Institute of Fundamental Technological Research

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.

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

This paper presents numerical investigations of the influence of friction on sheet deformation in Nakazima type formability tests. Numerical simulations have been performed using the authors’ own explicit dynamic finite element program. Numerical results have been compared with experimental data. Location of fracture was of major interest in this work. The studies confirmed that the fracture location near the center of the specimen as required by the standards can be obtained for low values of the friction coefficient. Numerical simulation combined with the inverse analysis has been used to estimate a real value of the friction coefficient in the Nakazima formability test.

formability test, explicit FE method, friction, fracture location

W artykule przedstawiono analizę numeryczną wpływu tarcia na rozkład odkształceń uzyskanych w próbach tłoczności przeprowadzonych metodą Nakazimy. Symulacje numeryczne zostały przeprowadzone w autorskim programie opartym na metodzie elementów skończonych z jawnym całkowaniem ruchu względem czasu. Wyniki numeryczne porównano z danymi eksperymentalnymi. Główną uwagę zwrócono na lokalizację miejsca pęknięcia. Badania potwierdziły, że miejsce pęknięcia w pobliżu środka próbki, zgodnie z wymaganiami norm, można uzyskać przy małych wartościach współczynnika tarcia. Symulacja numeryczna, w połączeniu z analizą odwrotną, została wykorzystana do oszacowania rzeczywistej wartości współczynnika tarcia w przeprowadzonych próbach tłoczności metodą Nakazimy.

próba tłoczności Nakazimy, wpływ tarcia, lokalizacja pękania, symulacje numeryczne MES, analiza odwrotna

Modelowanie i symulacje numeryczne są obecnie nieodłączną częścią projektowania i optymalizacji różnorodnych procesów technologicznych. Zastosowanie metod numerycznych w projektowaniu procesów mechanicznego urabiania i przeróbki rud metali jest w dalszym ciągu stosunkowo niewielkie. Procesy odspajania kawałków skały od calizny i ich rozdrobnienia z zastosowaniem różnego rodzaju maszyn, wiążą się silnie nieciągłymi zjawiskami zniszczenia materiału i są bardzo trudne do modelowania za pomocą standardowych metod numerycznych, takich jak metoda elementów skończonych, opartych na ciągłym sformułowaniu zagadnienia mechaniki ciała stałego. Duże możliwości w zastosowaniu do tych procesów ma intensywnie rozwijana w ostatnich latach metoda elementów dyskretnych, w której materiał jest reprezentowany przez liczny zbiór ziaren, oddziałujących między sobą poprzez siły kontaktu. Model ten w sposób naturalny uwzględnia materiał rozdrobniony. Uwzględnienie wiązań kohezyjnych między ziarnami oraz możliwości ich zrywania umożliwia modelowanie inicjacji i propagacji pęknięć w materiale. W niniejszej pracy zostaną przedstawione możliwości wykorzystania metody elementów dyskretnych do symulacji urabiania skał za pomocą noży stożkowych i dysków oraz do symulacji zachowania się materiału w młynie. Sprzężenie metody elementów dyskretnych z modelem przepływu płynu umożliwi modelowanie zawiesiny pyłowej rozdrabnianego materiału.

modelowanie dyskretne, mechaniczne urabianie, rudy metali

This paper presents experimental and numerical studies of magnetorheological (MR) fluids. Experimental studies have been focused on the investigation of MR fluid flow in the valve mode. An experimental device operating in the valve mode has been built and used for testing. Numerical investigations h ave included analysis of magnetic field, continuum based analytical modelling of the valve mode as well as micromechanical discrete element simulation of MR fluid. Analytical studies of the MR flow have been carried out using the conventional Buckingham equation with constant yield stress across the valve gap and the modified Buckingham equation with nonlinear yield stress distribution across the channel according to the magnetic field distributionm determined numerically. The analytical results have been compared with experimental data. A better performance of the modified Buckingham model has been observed. A micromechanical model of MR fluids has been developed within the discrete element framework. The DEM model has been verified qualitatively on a test example of forming chains by magnetized particles after application of an external magnetic field.

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.

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

Numerical studies of effect of parameter evaluation on a failure mode in discrete element models of rock materials have been performed. The discrete element formulation employs spherical particles with the cohesive interaction model combining linear elastic behaviour with brittle failure. Numerical studies consisted in simulation of the uniaxial compression test using a cylindrical specimen with particle size distributions characterized by high degree of heterogeneity. Two different approaches to evaluation of micromechanical constitutive parameters have been compared. In the first approach, the contact stiffness and strength parameters depend on the local particle size, while in the second approach, global uniform contact parameters are assumed for all the contacting pairs in function of average geometric measures characterizing the particle assembly. Significant differences in the failure pattern have been observed. The uniform constitutive parameters result in localized brittle-like fractures, while a distributed damage typical for a ductile failure is obtained for the model with local size-dependent parameters.

discrete element method, rock, modelling, failure mode, brittle, compression, contact

Friction, contact, metal sheet forming, Nakazima test, failure location

In the paper the structural one-dimensional hybrid dynamical model of the entire vibrating rotor-shaft system and the three-dimensional fmite element model of its cracked shaft zone were applied for a fatigue life prediction of the machine faulty segment under coupled bending-torsional-axial vibrations. The steady-state dynamic response amplitudes, obtained by means of the one-dimensional model of the system, have been used for the three-dimensional model as an input data for determination of maximal stresses and stress intensity factors at the crack tip. These quantities together with the Wohler curves enable us an approximate determination of load limits responsible for a probable further crack propagation. By means of the proposed approach one can predict a damage probability of the faulty rotor-shaft system of arbitrary structure operating under various dynamic and quasi-static loads affecting a crack of various sizes and shaft locations. From the investigations performed for various crack axial locations on the shaft with respect to bearing supports of the single- and double-span rotor-shaft systems, it follows that a strength of the cracked zone is much more sensitive to normal stresses due to bending and axial oscillations than to tangential stresses caused by torsional vibrations.

hybrid dynamical mode, vibrating rotor-shaft system, fatigue analysis