the granular medium, it is thus possible to keep this geometrical feature by using cluster of spherical discrete elements, which has the advantage to reduce dramatically the computation cost. Since the porosities found experimentally could not always be obtained with the numerical model—owing to the huge difference in shape, the notion of relative density, which requires a search for minimum and maximum porosities for the model, was chosen to compare the experimental and numerical results. Comparing the numerical simulations with the experimental triaxial tests conducted with relative densities and different confining pressures shows that the model is able to predict the experimental results.     

A new perspective on the mechanical evaluation of granular material

The mechanical strength of granules is an important parameter to be determined prior to any further downstream formulation processing. It is important to have a good gauge on the granule integrity to forecast any foreseeable powder issues associated with the material processability such as segregation, content uniformity, and material flow-ability. In this study, a systematic methodology has been developed to quantify the integrity of these granules subjected to a low frequency acoustic field to arrive at the Granule Integrity (GI) index. This methodology has been compared to existing well-established bulk characterization techniques reported in the literature such as Heckel analysis, Kawakita analysis, and Young’s modulus for four different processed samples. Heckel analysis is more amenable to examine the material deformability while Kawakita analysis is better suited to understand the mechanics of granular material. Individual granule strength measurements to determine Young’s modulus often show large variations across the bulk sample. The GI index in conjunction with the Kawakita analysis provides us with more mechanistic insight and understanding into the formation of these granules from a processing perspective. This paper shows the benefits of using the GI index as a practical and direct methodology to characterize the GI of bulk samples in an industrial setting.     

Study of the shear behavior of binary granular materials by DEM simulations and experimental triaxial tests

This paper aims at studying the shear behavior of mixtures of fine and coarse particles by classical triaxial tests. The work is performed both on experimental tests and computer simulations by discrete element method. The comparisons between experimental and simulation results on monosized and binary samples show that the DEM model can reproduce deviatoric curves satisfactorily in experimental conditions. The shear behavior of monosized and binary systems with the same initial void ratio differs significantly, suggesting that the state of compaction of the system is more influential than the initial void ratio. Comparison between compacted and uncompacted samples confirms that compaction increases the shear strength of granular matter. At the particle scale, the coordination number decreases with the augmentation of the volume fraction of coarse particles. The average rotation velocity of fine particles is higher than coarse particles, but their particle stress tensor is smaller than coarse ones.