Scipedia: Computational Particle Mechanics

Convergence study for the discrete particle method

María Jesús Samper — Mon, 06 Jul 2020 14:49:27 +0200

The Discrete Particle Method (DPM) is a numerical technique in the class of the discrete element methods for the modeling of cementitious material in the pre- and post-failure regimes. Because the DPM is not based on continuum mechanics, the conventional convergence properties of Galerkin based methods, such as the finite element method, are not expected to apply. This chapter presents the results of a study to assess the convergence properties of the DPM for elastic problems. The DPM belongs to the general class of methods denoted as discrete element methods. The benchmark problem is based on the vibrations of a concrete beam free in space. Axial oscillations are used to adjust DPM model parameters, bending oscillations are used to test convergence characteristics. Results show that the DPM solution converges to the equivalent converged finite element solution.

Adaptividad En El Método Sin Malla De Puntos Finitos

María Jesús Samper — Mon, 06 Jul 2020 11:57:49 +0200

En este trabajo se presentan un estimador del error a posteriori y un proceso de refinamiento adaptivo para el método sin malla de puntos finitos (MPF). El indicador del error se formula a partir de la evaluación del funcional de mínimos cuadrados, utilizado en el cálculo de la función de forma. Nuevos grados de libertad o nodos adicionales pueden ser incorporados sin dificultad en las regiones donde el estimador del error presenta un valor elevado, mediante las técnicas de refinamiento h y p. La validez del estimador del error propuesto se demuestra, mediante el desarrollo de problemas de la mecánica de sólidos y fluidos tanto 2D como 3D, utilizando un proceso de refinamiento adaptivo de la solución

On mesh-particle techniques

María Jesús Samper — Tue, 30 Jun 2020 16:01:30 +0200

The treatment of dilute solid (or liquid) phases via Lagrangian particles within mesh-based gas-dynamics (or hydrodynamic) codes is common in computational fluid dynamics. While these techniques work very well for a large spectrum of physical parameters, in some cases, notably for very light or very heavy particles, numerical instabilities appear. The present paper examines ways of mitigating these instabilities, and summarizes important implementational issues.

PFEM application in fluid structure interaction problems

María Jesús Samper — Thu, 11 Jun 2020 09:22:07 +0200

In the current paper the Particle Finite Element Method (PFEM), an inno-vative numerical method for solving a wide spectrum of problems involving the interaction of ﬂuid and structures, is brieﬂy presented. Many examples of the use of the PFEM with GiD support are shown. GiD framework provides a useful pre and post processor for the speciﬁc features of the method. Its advantages and shortcomings are pointed out in the present work

Comparison of a Material Point Method and a Galerkin Meshfree Method for the Simulation of Cohesive-Frictional Materials

María Jesús Samper — Wed, 10 Jun 2020 09:18:16 +0200

The simulation of large deformation problems, involving complex history-dependent constitutive laws, is of paramount importance in several engineering fields. Particular attention has to be paid to the choice of a suitable numerical technique such that reliable results can be obtained. In this paper, a Material Point Method (MPM) and a Galerkin Meshfree Method (GMM) are presented and verified against classical benchmarks in solid mechanics. The aim is to demonstrate the good behavior of the methods in the simulation of cohesive-frictional materials, both in static and dynamic regimes and in problems dealing with large deformations. The vast majority of MPM techniques in the literatrue are based on some sort of explicit time integration. The techniques proposed in the current work, on the contrary, are based on implicit approaches, which can also be easily adapted to the simulation of static cases. The two methods are presented so as to highlight the similarities to rather than the differences from "standard" Updated Lagrangian (UL) approaches commonly employed by the Finite Elements (FE) community. Although both methods are able to give a good prediction, it is observed that, under very large deformation of the medium, GMM lacks robustness due to its meshfree natrue, which makes the definition of the meshless shape functions more difficult and expensive than in MPM. On the other hand, the mesh-based MPM is demonstrated to be more robust and reliable for extremely large deformation cases.

Applications of the particle finite element method in dam engineering

María Jesús Samper — Tue, 09 Jun 2020 11:39:46 +0200

The paper presents the results of the application of the Particle Finite Element Method (PFEM) to the analysis of some of the more complex phenomena related to dam hydraulics: shock waves in spillways, aeration in bottom outlets, and erosion in the downstream river bed. Furthermore, the method has been applied to the study of the consequences of landslides in reservoirs: the wave generation, its propagation, and the affection to the dam.

A particle finite element-based model for droplet spreading analysis

María Jesús Samper — Tue, 02 Jun 2020 13:25:38 +0200

A particle finite element method-based model is proposed to analyze droplet dynamics problems, particularly droplet spreading on solid substrates (wetting). The model uses an updated Lagrangian framework to formulate the governing equations of the liquid. The curvature of the liquid surface is tracked accurately using a deforming boundary mesh. In order to predict the spreading rate of the droplet on the solid substrate and track the corresponding contact angle evolution, dissipative forces at the contact line are included in the formulation in addition to the Navier-slip boundary conditions at the solid–liquid interface. The inclusion of these boundary conditions makes it possible to account for the induced Young’s stress at the contact line and for the viscous dissipation along the solid–liquid interfacial region. These are found to be essential to obtain a mesh-independent physical solution. The temporal evolution of the contact angle and the contact line velocity of the proposed model are compared with spreading droplets and micro-sessile droplet injection experiments and are shown to be in good agreement.

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

María Jesús Samper — Tue, 12 May 2020 09:38:47 +0200

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

María Jesús Samper — Fri, 08 May 2020 15:44:07 +0200

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.

Continuous blending of SPH with finite elements

María Jesús Samper — Mon, 09 Mar 2020 16:41:03 +0100

This paper proposes a methodology for the continuous blending of the finite element method and smooth particle hydrodynamics. The coupled approximation with finite elements and particles, and the discretization of the boundary value problem with a coupled integration, are described. An integration correction is also proposed to stabilize the solution. Some numerical examples demonstrate the applicability of the method.

Coupling finite elements and particles for adaptivity: an application to consistently stabilized convection–diffusion

María Jesús Samper — Wed, 04 Mar 2020 16:33:26 +0100

A mixed approximation coupling finite elements and mesh-less methods is presented. It allows selective refinement of the finite element solution without remeshing cost. The distribution of particles can be arbitrary. Continuity and consistency is preserved. The behaviour of the mixed interpolation in the resolution of the convection-diffusion equation is analyzed.

A bonded discrete element method for modeling ship–ice interactions in broken and unbroken sea ice fields

María Jesús Samper — Thu, 19 Sep 2019 10:20:52 +0200

This work investigates the failure patterns of ice cakes and floe-icewhen loaded by amoving and sloping structure (ice-breaking ships and cones). In the paper, we introduce the most frequently encountered ice infested scenarios, the main characteristics of ice-breaking ships and the predicted failure modes of floe-ice depending on the loading conditions, the structure type and the ice feature dimensions and thickness. For the simulations, a local bonded discrete element method (DEM) is used to model sea ice and its fractures. The packing of bonded spherical particles which reproduce the ice continuum can break due
to ship–ice interactions and the failure modes are studied. A set of validation simulations are first carried out. A level ice sheet breaking against an installed ice-breaking cone with different slope angles is studied, and the results are compared with other DEM simulations. Then, a group of bonded DEM simulations are performed to predict the different failure modes produced when an ice-breaking ship bow contacts with ice cakes and floe-ice of different dimensions and thickness, typical in broken ice fields. Finally, the study of breaking a continuous level ice sheet is carried out by modeling with the bonded DEM an
“infinite” large domain of sea ice and loaded by a single-degree-of-freedom model of an ice-breaking ship.

Effect of the integration scheme on the rotation of non-spherical particles with the discrete element method

María Jesús Samper — Fri, 14 Jun 2019 12:54:59 +0200

The discrete element method (DEM) is an emerging tool for the calculation of the behaviour of bulk materials. One of the key features of this method is the explicit integration of the motion equations. Explicit methods are rapid, at the cost of a limited time step to achieve numerical stability. First- or second-order integration schemes based on a Taylor series are frequently used in this framework and shown to be accurate for the translational and rotational motion of spherical particles. However, they may lead to relevant inaccuracies when non-spherical particles are used since the orientation implies a modification in the second-order inertia tensor in the inertial reference frame. Specific integration schemes for non-spherical particles have been proposed in the literature, such as the fourth-order Runge–Kutta scheme presented by Munjiza et al. and the predictor–corrector scheme developed by Zhao and van Wachem which applies the direct multiplication algorithm for integrating the orientation. In this work, both methods are adapted to be used together with a velocity Verlet scheme for the translational integration. The performance of the resulting schemes, as well as that of the direct integration method, is assessed, both in benchmark tests with analytical solution and in real-scale problems. The results suggest that the fourth-order Runge–Kutta and the Zhao and van Wachem schemes are clearly more accurate than the direct integration method without increasing the computational time.

Advances in particle packing algorithms for generating the medium in the Discrete Element Method

María Jesús Samper — Fri, 14 Jun 2019 12:25:43 +0200

Several theoretical contributions in order to establish a particle packing methodology are presented. In this respect, a generic formulation of a new method for packing particles based on a constructive advancing front method, which uses Monte Carlo techniques for the generation of particle dimensions, is also shown. The method can be used to obtain virtual dense packings of particles with several geometrical shapes. It employs continuous, discrete and empirical statistical distributions in order to generate the dimensions of particles. The packing algorithm is very flexible and allows alternatives for: 1- The direction of the advancing front (inwards or outwards), 2- The selection of the local advancing front, 3- The method for placing a mobile particle in contact with others and 4- The overlap checks. The algorithm also allows obtaining highly porous media when it is slightly modified. Practical applications of the formulations are presented in the end of this paper.

Approximating the Basset force by optimizing the method of van Hinsberg et al.

María Jesús Samper — Thu, 25 Apr 2019 13:17:30 +0200

In this work we put the method proposed by van Hinsberg et al. to the test, highlighting its accuracy and efficiency in a sequence of benchmarks of increasing complexity. Furthermore, we explore the possibility of systematizing the way in which the method's free parameters are determined by generalizing the optimization problem that was considered originally. Finally, we provide a list of worked-out values, ready for implementation in large-scale particle-laden flow simulations.

General advancing front packing algorithm for the discrete element method

María Jesús Samper — Fri, 11 Jan 2019 13:44:19 +0100

A generic formulation of a new method for packing particles is presented. It is based on a constructive advancing front method, and uses Monte Carlo techniques for the generation of particle dimensions. The method can be used to obtain virtual dense packings of particles with several geometrical shapes. It employs continuous, discrete, and empirical statistical distributions in order to generate the dimensions of particles. The packing algorithm is very flexible and allows alternatives for: 1—the direction of the advancing front (inwards or outwards), 2—the selection of the local advancing front, 3—the method for placing a mobile particle in contact with others, and 4—the overlap checks. The algorithm also allows obtaining highly porous media when it is slightly modified. The use of the algorithm to generate real particle packings from grain size distribution curves, in order to carry out engineering applications, is illustrated. Finally, basic applications of the algorithm, which prove its effectiveness in the generation of a large number of particles, are carried out.

PFEM formulation for thermo-coupled FSI analysis. Application to nuclear core melt accident

María Jesús Samper — Tue, 19 Nov 2019 15:08:28 +0100

The aim of this paper is to present a Lagrangian formulation for thermo-coupled fluid–structure interaction (FSI) problems and to show its applicability to the simulation of hypothetical scenarios of a nuclear core melt accident. During this emergency situation, an extremely hot and radioactive lava-like material, the corium, is generated by the melting of the fuel assembly. The corium may induce collapse of the nuclear reactor devices and, in the worst case, breach the reactor containment and escape into the environment. This work shows the capabilities of the proposed formulation to reproduce the structural failure mechanisms induced by the corium that may occur during a meltdown scenario. For this purpose, a monolithic method for FSI problems, the so-called Unified formulation, is here enhanced in order to account for the thermal field and to model phase change phenomena with the Particle Finite Element Method (PFEM). Several numerical examples are presented. First, the convergence of the thermo-coupled method and phase change algorithm is shown for two academic problems. Then, two complex simulations of hypothetical nuclear meltdown situations are studied in 2D as in 3D.

Discrete/finite element modelling of rock cutting with TBM disc cutter

María Jesús Samper — Fri, 26 Apr 2019 11:24:54 +0200

This paper presents advanced computer simulation of rock cutting process typical for excavation works in civil engineering. Theoretical formulation of the hybrid discrete/finite element model has been presented. The discrete and finite element methods have been used in different subdomains of a rock sample according to expected material behaviour, the part which is fractured and damaged during cutting is discretized with the discrete elements while the other part is treated as a continuous body and it is modelled using the finite element method. In this way, an optimum model is created, enabling a proper representation of the physical phenomena during cutting and efficient numerical computation. The model has been applied to simulation of the laboratory test of rock cutting with a single TBM (tunnel boring machine) disc cutter. The micromechanical parameters have been determined using the dimensionless relationships between micro- and macroscopic parameters. A number of numerical simulations of the LCM test in the unrelieved and relieved cutting modes have been performed. Numerical results have been compared with available data from in-situ measurements in a real TBM as well as with the theoretical predictions showing quite a good agreement. The numerical model has provided a new insight into the cutting mechanism enabling us to investigate the stress and pressure distribution at the tool–rock interaction. Sensitivity analysis of rock cutting performed for different parameters including disc geometry, cutting velocity, disc penetration and spacing has shown that the presented numerical model is a suitable tool for the design and optimization of rock cutting process.

An Implicit Material Point Method Applied to Granular Flows

María Jesús Samper — Fri, 26 Apr 2019 11:07:59 +0200

The main objective of this work lies in the development of a variational implicit Material Point Method (MPM), implemented in the open source Kratos Multiphysics framework. The ability of the MPM technique to solve large displacement and large deformation problems is widely recognised and its use ranges over many problems in industrial and civil engineering. In the current work the continuum based implicit MPM is applied to engineering applications, where granular material flow is involved.

For the resolution of the length and time scale of these particular problems, both continuum and discrete models are typically used. Even if discrete techniques predict more feasible results, nowadays, their use is limited to the investigation of element tests of particles, or to the simulation of reduced systems, not allowing to make important decisions in the analysis and design of granular processes. Some advantages of MPM over discrete methods are tested, such as, the ability to simulate granular flow at the large scale with acceptable computational cost and the capability to get information of stress and strain state in a more straightforward way.

The focus of this paper is a comparative study between an irreducible and a mixed formulation, both implemented in the MPM code, to assess the improvement in accuracy and reliability of the numerical results when the latter formulation is adopted.

Numerical modelling of granular materials with spherical discrete particles and the bounded rolling friction model. Application to railway ballast

María Jesús Samper — Wed, 24 Apr 2019 14:16:45 +0200

The Discrete Element Method (DEM) was found to be an effective numerical method for the calculation of engineering problems involving granular materials. However, the representation of irregular particles using the DEM is a very challenging issue, leading to different geometrical approaches. This document presents a new insight in the application of one of those simplifications known as rolling friction, which avoids excessive rotation when irregular shaped materials are simulated as spheric particles. This new approach, called the Bounded Rolling Friction model, was applied to reproduce a ballast resistance test.