Instytut Podstawowych Problemów Techniki

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The main objective of this paper was to investigate the heat transfer of modified lightweight refractory concrete at the microscopic scale. In this work, such material was treated as a porous composite based on the compound of calcium aluminate cement and aluminosilicate cenospheres. The presence of air inclusions within the cenospheres was an essential factor in the reduction in thermal performance. Due to the intricacy of the subject investigated, our research employed numerical, theoretical, and experimental approaches. Scanning electron microscopy (SEM) imaging was performed to study the composite microstructure with a special focus on geometry, dimensions, and the distribution of cenospheres. Based on the experimental analysis, simplified geometrical models were generated to reproduce the main features of the composite matrix and cenospheres. A finite element framework was used to determine the effective thermal conductivity of such domains as well as the thermal stresses generated in the sample during the heat flow. A considerable difference in thermal properties was revealed by comparing the simulation results of the pure composite matrix and the samples, indicating a varying arrangement of cenosphere particles. The numerical results were complemented by a theoretical study that applied analytical models derived from the two-phase mixture theory—parallel and Landauer. A satisfactory agreement between numerical and theoretical results was achieved; however, the extension of both presented approaches is required.

Słowa kluczowe:

thermal conductivity,heat transfer,finite element method,thermal stress,microstructure,calcium aluminate cement,cenosphere,refractory concrete

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The problem of high-rate elastic-plastic deformation of micro-sized copper particles impacting against a copper substrate was investigated by applying the continuum-based formulation and finite element thermomechanical analysis. Comparative study of selected plasticity models was performed. The aim of the paper was to study strain rate-dependant plasticity for a wide range of strain rates. The strain-rate-dependant Johnson-Cook and Cowper-Symonds models were studied by comparing displacements, velocities, strains, strain rates, stresses, contact forces, and temperatures and their contribution to material yield stress. The study shows the importance of the high-strain rate yielding model and its adequacy for experimental data. Both models complement each other and may be regarded as soft and hard bounds of the solution. A new, combined, two-function model, containing two independent functions for each of the two ranges, is suggested. The proposed model describes a low strain rate sensitivity range using the Johnson-Cook expression, while allows fitting of the model for experimental results in a high strain rate sensitivity range, using a modified Cowper-Symonds expression. This combination is capable of describing both low and high strain rate regimes, giving the minimum deviation from experimental results.

Słowa kluczowe:

Finite element method, Thermomechanical analysis, High velocity particle impact, Continuum plasticity models, High strain-rate

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The general objective of the present paper is to improve the understanding of micromechanical mechanisms in granular materials and their representation in numerical models. Results of numerical investigations on micro–macro relationships in the discrete element model of granular material are presented. The macroscopic response is analysed in a series of simulations of the triaxial compression test. The numerical studies are focused on the influence of microscopic parameters on the initial response. The effect of the contact stiffness and friction coefficient on the effective elastic moduli is investigated. Numerical results are compared with the analytical estimations based on the kinematic Voigt's hypothesis as well as with selected numerical results of other authors. The comparisons show that a better agreement between the numerical and analytical results is observed for particle assemblies with higher coordination numbers. Higher coordination numbers are related to more compact specimens and for a given specimen can be associated with low values of the contact stiffness and a higher confining pressure.

Słowa kluczowe:

Discrete element method, Granular material, Triaxial test, Micro–macro relationship, Voigt hypothesis

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In the present paper, a possibility of an approximation of elastic particulate composite with a network of elastic springs that undertake only axial forces is considered. It is assumed that the springs are equivalent to two hemispheres interacting through a weaker interface member. In a frame of the suggested approach, the description of the composite is limited to translational degrees of freedom, therefore, only a normal interaction between the spheres was considered. The methodology for calculation of the axial stiffness of the elastic springs and obtained solutions of the stiffness in explicit form are the main novelty of the article. A comparison of the stiffnesses of the springs obtained by the proposed methodology and by the three dimensional Finite Element Method (FEM) has shown a good agreement between them in a wide range of the ratio of the modulus of elasticity of the particles and matrix at four different distances between surfaces of the particles. A possibility of the approximation of particulate composite by springs was tested and discussed in details by comparing results of a mechanical response of a sample (under three different loading cases) modelled as a three dimensional solid and as a system comprised of the springs. The solutions were obtained by the FEM.

Słowa kluczowe:

Spring network model, Lattice model, Particulate composites, Heterogeneous materials, Finite element modelling

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The present paper provides both experimental and DEM analyses of the filling and discharge of pea grains from a 3D flat-bottomed bin. In the DEM model, the fixed mean values of the experimentally determined single particle data, such as the particle density, Young's modulus, Poisson's ratio as well as the sliding and rolling friction coefficients were incorporated to analyse their effects on the macroscale indicators, such as the wall pressure, discharge velocities and material outflow parameters. The effect of rolling friction was studied based on the experimentally measured single particle rolling friction coefficient. This analysis is aimed at the quantitative prediction of flow parameters as related to the identification of material parameters.

Słowa kluczowe:

Visco-elastic granular material, Discrete element method, Rolling friction, Wall pressure, Material velocity, Outflow mass, Outflow rate, Biosystems, Pea grains

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The present paper provides a discrete element method (DEM) analysis of the filling and discharge processes of granular material in a 3D flat-bottomed bin. A granular aggregate of nearly round particles (20,400 pea grains, 7.2–7.8 mm in diameter) is considered. The numerical results are compared with the experimental data. The DEM analysis provides an accurate prediction of wall stress distribution and the outflow rate of discharge throughout the bottom orifice. The stress distribution developed within the granular material after filling and during the discharge phase is considered, and the transition from the active to passive stress state is discussed. This analysis aims to quantitatively predict the flow parameters related to the careful identification of the material parameters. The investigation presented may be useful for the ongoing development of DEM.

Słowa kluczowe:

Visco-elastic granular material, Discrete element method, Wall pressure, Granular material stress, Micro-properties, Bulk properties

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By using the discrete element method (DEM) a comparison and observations on material flow patterns in plane-wedged, space-wedged, and flat-bottomed hopper were accounted for. Numerical results obtained by combining data of individual particles, statistical processing of particle assemblies and evaluation of the field variables provided the essential characteristics for different regimes of the discharge flow (within steady or unsteady state of flow) and the differences in differently shaped hoppers due to different microscopic inter-particle friction. For validation of the performed simulations, velocity patterns developed in three-dimensional flat-bottomed hopper containing 20,400 pea grains were also analysed. To represent the continuum by avoiding the local effects produced by the individual grains, the simulation results were focused on the mean velocity distributions with data smoothening. The effect of rolling resistance on granular material flow was also considered.

Słowa kluczowe:

DEM, Mass flow rate, Velocity distribution, Plane-wedged, Space-wedged, Flat-bottomed hoppers

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The friction effect in filling and unsteady/steady discharge of three-dimensional wedge-shaped hopper was considered numerically by the discrete element method. The presented model is based on contact mechanics of a single spherical particle involving Hooke's law of spring interaction, static and dynamic friction as well as viscous damping forces. The hopper filling process en masse was performed while the modeling of uncontrolled and controlled discharge was simulated. The evolution of the kinetic energy of filling, the distribution of stresses within granular material and stresses acting on the walls, as well as the change in fields of material porosity were investigated at the stages of filling and discharge of the hopper. The variation of flow velocities, the discharged mass fractions as well as discharge fraction rates were analyzed. The friction effect was analyzed by varying inter-particle friction coefficient over the range of 0–0.6. A comparison of the numerical results with available continuum-based predictions was also presented.

Słowa kluczowe:

Visco-elastic granular material, 3D wedge-shaped hopper, Discrete element method, Wall pressure, Granular stresses, Fraction discharged, Bulk porosity

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The paper presents the application of the discrete element method to modelling of granular material filling and discharge in 3D flat-bottomed hopper. A mathematical model, as well as the developed software code, operates with spherical visco-elastic non-cohesive frictional particles. The evolution of granular flow, internal forces and densification (rarefaction) are characterized by macroscopic parameters such as the discharge rates, the porosity fields and the wall pressures, as well as by microscopic evaluations in terms of coordination number, velocity patter ns and inter-particle contact forces. It was shown that qualitative characterization of flow may be done even by relatively rough models with small number of particles, which required to be increased, however, for more precise description of the localize d phenomena. Unsatisfactory evaluation of the stress peak during discharge is p resented as an illustrative example. The main focus of the paper is the analysis of particle friction effect and the consistency of micro and macro-phenomena in the time-dependent flow process.

Słowa kluczowe:

discrete element method, spherical particles, visco-elastic granular material, three-dimensional flat bottomed hopper

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Multiobjective approach for optimization of the discharge flow parameters of viscoelastic frictional granular material in a wedge-shaped hopper with fixed outlet orifice is considered. The discharge time and the discharge flow rate are taken as optimality criteria, while the discharge mass of material and the shape of the hopper are considered as design variables. The discrete concept and numerical discrete element method (DEM) are applied to the analysis of granular flow. The filling problem considered as numerical generation of the initial conditions for discharge flow was initially solved. The presented DEM model was validated by examining the wall pressures and comparing them with the results of classical macroscopic pressure prediction. Variation of optimality criteria and Pareto set is demonstrated by the numerical results. Sensitivity of optimality criteria to interparticle friction is also investigated.

Słowa kluczowe:

Viscoelastic granular material, Hopper, Discrete element method, Optimization of flow parameters

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The 3D effects of the 2D mode I stress intensity factor for the plate with a V-shaped straight through-thickness notch are investigated by the finite element method and three-dimensional thicknessdependent correction of SIF is suggested. The correction relies on the assumed relationship between the SIF and the constraint factor (out-of-plane degree of freedom). The 3D finite element mesh generator combining the 2D in-plane adaptive unstructured mesh with the structured through-thickness mesh Is developed and applied for the analysis purposes. Three-dimensionality was examined by using two independent indicators, namely, stress- or strain-based constraint factors. The three-point bend and tensile center-cracked plates are investigated. The results demonstrated that the developed 3D corrections may be treated as upper bound estimates of the SIF for three-point bend plate,while directly obtained numerical values are considered as lower bound estimates. Analysis of the tensile center-cracked plate demonstrated a different nature of the 3D SIF profile, which cannot be simply explained as a transitional state between plain strain and plain stress. Therefore, the suggested 3D correction concept is of a particular character.

Słowa kluczowe:

Constraint factor, finite element method, plate with a notch, three-dimensional stress intensity factor

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The paper addresses discrete element (DEM) models of the heterogeneous particulate solids where the normal interaction between two deformable spherical particles bonded via weaker solid interface is considered. The integral interaction model aimed for evaluation of the bond stiffness was developed, where analytical expressions of the stiffness parameters reflecting individual contribution of the two particles and of the interface properties are derived. Application of the developed DEM model to particulate solid with many particles is considered. The accuracy and the suitability of this approach are evaluated by considering refined 3D Finite Element analysis.

Słowa kluczowe:

Heterogeneous Solid, Particles Interaction, DEM, FEM

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Streszczenie:

A general objective of the paper is to improve understanding of micromechanical mechanisms in granular materials and their representation in numerical models. Results of numerical investigation on micro-macro relationship is the discrete element model of granular material are presented. The macroscopic response was analysed in a series of simulations of the triaxial compression test. Numerical studies were focused on the influence of microscopic parameters on the elastic response. The effect of the contact stiffness and the contact stiffness ratio on the effective elastic moduli, the Young’s modulus and Poisson’s ratio, were investigated. Numerical results were compared with the analytical estimations.

Słowa kluczowe:

Discrete element method, granular material, triaxial test, micro-macro relationship, Voigt hypothesis, elastic moduli

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