Computational Particle Mechanics : Scipedia

Advances in the particle finite element method for the analysis of fluid-multibody interaction and bed erosion in free surface flows
E. Oñate, S. Idelsohn, M. Celigueta, R. Rossi

Comput. Methods Appl. Mech. Engrg., (2008). Vol. 197 (19-20), pp. 1777–1800

Abstract
We present some advances in the formulation of the Particle Finite Element Method (PFEM) for solving complex fluid-structure interaction problems with free surface waves. In particular, we present extensions of the PFEM for the analysis of the interaction between a collection of bodies in water allowing for frictional contact conditions at the fluid-solid and solid-solid interfaces via mesh generation. An algorithm to treat bed erosion in free surface flows is also presented. Examples of application of the PFEM to solve a number of fluid-multibody interaction problems involving splashing of waves, large motions of floating and submerged bodies and bed erosion situations are given.
Abstract
We present some advances in the formulation of the Particle Finite Element Method (PFEM) for solving complex fluid-structure interaction problems with free surface waves. [...]
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Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems
E. Oñate, J. Rojek

Comput. Methods Appl. Mech. Engrg., (2004). Vol 193, 3087-3128

Abstract
The paper presents combination of Discrete Element Method (DEM) and Finite Element Method (FEM) for dynamic analysis of geomechanics problems. Combined models can employ spherical (or cylindrical in 2D) rigid elements and finite elements in the discretization of different parts of the system. The DEM is a suitable tool to model soil/rock materials while the FEM in many cases can be a better choice to model other parts of the system considered. A typical example can be an idealization of rock cutting with a tool discretized with finite elements and rock or soil samples modelled with discrete elements. The FEM presented in the paper allows large elasto-plastic deformations in the solid regions. Such problems require the use of stabilized FEM to deal with the incompressibility constraint in order to eliminate the volumetric locking defect, especially when using triangular and tetrahedra elements with equal order interpolation for the displacement and the pressure variables. In the paper a stabilization based on the Finite Calculus (FIC) approach is used. Both theoretical algorithms of DEM and stabilized FEM are implemented in an explicit dynamic code. The paper presents some details of both formulations. A combined numerical algorithm is described finally. Selected numerical results illustrate the possibilities and performance of discrete/finite element analysis in geomechanics problems.
Abstract
The paper presents combination of Discrete Element Method (DEM) and Finite Element Method (FEM) for dynamic analysis of geomechanics problems. Combined models can employ spherical [...]
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Advances in the simulation of multi-fluid flows with the Particle Finite Element Method. Application to bubble dynamics
M. Mier-Torrecilla, S. Idelsohn, E. Oñate

Int. J. Numer. Meth. Fluids (2010). Vol. 67 (11), pp. 1516-1539

Abstract
In this work we extend the Particle Finite Element Method (PFEM) to multi-fluid flow problems with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking interfaces. We develop a numerical scheme able to deal with large jumps in the physical properties, included surface tension, and able to accurately represent all types of discontinuities in the flow variables. The scheme is based on decoupling the velocity and pressure variables through a pressure segregation method which takes into account the interface conditions. The interface is defined to be aligned with the moving mesh, so that it remains sharp along time, and pressure degrees of freedom are duplicated at the interface nodes to represent the discontinuity of this variable due to surface tension and variable viscosity. Furthermore, the mesh is refined in the vicinity of the interface to improve the accuracy and the efficiency of the computations. We apply the resulting scheme to the benchmark problem of a two-dimensional bubble rising in a liquid column presented in [[#cite-1|[1]]], and propose two breakup and coalescence problems to assess the ability of a multi-fluid code to model topology changes.
Abstract
In this work we extend the Particle Finite Element Method (PFEM) to multi-fluid flow problems with the aim of exploiting the fact that Lagrangian methods are specially well [...]
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A unified monolithic approach for multi-fluid flows and Fluid-Structure Interaction using the Particle Finite Element Method with fixed mesh
P. Becker, S. Idelsohn, E. Oñate

Computational Mechanics (2015). (preprint) Vol. 55, pp. 1091–1104

Abstract
This paper describes a strategy to solve multi-fluid and Fluid-Structure Interaction (FSI) problems using Lagrangian particles combined with a fixed Finite Element (FE) mesh . Our approach is an extension of the fluid-only PFEM-2 [1,2] which uses explicit integration over the streamlines to improve accuracy. As a result, the convective term does not appear in the set of equations solved on the fixed mesh. Enrichments in the pressure field are used to improve the description of the interface between phases.
Abstract
This paper describes a strategy to solve multi-fluid and Fluid-Structure Interaction (FSI) problems using Lagrangian particles combined with a fixed Finite Element (FE) mesh [...]
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Fluid-structure interaction using the Particle Finite Element Method
S. Idelsohn, E. Oñate, F. Pin, N. Calvo

Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195 (17-18), pp. 2100-2123

Abstract
In the present work a new approach to solve fluid-structure interaction problems is described. Both, the equations of motion for fluids and for solids have been approximated using a material (lagrangian) formulation. To approximate the partial differential equations representing the fluid motion, the shape functions introduced by the Meshless Finite Element Method (MFEM) have been used. Thus, the continuum is discretized into particles that move under body forces (gravity) and surface forces (due to the interaction with neighboring particles). All the physical properties such as density, viscosity, conductivity, etc., as well as the variables that define the temporal state such as velocity and position and also other variables like temperature are assigned to the particles and are transported with the particle motion. The so called Particle Finite Element Method (PFEM) provides a very advantageous and efficient way for solving contact and free-surface problems, highly simplifying the treatment of fluid-structure interactions. '''Key words: '''Fluid-Structure interaction, Particle methods, Lagrange formulations, Incompressible Fluid Flows, Meshless Methods, Finite Element Method.
Abstract
In the present work a new approach to solve fluid-structure interaction problems is described. Both, the equations of motion for fluids and for solids have been approximated [...]
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Discrete element simulation of rock cutting
J. Rojek, E. Oñate, C. Labra, H. Kargl

Int. J. Rock Mechanics and Mining Sciences (2011). Vol. 48 (6), pp. 996-1010

Abstract
This paper presents numerical modelling of rock cutting processes. The model consists of a tool–rock system. The rock is modelled using the discrete element method, which is suitable to study problems of multiple material fracturing such as those involved in rock cutting. Both 2D and 3D models are considered in this work. The paper presents a brief overview of the theoretical formulation and calibration of the discrete element model by a methodology combining the dimensional analysis with simulation of the unconfined compressive strength (UCS) and indirect tension (Brazilian) tests. The rock cutting process with roadheader picks, which is typical for underground excavation, has been simulated. The results of the 2D and 3D analyses have been compared with one another, and numerical results have been compared with the available experimental data.
Abstract
This paper presents numerical modelling of rock cutting processes. The model consists of a tool–rock system. The rock is modelled using the discrete element method, [...]
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High‐density sphere packing for discrete element method simulations
C. Labra, E. Oñate

Commun. Numer. Meth. Engng (2009). Vol. 25 (7), pp. 837-849

Abstract
The first step in a discrete element simulation is the discretization of the domain into a set of particles. The cost of generating a good cylindrical or spherical packing has resulted in a great number of approaches during the last years. A new algorithm is proposed for high‐density packing using a scheme that minimizes the distance between each particle. Using the support of a finite element mesh, less time is needed in order to achieve a low porosity configuration. In addition, a boundary constraint is introduced. The application of the same optimization scheme is used as a condition to force a good surface definition. The results obtained show a high efficiency for the generation of low porosity packing, achieving values smaller than 10% in 2D cases and 30% in 3D cases.
Abstract
The first step in a discrete element simulation is the discretization of the domain into a set of particles. The cost of generating a good cylindrical or spherical packing [...]
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Discrete/finite element modelling of rock cutting with TBM disc cutter
C. Labra, J. Rojek, E. Oñate

Rock Mechanics and Rock Engineering (2017). Vol. 50 (3), pp. 621-638

Abstract
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.
Abstract
This paper presents advanced computer simulation of rock cutting process typical for excavation works in civil engineering. Theoretical formulation of the hybrid discrete/finite [...]
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General advancing front packing algorithm for the discrete element method
C. Recarey Morfa, I. Pérez, M. Farías, E. Oñate, R. Valera, H. Casañas

Comp. Part. Mech (2018). Vol. 5, pp 13–33

Abstract
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.
Abstract
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 [...]
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A bonded discrete element method for modeling ship–ice interactions in broken and unbroken sea ice fields
O. Jou Devesa, M. Celigueta, S. Latorre, F. Arrufat, E. Oñate

Computational Particle Mechanics (2019). Vol. 6 (4), pp 739–765

Abstract
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.
Abstract
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 [...]
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Possibilities of the particle finite element method for fluid–soil–structure interaction problems
E. Oñate, M. Celigueta, S. Idelsohn, F. Salazar, B. Suarez

Computational Mechanics (2011). Vol. 48 (3), pp. 307-318

Abstract
We present some developments in the particle finite element method (PFEM) for analysis of complex coupled problems in mechanics involving fluid–soil–structure interaction (FSSI). The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the solid domains (the later including soil/rock and structures). A mesh connects the particles (nodes) defining the discretized domain where the governing equations for each of the constituent materials are solved as in the standard FEM. The stabilization for dealing with an incompressibility continuum is introduced via the finite calculus method. An incremental iterative scheme for the solution of the non linear transient coupled FSSI problem is described. The procedure to model frictional contact conditions and material erosion at fluid–solid and solid–solid interfaces is described. We present several examples of application of the PFEM to solve FSSI problems such as the motion of rocks by water streams, the erosion of a river bed adjacent to a bridge foundation, the stability of breakwaters and constructions sea waves and the study of landslides.
Abstract
We present some developments in the particle finite element method (PFEM) for analysis of complex coupled problems in mechanics involving fluid–soil–structure [...]
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An assessment of the potential of PFEM-2 for solving long real-time industrial applications
J. Gimenez, D. Ramajo, S. Damián, N. Nigro, S. Idelsohn

Comp. Part. Mech. (2016). Vol. 4 (3), pp. 251-267

Abstract
The latest generation of the particle finite element method (PFEM-2) is a numerical method based on the Lagrangian formulation of the equations, which presents advantages in terms of robustness and efficiency over classical Eulerian methodologies when certain kind of flows are simulated, especially those where convection plays an important role. These situations are often encountered in real engineering problems, where very complex geometries and operating conditions require very large and long computations. The advantages that the parallelism introduced in the computational fluid dynamics making affordable computations with very fine spatial discretizations are well known. However, it is not possible to have the time parallelized, despite the effort that is being dedicated to use space–time formulations. In this sense, PFEM-2 adds a valuable feature in that its strong stability with little loss of accuracy provides an interesting way of satisfying the real-life computation needs. After having already demonstrated in previous publications its ability to achieve academic-based solutions with a good compromise between accuracy and efficiency, in this work, the method is revisited and employed to solve several nonacademic problems of technological interest, which fall into that category. Simulations concerning oil–water separation, waste-water treatment, metallurgical foundries, and safety assessment are presented. These cases are selected due to their particular requirements of long simulation times and or intensive interface treatment. Thus, large time-steps may be employed with PFEM-2 without compromising the accuracy and robustness of the simulation, as occurs with Eulerian alternatives, showing the potentiality of the methodology for solving not only academic tests but also real engineering problems.
Abstract
The latest generation of the particle finite element method (PFEM-2) is a numerical method based on the Lagrangian formulation of the equations, which presents advantages [...]
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Multiscale analysis using a coupled discrete/finite element model
J. Rojek, E. Oñate

Interaction and Multiscale Mechanics: An International Journal (IMMIJ) (2007). Vol. 1 (1), pp. 1-31

Abstract
The present paper presents multiscale modelling via coupling of the discrete and finite element methods. Theoretical formulation of the discrete element method using spherical or cylindrical particles has been briefly reviewed. Basic equations of the finite element method using the explicit time integration have been given. The micr-macro transition for the discrete element method has been discussed. Theoretical formulations for macroscopic stress and strain tensors have been given. Determination of macroscopic constitutive properties using dimensionless micro-macro relationships has been proposed. The formulation of the multiscale DEM/FEM model employing the DEM and FEM in different subdomains of the same body has been presented. The coupling allows the use of partially overlapping DEM and FEM subdomains. The overlap zone in the two coupling algorithms is introduced in order to provide a smooth transition from one discretization method to the other. Coupling between the DEM and FEM subdomains is provided by additional kinematic constraints imposed by means of either the Lagrange multipliers or penalty function method. The coupled DEM/FEM formulation has been implemented in the authors’ own numerical program. Good performance of the numerical algorithms has been demonstrated in a number of examples.
Abstract
The present paper presents multiscale modelling via coupling of the discrete and finite element methods. Theoretical formulation of the discrete element method using spherical [...]
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An Implicit Material Point Method Applied to Granular Flows
I. Iaconeta, A. LARESE, R. Rossi, E. Oñate

Procedia Engineering (2017). Vol. 175, pp. 226-232

Abstract
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.
Abstract
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. [...]
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Effect of the integration scheme on the rotation of non-spherical particles with the discrete element method
J. Irazábal González, F. Salazar, M. Santasusana, E. Oñate

Computational Particle Mechanics (2019). Vol. 6 (4), pp 545–559

Abstract
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.
Abstract
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 [...]
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Advances in discrete element modelling of underground excavations
C. Labra, J. Rojek, E. Oñate, F. Zárate

Acta Geotechnica (2009). Vol. 3 (4), pp. 317-322

Abstract
The paper presents advances in the discrete element modelling of underground excavation processes extending modelling possibilities as well as increasing computational efficiency. Efficient numerical models have been obtained using techniques of parallel computing and coupling the discrete element method with finite element method. The discrete element algorithm has been applied to simulation of different excavation processes, using different tools, TBMs and roadheaders. Numerical examples of tunnelling process are included in the paper, showing results in the form of rock failure, damage in the material, cutting forces and tool wear. Efficiency of the code for solving large scale geomechanical problems is also shown
Abstract
The paper presents advances in the discrete element modelling of underground excavation processes extending modelling possibilities as well as increasing computational efficiency. [...]
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Fractional step like schemes for free surface problems with thermal coupling using the Lagrangian PFEM
R. Aubry, E. Oñate, S. Idelsohn

Computational Mechanics (2006). Vol. 38 (4-5), pp. 294-309

Abstract
The method presented in Aubry et al. (Comput Struc 83:1459–1475, 2005) for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian description of motion is extended to three dimensions (3D) with particular emphasis on mass conservation. A modified fractional step (FS) based on the pressure Schur complement (Turek 1999), and related to the class of algebraic splittings Quarteroni et al. (Comput Methods Appl Mech Eng 188:505–526, 2000), is used and a new advantage of the splittings of the equations compared with the classical FS is highlighted for free surface problems. The temperature is semi-coupled with the displacement, which is the main variable in a Lagrangian description. Comparisons for various mesh Reynolds numbers are performed with the classical FS, an algebraic splitting and a monolithic solution, in order to illustrate the behaviour of the Uzawa operator and the mass conservation. As the classical fractional step is equivalent to one iteration of the Uzawa algorithm performed with a standard Laplacian as a preconditioner, it will behave well only in a Reynold mesh number domain where the preconditioner is efficient. Numerical results are provided to assess the superiority of the modified algebraic splitting to the classical FS.
Abstract
The method presented in Aubry et al. (Comput Struc 83:1459–1475, 2005) for the solution of an incompressible viscous fluid flow with heat transfer using a fully Lagrangian [...]
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Approximating the Basset force by optimizing the method of van Hinsberg et al.
G. Casas, A. Ferrer, E. Oñate

Journal of Computational Physics (2018). Vol. 352, pp. 142-171

Abstract
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.
Abstract
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. [...]
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Foreword: special issue on particles finite element method in multi-physics problems
S. Idelsohn

Comp. Part. Mech (2017). Vol. 4 (3), pp. 249-249

Abstract
Particle-based methods in which each material particle is followed in a Lagrangian manner have been used successfully in the last years for different applications. One of the latest evolution of particle-based methods is the Particle Finite Element Method (PFEM). The PFEM combines the particle precept with the FEM shape functions using an auxiliary FE mesh. This mesh may be quickly rebuilt at each time step (PFEM with moving mesh) or may be a fixed mesh (PFEM with fixed mesh). In the last case, the results from the Lagrangian particles are projected at each time iteration on a fixed mesh. The idea of combining FMs with moving particles was originally used in the so-called Particle in Cell method and later in an extension called the Material Point Method (MPM), which uses an FE background mesh. Despite that both PFEM and MPM employ a fixed FE mesh and a set of Lagrangian particles, there are important differences in the way the particles are employed; in the MPM, all computations are performed on the mesh, while in the PFEM, the aim is to calculate as much as possible on the particles, leaving small corrections to be performed on the mesh. Furthermore, the most important difference is that in PFEM, the particles do not represent a fixed amount of mass but rather material points that transport only intrinsic properties. This allows using a variable number of particles and therefore simplifying refinement. The PFEM has been successfully used to solve the Navier–Stokes equations and fluid–structure interaction problems as well as solid mechanics problems. The advantages of the PFEM concerning the tracking of internal interfaces have also been explored and used to solve multi-fluid flows. The possibility to use PFEM to solve nonlinear problems with large time-steps in order to obtain an accurate and fast solution was also successfully presented for the solution of the homogeneous incompressible Navier–Stokes equations. This new strategy was named PFEM second generation (PFEM-2). The enhanced PFEM-2 version to solve multi-phase problems, preserves the large time-step goodnesses of the single-phase strategy, also includes enrichment strategies to capture discontinuities in the pressure gradient, i.e., pressure kinks. This special issue is a collection of nine technical papers presenting the state-of-the-art in modeling and simulations of solid and fluid mechanics problems at different scales involving the Particle Finite Element Method as well in his original version (PFEM) as in his new upgrade (PFEM-2).
Abstract
Particle-based methods in which each material particle is followed in a Lagrangian manner have been used successfully in the last years for different applications. One [...]
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Continuous blending of SPH with finite elements
S. Fernández-Méndez, J. Bonet, A. Huerta

Computers and Structures (2005). Vol. 83 (17-18), pp. 1448-1459

Abstract
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.
Abstract
This paper proposes a methodology for the continuous blending of the finite element method and smooth particle hydrodynamics. The coupled approximation with finite elements [...]
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Evaluating the performance of the particle finite element method in parallel architectures
J. Gimenez, N. Nigro, S. Idelsohn

Comp. Part. Mech. (2014). Vol. 1 (1), pp. 103-116

Abstract
This paper presents a high performance implementation for the particle-mesh based method called particle finite element method two (PFEM-2). It consists of a material derivative based formulation of the equations with a hybrid spatial discretization which uses an Eulerian mesh and Lagrangian particles. The main aim of PFEM-2 is to solve transport equations as fast as possible keeping some level of accuracy. The method was found to be competitive with classical Eulerian alternatives for these targets, even in their range of optimal application. To evaluate the goodness of the method with large simulations, it is imperative to use of parallel environments. Parallel strategies for Finite Element Method have been widely studied and many libraries can be used to solve Eulerian stages of PFEM-2. However, Lagrangian stages, such as streamline integration, must be developed considering the parallel strategy selected. The main drawback of PFEM-2 is the large amount of memory needed, which limits its application to large problems with only one computer. Therefore, a distributed-memory implementation is urgently needed. Unlike a shared-memory approach, using domain decomposition the memory is automatically isolated, thus avoiding race conditions; however new issues appear due to data distribution over the processes. Thus, a domain decomposition strategy for both particle and mesh is adopted, which minimizes the communication between processes. Finally, performance analysis running over multicore and multinode architectures are presented. The Courant–Friedrichs–Lewy number used influences the efficiency of the parallelization and, in some cases, a weighted partitioning can be used to improve the speed-up. However the total cputime for cases presented is lower than that obtained when using classical Eulerian strategies.
Abstract
This paper presents a high performance implementation for the particle-mesh based method called particle finite element method two (PFEM-2). It consists of a material derivative [...]
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Numerical modelling of granular materials with spherical discrete particles and the bounded rolling friction model. Application to railway ballast
J. Irazábal González, F. Salazar, E. Oñate

Computers and Geotechnics (2017). Vol. 85, pp. 220-229

Abstract
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.
Abstract
The Discrete Element Method (DEM) was found to be an effective numerical method for the calculation of engineering problems involving granular materials. [...]
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Advances in particle packing algorithms for generating the medium in the Discrete Element Method
C. Recarey, I. Pérez, R. Roselló, M. Muniz, E. Hernández, R. Giraldo, E. Oñate

Computer Methods in Applied Mechanics and Engineering (2019). Vol. 345, pp. 336-362

Abstract
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.
Abstract
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 [...]
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Applications of the particle finite element method in dam engineering
F. Salazar, D. Pozo, R. Morán Moya

"II Int. Conference on Particle-based Method - Fundamentals and Applications", pp. 1-11

Abstract
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.
Abstract
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: [...]
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Comparison of a Material Point Method and a Galerkin Meshfree Method for the Simulation of Cohesive-Frictional Materials
I. Iaconeta, A. LARESE, R. Rossi, Z. Guo

Materials (2017). Vol. 10 (10), pp. 1150

Abstract
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.
Abstract
The simulation of large deformation problems, involving complex history-dependent constitutive laws, is of paramount importance in several engineering fields. Particular attention [...]
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Possibilities of the particle finite element method for fluid-structure interaction problems with free surface waves
E. Oñate, S. Idelsohn, F. Del Pin, R. Aubry

Revue Européenne des Éléments Finis (2004). Vol. 13, pp. 637-666

Abstract
We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of a Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are thus viewed as particles which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral from, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility condition in the fluid is introduced via the finite calculus (FIC) method. A fractional step scheme for the transient coupled fluid-structure solution is described. Examples of application of the PFEM method to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.
Abstract
We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use [...]
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PFEM formulation for thermo-coupled FSI analysis. Application to nuclear core melt accident
A. Franci, E. Oñate, J. Carbonell, M. Chiumenti

Comput. Methods Appl. Mech. Engrg., (2017). Vol. 325, pp. 711-732

Abstract
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.
Abstract
The aim of this paper is to present a Lagrangian formulation for thermo-coupled fluid–structure interaction (FSI) problems and to show its applicability [...]
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Coupling finite elements and particles for adaptivity: an application to consistently stabilized convection–diffusion
S. Fernández-Méndez, A. Huerta

Lecture Notes in Computational Sciences and Engineering (2002). Vol. 26, pp. 117-129

Abstract
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.
Abstract
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 [...]
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Convergence study for the discrete particle method
D. Pelessone, J. Baum, R. Lohner, C. Charman, J. Baylot

(2003). Proceedings Second MIT Conference on Compurational Fluid and Solid Mechanics June 17–20, pp. 2093-2096

Abstract
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.
Abstract
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 [...]
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PFEM-based modeling of industrial granular flows
J. Cante, C. Dávalos, J. Hernández, J. Oliver, P. Jonsén, . G.Gustafsson, H. Häggblad

Computational particle mechanics (2014). Vol. 1 (1), pp. 47-70

Abstract
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.
Abstract
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 [...]
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A particle finite element-based model for droplet spreading analysis
E. Mahrous, A. Jarauta, T. Chan, P. Ryzhakov, A. Weber, R. Roy, M. Secanell

Physics of Fluids (2020). Vol. 32 (4), pp. 1-15 (Preprint)

Abstract
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.
Abstract
A particle finite element method-based model is proposed to analyze droplet dynamics problems, particularly droplet spreading on solid substrates (wetting). The model uses [...]
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On the numerical modeling of granular material flows via the Particle Finite Element Method (PFEM)
C. Dávalos, J. Cante, J. Hernández, J. Oliver

International Journal of Solids and Structures (2015). Vol. 71, pp. 99-125 (Preprint)

Abstract
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.
Abstract
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 [...]
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PFEM application in fluid structure interaction problems
M. Celigueta, A. LARESE, S. Latorre

4th CONFERENCE ON ADVANTAGES AND APPLICATIONS OF GID. The Personal Pre and Post Processor

Abstract
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
Abstract
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 [...]
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On mesh-particle techniques
R. Lohner, F. Camelli, J. Baum, F. Togashi, O. Soto

Comp. Part. Mech (2014). Vol. 1, pp. 199-209

Abstract
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.
Abstract
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. [...]
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Adaptividad En El Método Sin Malla De Puntos Finitos
F. Perazzo, R. Lohner, N. Ipinza

Mecánica Computacional (2006). Vol. XXV (11), pp. 1039-1050

Abstract
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
Abstract
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 [...]
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Advances in the particle finite element method for fluid-structure interaction problems
E. Oñate, S. Idelsohn, M. Celigueta, R. Rossi

Computational Mechanics (2006). Vol. 6, pp. 41-62

Abstract
We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of a Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are thus viewed as particles which can freely move and even separate from the main analysis domain representing, for instance, the effect of water drops. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral from, are solved as in the standard FEM. The necessary stabilization for dealing with the incompressibility of the fluid is introduced via the finite calculus (FIC) method. A fractional step scheme for the transient coupled fluid-structure solution is described. Examples of application of the PFEM to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.
Abstract
We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use [...]
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Analysis of the melting, burning and flame spread of polymers with the particle finite element method
E. Oñate, J. Marti, P. Ryzhakov, R. Rossi, S. Idelsohn

Computer Assisted Methods in Engineering and Sciences (2013). Vol. 20 (3), pp. 165-184

Abstract
A computational procedure for analysis of the melting, burning and flame spread of polymers under fire conditions is presented. The method, termed particle finite element method (PFEM), combines concepts from particle-based techniques with those of the standard finite element method (FEM). The key feature of the PFEM is the use of an updated Lagrangian description to model the motion of nodes (particles) in the thermoplastic material. Nodes are viewed as material points which can freely move and even separate from the main analysis domain representing, for instance, the effect of melting and dripping of polymer particles. A mesh connects the nodes defining the discretized domain where the governing equations are solved using the FEM. An incremental iterative scheme for the solution of the nonlinear transient coupled thermal-flow problem, including radiation, loss of mass by gasification and combustion is used. Examples of the possibilities of the PFEM for the modelling and simulation of the melting, burning and flame spread of polymers under different fire conditions are described.
Abstract
A computational procedure for analysis of the melting, burning and flame spread of polymers under fire conditions is presented. The method, termed particle finite element [...]
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