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• Lagrangian analysis of multiscale particulate flows with the particle finite element method

  E. Oñate, M. Celigueta, S. Latorre, G. Casas, R. Rossi, J. Rojek

  Comp. Part. Mech (2014). Vol. 1 pp. 85-102 (prepint) Vol. 1 pp. 85-102

  
  

  Abstract

  We present a Lagrangian numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the Particle Finite Element Method (PFEM) which blends concepts from particle-based techniques and the FEM. The basis of the Lagrangian formulation for particulate flows and the procedure for modelling the motion of small and large particles that are submerged in the fluid are described in detail. The numerical technique for analysis of this type of multiscale particulate flows using a stabilized mixed velocity-pressure formulation and the PFEM is also presented. Examples of application of the PFEM to several particulate flows problems are given.

  Abstract
  We present a Lagrangian numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the Particle [...]

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• Adjoint-based adaptive finite element method for the compressible Euler equations using finite calculus

  M. Kouhi, E. Oñate, D. Mavriplis

  Aerospace Science and Technology (2014). Vol. 46 pp. 422-435

  
  

  Abstract

  In this paper, an adjoint-based error estimation and mesh adaptation framework is developed for the compressible inviscid flows. The algorithm employs the Finite Calculus (FIC) scheme for the numerical solution of the flow and discrete adjoint equations in the context of the Galerkin finite element method (FEM) on triangular grids. The FIC scheme treats the instabilities normally generated in the numerical solution of the fluid equations through adding two stabilization terms, called streamline term and transverse term, to the original central-based discretized formulation. The non-linear system of equations resulting from the flow problem is solved implicitly using a damped Newton’s method accompanied with the exact Jacobian matrix. A defect corrected scheme is implemented to iteratively solve the linear system of equations related to the adjoint problem benefiting from the transpose of the Jacobian matrix. At each iteration, the linear systems of equations resulting from the fluid and adjoint problems are solved using a preconditioned GMRES method. Having calculated the error of a specified output functional locally, an h-refinement methodology based on the element subdivision is performed to refine the candidate elements. The quality of the numerical results proves the capability of the presented approach for the adjoint-based error estimation and mesh adaptation problems in different flow regimes.

  Abstract
  In this paper, an adjoint-based error estimation and mesh adaptation framework is developed for the compressible inviscid flows. The algorithm employs the Finite Calculus [...]

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• A simple FEM-DEM technique for fracture prediction in materials and structures

  F. Zárate, E. Oñate

  Comp. Part. Mech (2015). Vol. 2(3) pp. 301-314 (preprint)

  
  

  Abstract

  This paper presents a new computational technique for predicting the onset and evolution of fracture in a continuum in a simple manner combining the finite element method (FEM) and the discrete element method (DEM). Once a crack is detected at an element side in the FE mesh, discrete elements are generated at the nodes sharing the side and a simple DEM mechanism is considered to follow the evolution of the crack. The combination of the DEM with simple 3-noded linear triangular elements correctly captures the onset of fracture and its evolution, as shown in several examples of application in two and three dimensions.

  Abstract
  This paper presents a new computational technique for predicting the onset and evolution of fracture in a continuum in a simple manner combining the finite element method [...]

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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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