FE Analysis of Contractant Shear Zones in Loose Granular Materials

The paper focuses on the formation of contractant shear zones in initially loose cohesionless granular materials subject usually to continuous densification. For a simulation of the mechanical behaviour of a granular material during monotonous deformation paths, a micro-polar hypoplastic constitutive model was used which takes into account particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The FE investigations of shear localization were carried out with initially very loose quartz sand during four different rate boundary value problems: shearing of an infinite layer between two very rough walls, plane strain compression under constant lateral pressure, biaxial compression with rigid and deformable boundaries and passive earth pressure on a horizontally translating retaining wall. The calculations were carried out with a simple random distribution of the initial void ratio under conditions of large deformations and curvatures.     

FE-investigations of a deterministic and statistical size effect in granular bodies within a micro-polar hypoplasticity

The paper deals with numerical investigations of a deterministic and statistical size effect in granular bodies during shearing of an infinite layer under plane strain conditions and free dilatancy. For a simulation of the mechanical behavior of a cohesionless granular material during a monotonous deformation path, a micro-polar hypoplastic constitutive was used which takes into account particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The proposed model captures the essential mechanical features of granular bodies in a wide range of densities and pressures with a single set of constants. To describe a deterministic size effect, the calculations were carried out with an uniform distribution of the initial void ratio for four different heights of the granular layer: 5, 50, 500 and 2,000 mm. To investigate a statistical size effect, the distribution of the initial void ratio in infinite granular layers was assumed to be spatially correlated. As only primary stochastic calculations were performed, single examples of different random fields of the initial void ratio were generated. For this purpose a conditional rejection method was used.     

FE-studies on Shear Localization in an Anistropic Micro-polar Hypoplastic Granular Material

The effect of transverse isotropy on shear localization in cohesionless granular materials is numerically investigated upon monotonous plane strain deformation paths using a hypoplastic constitutive model enhanced by micro-polar terms. In this model, a so-called density function is reformulated and made anisotropic. Dense sand specimens under constant lateral pressure are numerically tested for uniform and stochastic distributions of the initial void ratio and for two different mean grain diameters.     

Behaviour of granular bodies in induced shear zones

This paper deals with the behaviour of granular bodies in induced shear zones. Shearing of an infinite narrow layer of sand between two very rough boundaries under conditions of free dilatancy is numerically modelled with a finite element method and a hypoplastic constitutive relation within a polar (Cosserat) continuum. The relation can reproduce the essential features of granular bodies during shear localisation. The material constants are easily determined from element test results and can be estimated from granulometric properties. The attention is laid on the influence of the initial void ratio, mean grain diameter, layer height, pressure level and grain roughness on the thickness of induced shear zones. In addition, the effect of dilatancy constraint on shear localisation is investigated. The results are also compared to solutions within a non-polar continuum. The FE-calculations demonstrate that polar effects manifested by the appearance of grain rotations and couple stresses are significant in shear zones and their thickness is mainly affected by the initial void ratio, the mean grain diameter and the layer height. Received: 16 November 1999     

Analysis of the influence of crushing on the behavior of granular materials under shear

The behavior of granular materials mainly depends on the mechanical and engineering properties of particles in its structural matrix. Crushing or breakage of granular materials under compression or shear occurs when the energy available is sufficient to overcome the resistance of the material. Relatively little systematic research has been conducted regarding how to evaluate or quantify particle crushing and how it effects the engineering properties of the granular materials. The aim of this study is to investigate the effect of crushing on the bulk behavior of granular materials by using manufactured granular materials (MGM) rather than using a naturally occurring cohesionless granular material. MGM allow changing only one particle parameter, namely the “crushing strength”. Four different categories of MGM (with different crushing strength) are used to study the effect on the bulk shear strength, stiffness modulus, friction and dilatancy angle “engineering properties”. A substantial influence on the stress–strain behavior and engineering properties of granular materials is observed. Higher confining stress causes some non-uniformity (strong variations/jumps) in volumetric strain and a constant volumetric strain is not always observed under large shear deformations due to crushing, i.e. there is no critical state with flow regime (with constant volumetric strain).     

FE-calculations of stress distribution under prismatic and conical sandpiles within hypoplasticity

The paper deals with the stress distribution beneath prismatic and conical sandpiles. The analysis was performed with the FEM and a micro-polar hypoplastic constitutive model. Several influence factors were studied including the method of pile construction, base roughness, heap inclination, mean grain diameter and initial void ratio of sand. Two methods of sandpile construction were examined: by uniform raining and by centric flow, respectively. The results indicate that the stress distribution under sandpiles is mainly influenced by the construction method. For uniform raining, the maximum stress was observed under the pile centre, while for centric flow, a stress dip was obtained under the pile centre.     

A study of principle stress rotation on granular soils using DEM simulation of hollow cylinder test

This study presents the numerical modeling of a hollow cylinder test (HCT) on granular soils by modifying the TRUBAL code. The discrete element method (DEM) was employed for this purpose. Owing to the significant expenditure of the HCT, a verified numerical modeling for this test was developed. The introduced numerical model (HCTBALL) defines plane and cylindrical walls for the boundary conditions to be applied. In addition, the article presents an efficient method to apply the torque. The displacements of the inner and outer walls are interdependent while torsion was applied to control the intermediate principal stress parameter (b). To verify the model, the paper employs results from experimental HCTs on Firoozkooh sand under both monotonic loading and drained conditions. A comparison of the presented model and the experimental results shows that both are closely concordant.It was shown that the deviatoric stress decreases as the principal stress angle (α) increases. In addition, it was observed that by increasing the confining pressure, the internal friction angle (φ′) decreases; however, at higher confining pressures, this reduction is insignificant. Furthermore, this study investigates the coordination number and its relationship to volumetric strain variations.     

A finite element model for contact analysis of multiple Cosserat bodies

The objective of this paper is to develop a finite element model for multi-body contact analysis of Cosserat materials. Based on the parametric virtual work principle, a quadratic programming method is developed for finite element analysis of contact problems. The contact problem with friction between two Cosserat bodies is treated in the same way as in plastic analysis. The penalty factors, that are normally introduced into the algorithm for contact analysis, have a direct influence on accuracy of solution. There is no available rule for choosing a reasonable value of these factors for simulation of contact problems of Cosserat materials, and they are therefore cancelled through a special technique so that the numerical results can be of high accuracy. Compared with the conventional work on Cosserat elasticity, the newly developed model is on the contact analysis of the Cosserat materials and is seldom found in the existing literatures. Four examples are computed to illustrate the validity and importance of the model developed.     

Evaluation of shear flow in composite wind turbine blades

The present work addresses the evaluation of the shear flow as an extension of the Jourawski’s formula. This idea is developed here for the case of a multi-celled composite thin-walled section. Firstly, the explicit formulation of the shear flow due to shear forces and torsion is derived, noting the simplificative hypothesis adopted. Then, the implemented model is verified by means of a benchmark problem with a known analytical solution. Finally, this model is utilized to evaluate the shear flow on an actual blade configuration, comparing the results obtained with those of a Finite Element model of the same blade, with a similar discretization.     

Numerical study of shear banding evolution in bulk metallic glass composites

In this article, a systematic simulation was performed to demonstrate the detailed shear banding evolution in bulk metallic glass (BMG) composites subjected to the tension, and the relation between microstructures and tensile ductility was therefore elucidated. Free volume was adopted as an internal state variable to characterize the shear banding nucleation, growth and coalescence in BMG matrix with the help of free volume theory, which was incorporated into ABAQUS finite element method (FEM) code as a user material subroutine. The present numerical method was firstly verified by comparing with the corresponding experimental results, and then parameter analyses were conducted to discuss the impacts of particle volume fraction, particle shape, particle orientation and particle yielding strength on the enhancement efficiency of the tensile ductility of BMG composites.     

Simulation of strain localization with gradient enhanced damage models

The incorporation of higher order strain gradients into the constitutive equations of continuum damage mechanics is presented. Thereby, not only scalar-valued isotropic damage models but also anisotropic damage models allowing for directional dependent stiffness degradation are elaborated. An elegant possibility of describing anisotropic material behavior based on the microplane theory is demonstrated. Its conceptual simplicity originates from the idea of modeling the material behavior through uniaxial stress–strain laws on several individual material planes. For each plane individual damage loading functions are introduced allowing for different failure modes. In order to account for long ranging microstructural mechanisms, second-order gradients of the strains are incorporated in each of these damage loading functions. The overall response can be determined by an integration of the resulting microplane laws over the solid angle. The features of gradient enhanced continuum damage are demonstrated by means of several selected examples.     

Efficiency of algorithms for shear stress amplitude calculation in critical plane class fatigue criteria

Fatigue criteria that belong to the critical plane class necessitate unambiguous definitions of the amplitude and mean value of the shear stress acting on a material plane. This is achieved through the construction of the minimum circle circumscribing the path described by the tip of the shear stress vector on each plane. By definition, the centre and the radius of this circle provide the mean shear stress and the shear stress amplitude, respectively. The search of the minimum enclosing circle is an optimisation problem for which efficient numerical solution schemes are required. Several algorithms exist for similar situations; however these are not necessarily related to the fatigue strength of metals. In this paper some algorithms are studied to assess their computational efficiency within the engineering framework of the application of fatigue criteria of the critical plane type.     

Effects of particle shapes to achieve angle of repose and force displacement behaviour on granular assembly

Circular or spherical particles in Discrete Element Method (DEM) possess limitations on achieving desired angle of repose for some granular assemblies. However, by using various shapes/clumps of particles, the limitation posed by the circular or spherical particles on achieving angle of repose can be minimized. In this paper, 2D DEM simulation has been used to investigate the effect of particle shapes on (a) angle of repose, where the aim is to achieve the angle of repose of 35° observed in a laboratory scale sand pile experiment, and (b) force displacement behaviour of granular assembly. The simulated results show that the particle shapes have strong influence on the angle of repose but have a less effect on force displacement behaviour on the granular assembly.     

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.     

Flow of granular materials in a bladed mixer: Effect of particle properties and process parameters on impeller torque and power consumption

The torque and power needed to drive an impeller are important quantities that can indicate flow behavior and can be used to control processes, especially mixing and granulation in the pharmaceutical industry. In this study, experiments were conducted on monodisperse spherical glass beads flowing in a cylindrical bladed mixer agitated by an impeller. The impeller torque was measured using a rotating platform and a data recording device, and the power draw for the motor driving the impeller was measured using a power meter. The effect of various impeller blade designs and material properties on the torque and power were investigated as a function of the impeller blade rotation rate. It was found that the torque exerted on a granular bed and the power consumption were a strong function of the impeller blade configuration, the position of the blades in a deep granular bed, the fill height of the glass beads, and the size and friction coefficient of the particles. It was observed that the time-averaged torque and power consumption for different particle sizes qualitatively scaled with particle diameter. A scale-up relationship for a deep granular bed was developed: the time-averaged torque and average adjusted power consumption scaled with square of the material fill height.     

Simulation of granular crystallization of cubic particles in twisting container using discrete element method

Granular compaction is a process in which the volume fraction, or density, of the granular materials increases when an excitation is applied. A recent experiment reported that twisting a large number of cubic particles in a cylindrical container leads to an ordered and dense arrangement. This structure is similar to the crystal lattice formed in solidification process. In this article, this phenomenon is repeated by using discrete element method (DEM) simulation. Two different shaped containers are used and it is found that the rectangular angles between the sidewalls and the bottom,namely wall effect, plays a key role. In addition, gravitation is also a very important parameter in this process. The higher gravitation added, the faster crystallization process is achieved. On the contrary, shear force due to friction between particles may slow down this process.     

Effect of lamination sequence on the localization and shear crippling instability in thick imperfect cross-ply rings under external pressure

Effect of lamination sequence on the compressive response of a thick plane strain cross-ply ring (very long cylindrical shell) weakened by the presence of a modal imperfection is investigated. A fully nonlinear finite element analysis, that employs a cylindrically curved 16-node layer-element, and is based on the assumption of layer-wise linear displacements distribution through thickness (LLDT), is utilized in the analysis of the afore-mentioned cross-ply ring. Hitherto unavailable numerical results pertaining to the influence of lamination sequence on the localization of buckling patterns and the ensuing shear crippling instability are also presented.     

Computational modeling of high performance cementitious thin shell elements under in-plane shear

High-performance cementitious materials are widely used in the construction of thin shell elements. This study investigates a simulation method based on composite layered shells for the nonlinear analysis of high-performance cementitious elements under in-plane shear. A tube torsion test is simulated and analyzed with MSC-MARC and its results are compared to an alternative calculation method, the Simplified Model for Combined Stress resultants (SMCS), as well as with experimental data. The simulation method is found to produce accurate results for fully under-reinforced elements with a range of strong to weak reinforcement ratios less than 2.     

In situ observation of crack nuclei in poly-granular graphite under ring-on-ring equi-biaxial and flexural loading

Fracture tests of graphite are known to exhibit sensitivity to stress state, such as a difference between their flexural and tensile strengths. Bi-axial tensile and flexural loading are representative of the stress states in some regions of graphite components in nuclear fission reactors, where loading develops from fast neutron irradiation-induced dimensional change and thermal strains. Study of the behaviour of the inherent defects that determine strength variability requires in situ observation of crack nucleation. To this end, digital image correlation can be used to monitor the evolution of displacement fields and hence the cracks on the surface of large samples whilst under load. In this study, a ring-on-ring flexural test setup was developed to apply equi-biaxial tensile stress to large disc specimens of graphite along with the conventional four-point-bend test. A 17% reduction in mean flexural strength was observed for the equi-biaxial loading, relative to uniaxial loading. DIC was used to characterise the observed fracture nuclei. Linear elastic fracture mechanics analysis was shown to be inadequate to explain the strength reduction. It is suggested that fictitious crack models, originally developed to simulate the behaviour of concrete structures, can be utilised to explain the behaviour.