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• Advances in the DEM and coupled DEM and FEM techniques in non linear solid mechanics

  E. Oñate, F. Zarate, M. Celigueta, J. González, J. Miquel, J. Puigbó, F. Arrufat, S. Latorre, M. Santasusana

  Eugenio Oñate's Research Reports (2019).

  
  

  Abstract

  In this chapter we present recent advances in the Discrete Element Method (DEM) and in the coupling of the DEM with the Finite Element Method (FEM) for solving a variety of problems in non linear solid mechanics involving damage, plasticity and multifracture situations.

  Abstract
  In this chapter we present recent advances in the Discrete Element Method (DEM) and in the coupling of the DEM with the Finite Element Method (FEM) for solving a variety of [...]

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• A stabilized finite element formulation for high‐speed inviscid compressible flows using finite calculus

  M. Kouhi, E. Oñate

  Int. J. Numer. Meth. Engng. (2014). Vol. 74(2) pp. 872-897

  
  

  Abstract

  This paper aims at the development of a new stabilization formulation based on the Finite Calculus (FIC) scheme for solving the Euler equations using the Galerkin finite element method (FEM) on unstructured triangular grids. The FIC method is based on expressing the balance of fluxes in a space-time domain of finite size. It is used to prevent the creation of instabilities typically present in numerical solutions due to the high convective terms and sharp gradients. Two stabilization terms, respectively called streamline term and transverse term, are added via the FIC formulation to the original conservative equations in the spacetime domain. An explicit fourth order Runge-Kutta scheme is implemented to advance the solution in time. The presented numerical test examples for inviscid flows prove the ability of the proposed stabilization technique for providing appropriate solutions especially near shock waves. Although the derived methodology delivers precise results with a nearly coarse mesh, a mesh refinement technique is coupled to the solution process for obtaining a suitable mesh particularly in the high gradient zones.

  Abstract
  This paper aims at the development of a new stabilization formulation based on the Finite Calculus (FIC) scheme for solving the Euler equations using the Galerkin finite element [...]

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• Simple and efficient numerical tools for the analysis of parachutes

  R. Flores, E. Ortega, E. Oñate

  Engineering Computations (2014). Vol. 31(5) pp. 957-985

  
  

  Abstract

  This work describes a set of simple yet effective, numerical method for the design and evaluation of parachute-payload system. The developments include a coupled fluidstructural solver for unsteady simulations of ram-air type parachutes. For an efficient solution of the aerodynamic problem, an unsteady panel method has been chosen exploiting the fact that large areas of separated flow are not expected under nominal flight conditions of ram-air parachutes. A dynamic explicit finite element solver is used for the structure. This approach yields a robust solution even when highly non-linear effects due to large displacements and material response are present. The numerical results show considerable accuracy and robustness. An added benefit of the proposed aerodynamic and structural techniques is that they can be easily vectored and thus suitable for use in parallel architectures. The main features of the computational tools are described and several numerical examples are provided to illustrate the performance and capabilities of the technique.

  Abstract
  This work describes a set of simple yet effective, numerical method for the design and evaluation of parachute-payload system. The developments include a coupled fluidstructural [...]

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• A local constitutive model for the discrete element method. Application to geomaterials and concrete

  E. Oñate, F. Zárate, J. Miquel, M. Santasusana, M. Celigueta, F. Arrufat, R. Gandikota, K. Valiullin, L. Ring

  Computational Particle Mechanics (2015). Vol. 2(2) pp. 139-160

  
  

  Abstract

  This paper presents a local constitutive model for modelling the linear and non linear behavior of soft and hard cohesive materials with the discrete element method (DEM). We present the results obtained in the analysis with the DEM of cylindrical samples of cement, concrete and shale rock materials under a uniaxial compressive strength (UCS) test, different triaxial tests, a uniaxial strain compaction (USC) test and a brazilian tensile strength (BTS) test. DEM results compare well with the experimental values in all cases.

  Abstract
  This paper presents a local constitutive model for modelling the linear and non linear behavior of soft and hard cohesive materials with the discrete element method (DEM). [...]

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• Application of an enhanced discrete element method to oil and gas drilling processes

  P. Ubach, F. Arrufat, L. Ring, R. Gandikota, F. Zárate, E. Oñate

  Comp. Part. Mech (2016). Vol. 3(1) pp. 39-4 (preprint)

  
  

  Abstract

  The authors present results on the use of the discrete element method (DEM) for the simulation of drilling processes typical in the oil and gas exploration industry. The numerical method uses advanced DEM techniques using a local definition of the DEM parameters and combined FEM-DEM procedures. This paper presents a step by step procedure to build a DEM model for analysis of the soil region coupled to a FEM model for discretizing the drilling tool that reproduces the drilling mechanics of a particular drill bit. A parameter study has been performed to determine the model parameters in order to maintain accurate solutions with reduced computational cost.

  Abstract
  The authors present results on the use of the discrete element method (DEM) for the simulation of drilling processes typical in the oil and gas exploration industry. The numerical [...]

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• Particle methods in Computational Fluid Dynamics

  S. Idelsohn, E. Oñate, P. Becker

  (2018). Vol. 3 Encyclopedia of Computational Mechanics. Second Edition. Edited by E. Stein, R. de Borst and T. J. R. Hughes (Eds.), John Wiley & Sons, pp. 1-41

  
  

  Abstract

  Particle methods in Computational Fluid Dynamics (CFD) are numerical tools for the solution of the equations of f luid dynamics obtained by replacing the fluuid continuum with a finite set of particles. For mathematicians, particles are just points from which properties of the uid can be interpolated. For physicists the particles are material points, which can be treated like any other particle system. Either way, particle methods have a number of attractive features. One of the key attributes is that pure advection is treated exactly. For example, if the particles are given a determined colour and the velocity is specified, the transport of colours by the particle system is exact. The convection of properties also eases the solution of multi material problems, simplifying the detection of interfaces. The use of particles also allows to bridge the gap between the continuum and fragmentation in a natural way, for example in fracture or droplets problems. Since the computation domain, the particles, matches exactly the material domain of interest, the computational resources are optimized with the corresponding reduction in storage and calculation time compared to other methods. Finally, because of the close similarity between particle methods and the physics of the problems to be solved, it is often possible to account for complex physics more easily than with other methods.

  Abstract
  Particle methods in Computational Fluid Dynamics (CFD) are numerical tools for the solution of the equations of f luid dynamics obtained by replacing the fluuid continuum [...]

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• An implicit stabilized finite element method for the compressible Navier–Stokes equations using finite calculus

  M. Kouhi, E. Oñate

  Computational Mechanics (2015). Vol. 56(1) pp. 113-129

  
  

  Abstract

  A new implicit stabilized formulation for the numerical solution of the compressible NavierStokes equations is presented. The method is based on the Finite Calculus (FIC) scheme using the Galerkin finite element method (FEM) on triangular grids. Via the FIC formulation, two stabilization terms, called streamline term and transverse term, are added to the original conservation equations in the space-time domain. The non-linear system of equations resulting from the spatial discretization is solved implicitly using a damped Newton method benefiting from the exact Jacobian matrix. The matrix system is solved at each iteration with a preconditioned GMRES method. The efficiency of the proposed stabilization technique is checked out in the solution of 2D inviscid and laminar viscous flow problems where appropriate solutions are obtained especially near the boundary layer and shock waves. The work presented here can be considered as a follow up of a previous work of the authors [24]. In that paper, the stabilized Galerkin FEM based on the FIC formulation was derived for the Euler equations together with an explicit scheme. In the present paper, the extension of this work to the Navier-Stokes equations using an implicit scheme is presented.

  Abstract
  A new implicit stabilized formulation for the numerical solution of the compressible NavierStokes equations is presented. The method is based on the Finite Calculus (FIC) [...]

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• An accurate FIC-FEM formulation for the 1D advection-diffusion-reaction equation

  E. Oñate, J. Miquel, P. Nadukandi

  Computer Methods in Applied Mechanics and Engineering (2016). Vol. 298() pp. 373-406

  
  

  Abstract

  In this paper we present an accurate stabilized FIC-FEM formulation for the 1D advection-diffusion-reaction equation in the exponential and propagation regimes using two stabilization parameters. Both the steady-state and transient solutions are considered. The stabilized formulation is based on the standard Galerkin FEM solution of the governing differential equations derived via the Finite Increment Calculus (FIC) method. The steady-state problem is considered first. The optimal value of the two stabilization parameters ensuring an exact (nodal) FEM solution using uniform meshes of linear 2-noded elements is obtained. In the absence of the absorption term the formulation simplifies to the standard one-parameter Petrov-Galerkin method for the advection-diffusion problem. For the diffusion-reaction case one stabilization parameter is just needed and the diffusion-type stabilization term is identical to that obtained by Felippa and O˜ nate [16] using a variational FIC approach. A procedure for computing the stabilization parameters for the transient problem is proposed. The accuracy of the new FIC-FEM formulation is demonstrated in the solution of steady-state and transient 1D advection-diffusion-radiation problems for a the range of physical parameters and boundary conditions. Finally we outline the procedure to extend the 1D FIC-FEM formulation to multidimensions.

  Abstract
  In this paper we present an accurate stabilized FIC-FEM formulation for the 1D advection-diffusion-reaction equation in the exponential and propagation regimes using two stabilization [...]

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• On the effect of the bulk tangent matrix in partitioned solution schemes for nearly incompressible fluids

  A. Franci, E. Oñate, J. Carbonell

  Int. J. Numer. Meth. Engng. (2015). Vol. 102(3-4) pp. 257-277

  
  

  Abstract

  The purpose of this paper is to study the effect of the bulk modulus in the iterative matrix for the analysis of quasi-incompressible free surface fluid flows using a mixed Lagrangian finite element formulation and a partitioned solution scheme. A practical rule to set up the value of a pseudo-bulk modulus a priori in the tangent bulk stiffness matrix for improving the conditioning of the linear system of algebraic equations is also given. The efficiency of the proposed strategy is tested in several problems analyzing the advantage of the modified bulk tangent matrix with regard to the stability of the pressure field, the convergence rate and the computational speed of the analyses. The technique has been tested on the FIC/PFEM Lagrangian formulation presented in [19] but it can be easily extended to other quasi-incompressible stabilized finite element formulations. Copyright c 2010 John Wiley & Sons, Ltd.

  Abstract
  The purpose of this paper is to study the effect of the bulk modulus in the iterative matrix for the analysis of quasi-incompressible free surface fluid flows using a mixed [...]

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• A Particle Finite Element Method (PFEM) for analysis of industrial forming processes

  E. Oñate, A. Franci, J. Puigbó

  Computational Mechanics (2014). Vol. 54 pp. 85-107 Vol. 54 pp. 85-107

  
  

  Abstract

  We present a generalized Lagrangian formulation for analysis of industrial forming processes involving thermally coupled interactions between deformable continua. The governing equations for the deformable bodies are written in a unified manner that holds both for fluids and solids. The success of the formulation lays on a residual-based expression of the mass conservation equation obtained using the Finite Calculus (FIC) method that provides the necessary stability for quasi/fully incompressible situations. The governing equations are discretized with the FEM via a mixed formulation using simplicial elements with equal linear interpolation for the velocities, the pressure and the temperature. The merits of the formulation are demonstrated in the solution of 2D and 3D thermally-coupled forming processes using the Particle Finite Element Method (PFEM).

  Abstract
  We present a generalized Lagrangian formulation for analysis of industrial forming processes involving thermally coupled interactions between deformable continua. The governing [...]

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