Spectrophotometric analysis of disintegration mechanisms (abrasion and crushing) of agglomerates during the disc granulation of dolomite

The analysis of mechanisms which affect the formation of agglomerates and determine the granulation process in a broad sense encounters difficulties related to the many ways of the formation of granules. The aim of the study was to perform a qualitative and quantitative analysis of granulation mechanisms with special reference to agglomerates’ disintegration in the disc granulation process. This paper contains an analysis of disintegration mechanisms (abrasion and crushing) of agglomerates during the disc granulation of dolomite. The analysis of the mechanisms taking place during the process concerns the granulation stage after wetting. During the research, each time after the wetting stage, the size fraction 10–12.5 mm was substituted with an analogous fraction wetted by means of an aqueous solution of a coloring agent and the process was continued. After the specified time of granulation, the obtained product was sieved through laboratory sieves and then the content of the provided coloring agent in different size fractions was analyzed by means of a spectrophotometer. Measuring the absorbance of the analyzed samples and granulometric composition of the bed, the level and cause of the migration of material of the tested fraction into other size classes were determined, and at the same time, the occurring granulation mechanisms were analyzed. The proposed model and measurement method consisting of determining the absorbance of the tested granulometric fraction enable the qualitative and quantitative analysis of granulation mechanisms are encountered during the carrying-out of the process after wetting the bed.     

Probabilistic calibration of discrete element simulations using the sequential quasi-Monte Carlo filter

The calibration of discrete element method (DEM) simulations is typically accomplished in a trial-and-error manner. It generally lacks objectivity and is filled with uncertainties. To deal with these issues, the sequential quasi-Monte Carlo (SQMC) filter is employed as a novel approach to calibrating the DEM models of granular materials. Within the sequential Bayesian framework, the posterior probability density functions (PDFs) of micromechanical parameters, conditioned to the experimentally obtained stress–strain behavior of granular soils, are approximated by independent model trajectories. In this work, two different contact laws are employed in DEM simulations and a granular soil specimen is modeled as polydisperse packing using various numbers of spherical grains. Knowing the evolution of physical states of the material, the proposed probabilistic calibration method can recursively update the posterior PDFs in a five-dimensional parameter space based on the Bayes’ rule. Both the identified parameters and posterior PDFs are analyzed to understand the effect of grain configuration and loading conditions. Numerical predictions using parameter sets with the highest posterior probabilities agree well with the experimental results. The advantage of the SQMC filter lies in the estimation of posterior PDFs, from which the robustness of the selected contact laws, the uncertainties of the micromechanical parameters and their interactions are all analyzed. The micro–macro correlations, which are byproducts of the probabilistic calibration, are extracted to provide insights into the multiscale mechanics of dense granular materials.     

Numerical simulation of 2D granular flow entrainment using DEM

To understand the entrainment process in granular flow, numerical experiments have been conducted using a Discrete Element Method model. A flow channel of 8 m long with \(15^\circ \) slope is setup with monitoring points located in an erodible bed. Particles, ranging from 3 to 4 mm in diameters, are used in the simulations. In the simulations, translational, rotational and average velocities, total volume, shear stresses are calculated in the measurement circles. The sizes of the measurement circles have been varied to see their effects on the results. It is found the minimum size of the measurement circles should include 20–30 particles. An new analytical model has been developed to calculate entrainment in granular flow. Results of the numerical experiment are compared with analytical model. Shear stresses at the interface between flowing particles in motion and the immobile particles in the channel bed, change of depth of erosion and entrainment rate are used to verify the analytical model. It is found that the calculated shear stresses in the PFC model agree well with the shear stresses calculated using Mohr–Coulomb frictional relationship in the analytical model. The calculated depth of erosion using the new analytical model is also compared with that from dynamic and static entrainment model. The results indicates that the analytical model is able to capture the mechanism of erosion and it can be used in granular flow analysis.     

Discrete modeling of sand–tire mixture considering grain-scale deformability

Mixing sand or soil with small pieces of tire is common practice in civil engineering applications. Although the properties of the soil are changed, it is environmentally friendly and sometimes economical. Nevertheless, the mechanical behavior of such mixtures is still not fully understood and more numerical investigations are required. This paper presents a novel approach for the modeling of sand–tire mixtures based on the discrete element method. The sand grains are represented by rigid agglomerates whereas the tire grains are represented by deformable agglomerates. The approach considers both grain shape and deformability. The micromechanical parameters of the contact law are calibrated based on experimental results from the literature. The effects of tire content and confining pressure on the stress–strain response are investigated in detail by performing numerical triaxial compression tests. The main results indicate that both strength and stiffness of the samples decrease with increasing tire content. A tire contact of 40% is identified as the boundary between rubber-like and sand-like behavior.     

Design methodology of magnetic fields and structures for magneto-mechanical resonator based on topology optimization

Magneto-mechanical resonators—magnetically-driven vibration devices—are used in many mechanical and electrical devices. We develop topology optimization (TO) to configure the magnetic fields of such resonators to enable large vibrations under specified current input to be attained. A dynamic magneto-mechanical analysis in the frequency domain is considered where we introduce the surface magnetic force calculated from the Maxwell stress tensor. The optimization problem is then formulated involving specifically the maximization of the dynamic compliance. This formulation is implemented using the solid-isotropic-material-with-penalization method for TO by taking into account the relative permeability, Young’s modulus, and the mass density of the magnetic material as functions of the density function. Through the 2D numerical studies, we confirm that this TO method works well in designing magnetic field patterns and providing matching between the external current frequency and eigenfrequency of the vibrating structure.     

Relaxing high-dimensional constraints in the direct solution space method for early phase development

Early phase distributed system design can be accomplished using solution spaces that provide an interval of permissible values for each functional parameter. The feasibility property guarantees fulfillment of all design requirements for all possible realizations. Flexibility denotes the size measure of the intervals, with higher flexibility benefiting the design process. Two methods are available for solution space identification. The direct method solves a computationally cheap optimization problem. The indirect method employs a sampling approach that requires a relaxation of the feasibility property through re-formulation as a chance constraint. Even for high probabilities of fulfillment, \(P>0.99\), this results in substantial increases in flexibility, which offsets the risk of infeasibility. This work implements the chance constraint formulation into the direct method for linear constraints by showing that its problem statement can be understood as a linear robust optimization problem. Approximations of chance constraints from the literature are transferred into the context of solution spaces. From this, we derive a theoretical value for the safety parameter \(\varOmega\). A further modification is presented for use cases, where some intervals are already predetermined. A problem from vehicle safety is used to compare the modified direct and indirect methods and discuss suitable choices of \(\varOmega\). We find that the modified direct method is able to identify solution spaces with similar flexibility, while maintaining its cost advantage.     

An approach for robust PDE-constrained optimization with application to shape optimization of electrical engines and of dynamic elastic structures under uncertainty

We present a robust optimization framework that is applicable to general nonlinear programs (NLP) with uncertain parameters. We focus on design problems with partial differential equations (PDE), which involve high computational cost. Our framework addresses the uncertainty with a deterministic worst-case approach. Since the resulting min–max problem is computationally intractable, we propose an approximate robust formulation that employs quadratic models of the involved functions that can be handled efficiently with standard NLP solvers. We outline numerical methods to build the quadratic models, compute their derivatives, and deal with high-dimensional uncertainties. We apply the presented approach to the parametrized shape optimization of systems that are governed by different kinds of PDE and present numerical results.     

Investigating the flow of rod-like particles in a horizontal rotating drum using DEM simulation

Understanding the flow and mixing of rod-like particles is fundamental because of the widespread use of rods in the process industry. In this paper, discrete element method is used to investigate the flow and mixing of rod-like particles in a horizontal rotating drum, with rod-like particles being modeled by super-ellipsoids. The influence of the aspect ratio of the rod and the rotation speed of the drum on the flow of rod-like particles is studied. The investigation of spherical particles is also included in this paper to reveal the differences between rod-like and spherical particles. The simulation results show that the flow of rods is more intermittent than that of spheres and that there is more intermittent flow for rod-like particles with larger aspect ratios. Both the aspect ratio of the rod and the rotation speed of the drum considerably influence particle mixing. The mixing rate, as quantified by the slope of the variation in the mixing index with respect to drum revolution, increases as rotation speed and aspect ratio decrease. The study of particle orientation indicates that rod-like particles have a preferred orientation during rotation of the drum: the major axis of the rod inclines to be parallel to the end plate of the drum.     

Mobility in granular materials upon cyclic loading

We investigate the ability to move of large objects—referred to as intruders—embedded in a granular material and subjected to cyclic loadings. A discrete element method is used to simulate the dynamics response of intruders subjected to a vertical uplift cyclic force, exploring a wide range of loading magnitudes and frequencies. The analysis of the intruder and grains displacements over many cycles reveals three mobility regimes. In the first two regimes, called confined and failure the intruder either do not significantly move or consistently moves upward after each cycles. We introduce a physically based model considering an inertial drag force to rationalise the existence of these regimes depending on the loading frequency and magnitude. We further evidence a third intermediate regime of creep, where intruder trajectories exhibit long periods of confinement punctuated by shorter periods of sustained uplift motion. Finally, we observe unexpected failures at low loading magnitudes and specific frequencies, which we attribute to a process of elasto-inertial resonance. These results highlight the important differences in the mobility of intruders upon constant and cyclic loadings.