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The book contains 11 chapters written by relevant scientists in the field of particle-based methods and their applications in engineering and applied sciences. The chapters cover most particle-based techniques used in practice including the discrete element method, the smooth particle hydrodynamic method and the particle finite element method. The book will be of interest to researchers and engineers interested in the fundamentals of particle-based methods and their applications.



Advances in the Particle Finite Element Method (PFEM) for Solving Coupled Problems in Engineering

We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems on fluid and solid mechanics in engineering accounting for fluid-structure interaction and coupled thermal effects, material degradation and surface wear. The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the structure domains. Nodes are viewed as material points 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 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. An incremental iterative scheme for the solution of the non linear transient coupled fluid-structure problem is described. The procedure for modelling frictional contact conditions at fluid-solid and solidsolid interfaces via mesh generation are described. A simple algorithm to treat soil erosion in fluid beds is presented. An straight forward extension of the PFEM to model excavation processes and wear of rock cutting tools is described. Examples of application of the PFEM to solve a wide number of coupled problems in engineering such as the effect of large waves on breakwaters and bridges, the large motions of floating and submerged bodies, bed erosion in open channel flows, the wear of rock cutting tools during excavation and tunneling and the melting, dripping and burning of polymers in fire situations are presented.
E. Oñate, S. R. Idelsohn, M. A. Celigueta, R. Rossi, J. Marti, J. M. Carbonell, P. Ryzhakov, B. Suárez

Advances in Computational Modelling of Multi-Physics in Particle-Fluid Systems

The current work presents the recent advances in computational modelling strategies for effective simulations of multi physics involving fluid, thermal and magnetic interactions in particle systems. The numerical procedures presented comprise the Discrete Element Method for simulating particle dynamics; the Lattice Boltzmann Method for modelling the mass and velocity field of the fluid flow; the Discrete Thermal Element Method and the Thermal Lattice Boltzmann Method for solving the temperature field. The coupling of the fields is realised through hydrodynamic and magnetic interaction force terms. Selected numerical examples are provided to illustrate the applicability of the proposed approach.
Y. T. Feng, K. Han, D. R. J. Owen

Large Scale Simulation of Industrial, Engineering and Geophysical Flows Using Particle Methods

Particle based computational methods, such as DEM and SPH, are shown to be widely applicable as tools to understand complex large scale particulate and fluid flows in industrial processing, civil, marine and coastal engineering and geohazards.
Paul W. Cleary, Mahesh Prakash, Matt D. Sinnott, Murray Rudman, Raj Das

Parallel Computation Particle Methods for Multi-Phase Fluid Flow with Application Oil Reservoir Characterization

This contribution presents a strategy for programming mechanics simulations including particle methods on multi-core shared memory machines.
John R. Williams, David Holmes, Peter Tilke

The Particle Finite Element Method for Multi-Fluid Flows

This paper presents the Particle Finite Element Method (PFEM) and its application to multi-fluid flows. Key features of the method are the use of a Lagrangian description to model the motion of the fluid particles (nodes) and that all the information is associated to the particles. A mesh connects the nodes defining the discretized domain where the governing equations, expressed in an integral form, are solved as in the standard FEM.We have extended the method to problems involving several different fluids with the aim of exploiting the fact that Lagrangian methods are specially well suited for tracking any kind of interfaces.
S. R. Idelsohn, M. Mier-Torrecilla, J. Marti, E. Oñate

On Material Modeling by Polygonal Discrete Elements

The contribution gives an overview on a discrete element model with polygonal particles in a two-dimensional setting allowing the simulation of granular as well as quasi-brittle material response. It briefly describes the basic formulation for geometry and applied contact models in normal and tangential direction, supplemented by friction on a background plate. Special emphasis is put on modeling of cohesion; three different models with an increasing complexity are introduced, namely an overlay brittle beam lattice, a beam with damage and an interface model. Homogenization of the discrete particle response is utilized deriving variables like stresses and strains for an interpretation in the context of classical and micropolar continua. Several numerical examples for different loading scenarios are added, among them the simulation of a quasi-brittle material sample with a heterogeneousmicrostructure. In addition conceptual small scale experimentswith regular particles of steel nuts have been performed; results from tests and simulations for samples with and without cohesion are compared.
B. Schneider, G. A. D’Addetta, E. Ramm

Discrete Numerical Analysis of Failure Modes in Granular Materials

The question of failure for geomaterials, and more generally for nonassociative materials, is revisited through the second-order work criterion defining, for such media, a whole domain of bifurcation included in the plastic limit surface. In a first theoretical part of the chapter, relations between the vanishing of the second-order work, the existence of limit states and the occurrence of failures characterized by a transition from a quasi-static pre-failure regime to a dynamic post-failure regime, are presented and illustrated from discrete element computations. Then boundaries of the bifurcation domain and cones of unstable loading directions are given in fully three-dimensional loading conditions for a phenomenological incrementally non-linear relation, and in axisymmetric loading conditions for a numerical discrete element model. Finally, conditions for the triggering and the development of failure inside the bifurcation domain are described and emphasized from direct simulations with the discrete element method for proportional stress loading paths.
Luc Sibille, Florent Prunier, François Nicot, Félix Darve

Homogenization of Granular Material Modeled by a 3D DEM

Within this contribution the mechanical behavior of dry frictional granular material is modeled by a three-dimensional discrete element method (DEM). The DEM uses a superquadric particle geometry which allows to vary the elongation and angularity of the particles and therefore enables a better representation of real grain shapes compared to standard spherical particles. To reduce computation times an efficient parallelization scheme is developed which is based on the Verlet list concept and the sorting of particles according to their spatial position. The macroscopic mechanical behavior of the particle model is analyzed through standard triaxial tests of periodic cubical samples. A technique to accurately apply stress boundary conditions is presented in detail. Finally, the triaxial tests are used to analyze the influence of the sample size and the particle shape on the resulting stress-strain behavior.
C. Wellmann, P. Wriggers

Some Consideration on Derivative Approximation of Particle Methods

In this paper, the accuracy of the derivative approximation of the particle methods is discussed. Especially, we show that the issue of decreasing accuracy on a boundary area in the SPH method is due to the lack of the boundary integration. Through some numerical examples, the convergence of error norm of energy obtained by the SPH and the MPS methods is studied.
Hitoshi Matsubara, Shigeo Iraha, Genki Yagawa, Doosam Song

Discrete Element Modelling of Rock Cutting

This paper presents numerical modelling of rock cutting processes. The model consists of a tool-rock system. 3D geometry is considered in the model. The rock is modelled using the discrete element method, which is suitable to study problems of multiple material fracturing like that of rock cutting. The paper presents brief overview of the theoretical formulation and calibration of the discrete element model by simulation of the unconfined compressive strength (UCS) and indirect tension (Brazilian) tests. Numerical examples illustrate the paper. Rock cutting processes typical for underground excavation using both roadheader and TBM cutting tools are simulated. Numerical results are compared with the available experimental data.
Jerzy Rojek, Eugenio Oñate, Carlos Labra, Hubert Kargl
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