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• A FEM-DEM technique for studying the motion of particles in non-Newtonian fluids. Application to the transport of drill cuttings in wellbores

  M. Celigueta, K. Deshpande, S. Latorre, E. Oñate

  Comp. Part. Mech (2016). Vol. 3(2) pp. 263-276 (preprint)

  
  

  Abstract

  We present a procedure for coupling the finite element method (FEM) and the discrete element method (DEM) for analysis of the motion of particles in non-Newtonian fluids. Particles are assumed to be spherical and immersed in the fluid mesh. A new method for computing the drag force on the particles in a non-Newtonian fluid is presented. A drag force correction for non-spherical particles is proposed. The FEM-DEM coupling procedure is explained for Eulerian and Lagrangian flows and the basic expressions of the discretized solution algorithm are given. The usefulness of the FEM-DEM technique is demonstrated in its application to the transport of drill cuttings in wellbores.

  Abstract
  We present a procedure for coupling the finite element method (FEM) and the discrete element method (DEM) for analysis of the motion of particles in non-Newtonian fluids. [...]

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• Unified Lagrangian formulation for solid and fluid mechanics and FSI problems

  A. Franci, E. Oñate, J. Puigbó

  Comput. Methods Appl. Mech. Engrg. (2016). Vol. 107(11) pp. 970-990 (preprint) Vol. 298, pp. 520-547

  
  

  Abstract

  We present a Lagrangian monolithic strategy for solving fluid-structure interaction (FSI) problems. The formulation is called Unified because fluids and solids are solved using the same solution scheme and unknown variables. The method is based on a mixed velocity-pressure formulation. Each time step increment is solved via an iterative partitioned two-step procedure. The Particle Finite Element Method (PFEM) is used for solving the fluid parts of the domain, while for the solid ones the Finite Element Method (FEM) is employed. Both velocity and pressure fields are interpolated using linear shape functions. For quasiincompressible materials, the solution scheme is stabilized via the Finite Calculus (FIC) method. The stabilized elements for quasi-incompressible hypoelastic solids and Newtonian fluids are called VPS/S-element and VPS/F-element, respectively. Other two non-stabilized elements are derived for hypoelastic solids. One is based on a Velocity formulation (V-element) and the other on a mixed Velocity-Pressure scheme (VP-element). The algorithms for coupling the solid elements with the VPS/F fluid element are explained in detail. The Unified formulation is validated by solving benchmark FSI problems and by comparing the numerical solution to the ones published in the literature.

  Abstract
  We present a Lagrangian monolithic strategy for solving fluid-structure interaction (FSI) problems. The formulation is called Unified because fluids and solids are solved [...]

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• Finite increment calculus (FIC). A framework for deriving enhanced computational methods in mechanics

  E. Oñate

  Adv. Model. and Simul. in Eng. Sci (2016). Vol. 3 pp. 14 Vol. 3 (14)

  
  

  Abstract

  In this paper we present an overview of the possibilities of the finite increment calculus (FIC) approach for deriving computational methods in mechanics with improved numerical properties for stability and accuracy. The basic concepts of the FIC procedure are presented in its application to problems of advection-diffusion-reaction, fluid mechanics and fluid-structure interaction solved with the finite element method (FEM). Examples of the good features of the FIC/FEM technique for solving some of these problems are given. A brief outline of the possibilities of the FIC/FEM approach for error estimation and mesh adaptivity is given.

  Abstract
  In this paper we present an overview of the possibilities of the finite increment calculus (FIC) approach for deriving computational methods in mechanics with improved numerical [...]

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• Accurate FIC-FEM formulation for the multidimensional steady-state advection diffusion–absorption equation

  E. Oñate, P. Nadukandi, J. Miquel

  Comput. Methods Appl. Mech. Engrg., (2017). Vol. 327, pp. 352-368

  
  

  Abstract

  In this paper we present an accurate stabilized FIC-FEM formulation for the multidimensional steady-state advection-diffusion-absorption equation. The stabilized formulation is based on the Galerkin FEM solution of the governing differential equations derived via the Finite Increment Calculus (FIC) method using two stabilization parameters. The value of the two stabilization parameters ensuring an accurate nodal FEM solution using uniform meshes of linear elements is obtained from the optimal values for the 1D problem. The accuracy of the new FIC-FEM formulation is demonstrated in the solution of 2D steadystate advection-diffusion-absorption problems for a range of physical parameters and boundary conditions.

  Abstract
  In this paper we present an accurate stabilized FIC-FEM formulation for the multidimensional steady-state advection-diffusion-absorption equation. The stabilized formulation [...]

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• Accurate modelling of the elastic behavior a continuum with the Discrete Element Method

  M. Celigueta, S. Latorre, F. Arrufat, E. Oñate

  Computational Mechanics (2017). (prepint) Vol. 60 (6), pp. 997-1010

  
  

  Abstract

  The Discrete Element Method (DEM) has been used for modeling continua, like concrete or rocks. However, it requires a big calibration effort, even to capture just the linear elastic behavior of a continuum modelled via the classical force-displacement relationships at the contact interfaces between particles. In this work we propose a new way for computing the contact forces between discrete particles. The newly proposed forces take into account the surroundings of the contact, not just the contact itself. This brings in the missing terms that provide an accurate approximation to an elastic continuum, and avoids calibration of the DEM parameters for the purely linear elastic range.

  Abstract
  The Discrete Element Method (DEM) has been used for modeling continua, like concrete or rocks. However, it requires a big calibration effort, even to capture just the linear [...]

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• Design of an inflatable, modular and portable footbridge

  A. Rodríguez, E. Oñate, J. Marcipar

  Monograph CIMNE (2017). M175

  
  

  Abstract

  Optimization of the use of resources and adaptability of the structures to their environment are new concerns in architecture and structural engineering. At the same time, ephemeral structures are gaining relevance in the market for their uses in maintenance and repair, organization of events, rescue and emergencies and temporary works. Inflatable structures satisfy two of the points aforementioned: they require small amounts of materials and are adequate for ephemeral structures, due to their low deflated volume and lightness. They are also adaptable in the sense that their overpressure determines their load carrying capacity. However, they are inadequate for environments where high external loads may be present. Tensairity appears as a solution to this problem, increasing the carrying capacity of inflatable structures without renouncing to their advantages. This technology adds two extra structural elements to inflatable beams, with greater strengths, in order to redistribute stresses along it. The inflatable element serves then to couple the two stiff elements and to avoid buckling. This work presents and explores design possibilities of Tensairity beams with special focus on their computational modelling. Then, research is carried out regarding modular Tensairity beams, thought as a solution for deployable footbridges. A prototype was built and tested in serviceability conditions to prove the fitness of the proposal to a commercial level.

  Abstract
  Optimization of the use of resources and adaptability of the structures to their environment are new concerns in architecture and structural engineering. At the same time, [...]

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• Numerical analysis of railway ballast behaviour using the Discrete Element Method

  J. Irazábal González, E. Oñate, F. Salazar

  Monograph CIMNE (2017). M174

  
  

  Abstract

  The development of high-speed train lines has increased significantly during the last twenty-five years, leading to more demanding loads in railway infrastructures. Most of these infrastructures were constructed using railway ballast, which is a layer of granular material placed under the sleepers whose roles are: resisting to vertical and horizontal loads and facing climate action. Moreover, the Discrete Element Method was found to be an effective numerical method for the calculation of engineering problems involving granular materials. For these reasons, the main objective of the work is the development of a numerical modelling tool based on the Discrete Element Method which allows the users to understand better the mechanical behaviour of railway ballast. The first task was the review of the specifications that ballast material must meet. Then, the features of the available Discrete Elements code, called ''DEMPack'', were analysed. After those revisions, it was found that the code needed some improvement in order to reproduce correctly and efficiently the behaviour of railway ballast. The main deficiencies identified in the numerical code were related to the contact between discrete element particles and planar boundaries and to the geometrical representation of such a irregular material as ballast. Contact interactions between rigid boundaries and Discrete Elements are treated using a new methodology called the Double Hierarchy method. This new algorithm is based on characterising contacts between rigid parts (meshed with a Finite Element-like discretisation) and spherical Discrete Elements. The procedure is described in the course of the work. Moreover, the method validation and the assessment of its limitations are also displayed. The representation of irregular particles using the Discrete Element Method is a very challenging issue, leading to different geometrical approaches. In this work, a deep revision of those approaches was performed. Finally, the most appropriate methods were chosen: spheres with rolling friction and clusters of spheres. The main advantage of the use of spheres is their low computational cost, while clusters of spheres stand out for their geometrical versatility. Some improvements were developed for describing the movement of each kind of particles, specifically, the imposition of the rolling friction and the integration of the rotation of clusters of spheres. In the course of this work the way to fill volumes with particles (spheres or clusters) was also analysed. The aim is to control properly the initial granulometry and compactness of the samples used in the calculations. After checking the correctness of the numerical code with simplified benchmarks, some laboratory tests for evaluating railway ballast behaviour were computed. The aim was to calibrate the ballast material properties and validate the code for the representation of railway ballast. Once the material properties were calibrated, some examples of a real train passing through a railway ballast track were reproduced numerically. This calculations allowed to prove the possibilities of the implemented tool. This publication is a revised version of the text of the PhD Thesis “Numerical analysis of railway ballast behaviour using the Discrete Element Method” of Joaquín Irazábal, presented at the Technical University of Catalonia on October 6th 2017

  Abstract
  The development of high-speed train lines has increased significantly during the last twenty-five years, leading to more demanding loads in railway infrastructures. Most of [...]

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• Modeling of ground excavation with the particle finite element method

  J. Puigbó, E. Oñate, B. Suárez

  Monograph CIMNE (2010). M116

  
  

  Abstract

  The present work introduces a new application of the Particle Finite Element Method (PFEM) for the modeling of excavation problems. Lagrangian descriptions of motion of the continuum medium are the natural way of describing motion in solid mechanics. Particle finite element methods are based in these solid mechanics settings that can treat large material deformations and rapidly changing boundaries. These capabilities are very suitable for modeling fluid motions and moving free surfaces. That is the reason that the most of the research and applications of PFEM can be found in the context of computational fluid dynamics (CFD) instead of solid mechanics. The satisfying results in modeling fluids have been the motivation to use this method in dynamic solid mechanics. The simulation of an excavation process is a non-linear dynamic problem. It contains geometrical, material and contact non-linearities. Modeling the contact process can be classiffied as the main difficulty. The simulation face the problems of: the detection of a changing geometry, the detection of contact between several solid domains, the estimation of correct interacting forces, the computation of the wear related to this contact forces and the removing of the material that has been excavated from the model. The PFEM have its fundamentals in the classical non linear finite element analysis. The formulation provides a foundation in the updated lagrangian formulation for solids. The dynamic problem is integrated using an implicit scheme. Remeshing strategies are employed in order to identify the boundary surfaces. A remeshing of the domain is introduced for the detection of rapidly changing boundaries. The Delaunay tessellation and the alpha-shape concept together, are used as a methodology to de_ne the boundary from a cloud of points. At the same time an interface mesh is created for contact recognition. A particular constitutive contact law has been developed for capturing contact normal and frictional forces using this mesh. By means of an Archard-type law, the excavation and damage caused in the ground is quantified. The erosion and wear parameters of the grounds under study determine the excavability. The behavior of the geomaterials is described using a Damage Model which model fracture in the continuum. The update and storage of the variables in particles have especial schemes for its correct treatment. The method and the meshing process is adapted for the simulation of an excavation problem. PFEM is presented as a very suitable tool for the treatment of excavation problem. The method gives solution for the analysis of all processes that derive from it. The method has a high versatility and a reasonable computational cost. The obtained results are really promising.

  Abstract
  The present work introduces a new application of the Particle Finite Element Method (PFEM) for the modeling of excavation problems. Lagrangian descriptions of motion of the [...]

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• Stabilized finite element methods for convection-diffusion-reaction, Helmholtz and Stokes problems

  P. Nadukandi, E. Oñate, J. García-Espinosa

  Monograph CIMNE (2012). M130

  
  

  Abstract

  We present three new stabilized finite element (FE) based Petrov–Galerkin methods for the convection–diffusion–reaction (CDR), the Helmholtz and the Stokes problems, respectively. The work embarks upon a priori analysis of some consistency recovery procedures for some stabilization methods belonging to the Petrov–Galerkin framework. It was found that the use of some standard practices (e. g.M-Matrices theory) for the design of essentially non-oscillatory numerical methods is not appropriate when consistency recovery methods are employed. Hence, with respect to convective stabilization, such recovery methods are not preferred. Next, we present the design of a high-resolution Petrov–Galerkin (HRPG) method for the CDR problem. The structure of the method in 1d is identical to the consistent approximate upwind (CAU) Petrov–Galerkin method [68] except for the definitions of the stabilization parameters. Such a structure may also be attained via the Finite Calculus (FIC) procedure [141] by an appropriate definition of the characteristic length. The prefix high-resolution is used here in the sense popularized by Harten, i. e.second order accuracy for smooth/regular regimes and good shock-capturing in non-regular regimes. The design procedure in 1d embarks on the problem of circumventing the Gibbs phenomenon observed in L2 projections. Next, we study the conditions on the stabilization parameters to circumvent the global oscillations due to the convective term. A conjuncture of the two results is made to deal with the problem at hand that is usually plagued by Gibbs, global and dispersive oscillations in the numerical solution. A multi dimensional extension of the HRPG method using multi-linear block finite elements is also presented. Next, we propose a higher-order compact scheme (involving two parameters) on structured meshes for the Helmholtz equation. Making the parameters equal, we recover the alpha-interpolation of the Galerkin finite element method (FEM) and the classical central finite difference method. In 1d this scheme is identical to the alphainterpolation method [140] and in 2d choosing the value 0.5 for both the parameters, we recover the generalized fourth-order compact Padé approximation [81, 168] (therein using the parameter gamma = 2). We follow [10] for the analysis of this scheme and its performance on square meshes is compared with that of the quasi-stabilized FEM [10]. Generic expressions for the parameters are given that guarantees a dispersion accuracy of sixth-order should the parameters be distinct and fourth-order should they be equal. In the later case, an expression for the parameter is given that minimizes the maximum relative phase error in 2d. A Petrov–Galerkin formulation that yields the aforesaid scheme on structured meshes is also presented. Convergence studies of the error in the L2 norm, the H1 semi-norm and the l1 Euclidean norm is done and the pollution effect is found to be small. Finally, we present a collection of stabilized FE methods derived via first-order and second-order FIC procedures for the Stokes problem. It is shown that several well known existing stabilized FE methods such as the penalty technique, the Galerkin Least Square (GLS) method [93], the Pressure Gradient Projection (PGP) method [35] and the orthogonal sub-scales (OSS) method [34] are recovered from the general iii residual-based FIC stabilized form. A new family of Pressure Laplacian Stabilization (PLS) FE methods with consistent nonlinear forms of the stabilization parameters are derived. The distinct feature of the family of PLS methods is that they are nonlinear and residual-based, i. e.the stabilization terms depend on the discrete residuals of the momentum and/or the incompressibility equations. The advantages and disadvantages of these stabilization techniques are discussed and several examples of application are presented.

  Abstract
  We present three new stabilized finite element (FE) based Petrov–Galerkin methods for the convection–diffusion–reaction (CDR), the Helmholtz and the Stokes [...]

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• Clasificadores basados en máquinas de soporte vertical para el diagnóstico y predicción de la enfermedad de Alzheimer

  G. Gavidia, E. Soudah, E. Oñate

  Monograph CIMNE (2012). M131

  
  

  Abstract

  En este trabajo, se estableció una metodología de soporte al diagnostico de AD, principalmente en sus etapas MCI ocasionado por AD y demencia ocasionada por AD. Para este fin fueron obtenidos casos clínicos de dos proyectos de investigación en demencia del tipo AD de reconocida trayectoria: las bases de datos Alzheimer's Disease Neuroimaging Initiative (ADNI) (www.loni.ucla.edu/ADNI) y la base de datos The Open Access Series of Imaging Studies (OASIS) (http://www.oasis-brains.org/). Asimismo, fueron establecidas dos tareas principales: la selección de variables predictoras de AD y la construcción de modelos de clasificacion basados en máquinas de soporte vectorial (SVM), entrenados a partir de las variables seleccionadas. Las variables predictoras seleccionadas estuvieron conformadas por biomarcadores morfométricos y características socio-demográficas y neuropsicológicas. Estas variables deberan ser útiles para la discriminación de casos clínicos en tres estados: (1) Estado normal (generalmente personas mayores sanas); (2) Estado MCI ocasionado por AD; y (3) Etapa de demencia ocasionada por AD. Por otro lado, los modelos SVM estarán enfocados a dos tareas principales: (1) Diagnóstico de AD mediante la discriminación entre sujetos sanos y sujetos con AD; y (2) Predicción de AD, orientada a la discriminación de sujetos MCI con riesgo de convertirse a AD y sujetos MCI sin riesgo de conversión. Asimismo, estos modelos deberán garantizar resultados aceptables, respecto a la sensibilidad y especificidad de las tareas de clasificación. Los resultados obtenidos en esta investigación son prometedores. Por un lado, el subconjunto de variables seleccionadas como relevantes para el diagnóstico de AD, tienen correlación con los resultados de investigaciones previas. Asimismo, en la etapa de testeo, los resultados demostraron que los modelos SVM son de gran utilidad para el soporte diagnóstico clínico de esta enfermedad, siendo capaces de discriminar sujetos con AD de sujetos sanos (diagnóstico) con una exactitud mayor al 99% y distinguir a los sujetos MCI con riesgo de conversión a AD de los sujetos MCI sin riego de conversión (predicción) con una exactitud superior al 94%.

  Abstract
  En este trabajo, se estableció una metodología de soporte al diagnostico de AD, principalmente en sus etapas MCI ocasionado por AD y demencia ocasionada por [...]

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