On the numerical modeling of granular material flows via the Particle Finite Element Method (PFEM)

The aim of this work is to describe a numerical framework for reliably and robustly simulating the different kinematic conditions exhibited by granular materials while spreading ---from a stagnant condition, when the material is at rest, to a transition to granular flow, and back to a deposit profile. The gist of the employed modeling approach was already presented by the authors in a recent work (Cante et al., 2014), but no proper description of the underlying numerical techniques was provided therein. The present paper focuses precisely on the detailed discussion of such numerical techniques, as well as on its rigorous validation with the experimental results obtained by Lajeunesse, et al. in Ref. ( Lajeunesse et al., 2004). The constitutive model is based on the concepts of large strains plasticity. The yield surface is defined in terms of the Drucker Prager yield function, endowed with a deviatoric plastic flow and the elastic part by a hypoelastic model. The plastic flow condition is assumed nearly incompressible, so a u - p mixed formulation, with a stabilization of the pressure term via the Polynomial Pressure Projection (PPP), is employed. The numerical scheme takes as starting point the Particle Finite Element Method (PFEM) in which the spatial domain is continuously redefined by a different nodal reconnection, generated by a Delaunay triangulation. In contrast to classical PFEM approximations ( Idelsohn et al., 2004), in which the free boundary is obtained by a geometrical technique (a-shape method), in this work the boundary is treated as a material surface, and the boundary nodes are removed or inserted by means of an error function. One of the novelties of this work is the use of the so-called Impl-Ex hybrid integration technique to enhance the spectral properties of the algorithmic tangent moduli and thus reduce the number of iterations and robustness of the accompanying Newton-Raphson solution algorithm (compared with fully implicit schemes respectively). The new set of numerical tools implemented in the PFEM algorithm – including new discretization techniques, the use of a projection of the variables between meshes, and the constraint of the free-surface instead using classic a-shape – allows us to eliminate the negative Jacobians present during large deformation problems, which is one of the drawbacks in the simulation of granular flows. Finally, numerical results are compared with the experiments developed in Ref. (Lajeunesse et al., 2004), where a granular mass, initially confined in a cylindrical container, is suddenly allowed to spread by the sudden removal of the container. The study is carried out using different geometries with varying initial aspect ratios. The excellent agreement between computed and experimental results convincingly demonstrates the reliability of the model to reproduce different kinematic conditions in transient and stationary regimes

PFEM-based modeling of industrial granular flows

The potential of numerical methods for the solution and optimization of industrial granular flows problems is widely accepted by the industries of this field, the challenge being to promote effectively their industrial practice. In this paper, we attempt to make an exploratory step in this regard by using a numerical model based on continuous mechanics and on the so-called Particle Finite Element Method (PFEM). This goal is achieved by focusing two specific industrial applications in mining industry and pellet manufacturing: silo discharge and calculation of power draw in tumbling mills. Both examples are representative of variations on the granular material mechanical response—varying from a stagnant configuration to a flow condition. The silo discharge is validated using the experimental data, collected on a full-scale flat bottomed cylindrical silo. The simulation is conducted with the aim of characterizing and understanding the correlation between flow patterns and pressures for concentric discharges. In the second example, the potential of PFEM as a numerical tool to track the positions of the particles inside the drum is analyzed. Pressures and wall pressures distribution are also studied. The power draw is also computed and validated against experiments in which the power is plotted in terms of the rotational speed of the drum

Quelques réalisations industrielles de marche en déchargeur essais et réalisations

The problem of running Kaplan sets for sluice operation first arose in the design of the power units the Châteauneuf-du-Rhône plant in 1954. It was originally proposed to achieve this by off-cam operation of the guide vanes and runner blades whilst maintaining the power unit in synchronous operation. The initial results were disappointing for it was found that only a very limited amount of flow could be handled in this way. Further tests were run at Logis-Neuf, but without synchronous power unit operation, and a satisfactory procedure was developed based on operation with the runner blades fully open and the guide vanes partly closed, which sets in automatically whenever the plant cuts out and can also be gone over to from no-load operation. It was found that a much higher flow could be dealt with at Beauchastel by making use of the gate in the draught tube after the runner, in which most of the energy is dissipated. Turbine operation was seen to remain remarkably smooth. The Bourg-lès-Valence plant will be designed for the same kind of operation, but with a faster-acting draught tube gate than at Logis-Neuf to bring it on sooner, and with an electrical turbine governor to simplify control. Fixed guide vane power sets at the Ambialet plant are performing very satisfactorily in sluice operation with the draught tube gate partly closed

Computational Homogenization of Inelastic Materials using Model Order Reduction

The present work is concerned with the application of projection-based, model reduction techniques to the efficient solution of the cell equilibrium equation appearing in (otherwise prohibitively costly) two-scale, computational homogenization problems. The main original elements of the proposed Reduced-Order Model (ROM) are fundamentally three. Firstly, the reduced set of empirical, globally-supported shape functions are constructed from pre-computed Finite Element (FE) snapshots by applying, rather than the standard Proper Orthogonal Decomposition (POD), a partitioned version of the POD that accounts for the elastic/inelastic character of the solution. Secondly, we show that, for purposes of fast evaluation of the nonaffine term (in this case, the stresses), the widely adopted approach of replacing such a term by a low-dimensional interpolant constructed from POD modes, obtained, in turn, from FE snapshots, leads invariably to ill-posed formulations. To safely avoid this ill-posedness, we propose a method that consists in expanding the approximation space for the interpolant so that it embraces also the gradient of the global shape functions. A direct consequence of such an expansion is that the spectral properties of the Jacobian matrix of the governing equation becomes affected by the number and particular placement of sampling points used in the interpolation. The third innovative ingredient of the present work is a points selection algorithm that does acknowledge this peculiarity and chooses the sampling points guided, not only by accuracy requirements, but also by stability considerations. The efficiency of the proposed approach is critically assessed in the solution of the cell problem corresponding to a highly complex porous metal material under plane strain conditions. Results obtained convincingly show that the computational complexity of the proposed ROM is virtually independent of the size and geometrical complexity of the considered representative volume, and this affords gains in performance with respect to finite element analyses of above three orders of magnitude without significantly sacrificing accuracy hence the appellation High-Performance ROM.Fil: Hernandez, J. A.. Universidad Politécnica de Catalunya; EspañaFil: Oliver, J.. Universidad Politécnica de Catalunya; EspañaFil: Huespe, Alfredo Edmundo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; ArgentinaFil: Caicedo, M.. Universidad Politécnica de Catalunya; EspañaFil: Cante, J. C.. Universidad Politécnica de Catalunya; Españ

High-performance model reduction techniques in computational multiscale homogenization

A novel model-order reduction technique for the solution of the fine-scale equilibrium problem appearing in computational homogenization is presented. The reduced set of empirical shape functions is obtained using a partitioned version — that accounts for the elastic/inelastic character of the solution — of the Proper Orthogonal Decomposition (POD). On the other hand, it is shown that the standard approach of replacing the nonaffine term by an interpolant constructed using only POD modes leads to ill-posed formulations. We demonstrate that this ill-posedness can be avoided by enriching the approximation space with the span of the gradient of the empirical shape functions. Furthermore, interpolation points are chosen guided, not only by accuracy requirements, but also by stability considerations. The approach is assessed in the homogenization of a highly complex porous metal material. Computed results show that computational complexity is independent of the size and geometrical complexity of the Representative Volume Element. The speedup factor is over three orders of magnitude — as compared with finite element analysis — whereas the maximum error in stresses is less than 10%.Fil: Hernandez, J. A.. Technical University of Catalonia; EspañaFil: Oliver, J.. Technical University of Catalonia; EspañaFil: Huespe, Alfredo Edmundo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; Argentina. Universidad Politecnica de Catalunya; EspañaFil: Caicedo, M. A.. Technical University of Catalonia; EspañaFil: Cante, J. C.. Technical University of Catalonia; Españ