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• Finite element analysis of sheet metal forming problems using a viscous voided shell formulation

  E. Oñate, C. Agelet de Saracibar

  (1988). Modelling of Metal Forming Processes, J.L. Chenot y E. Oñate (Eds.), Kluwer Academic Publisher, pp. 163-178

  
  

  Abstract

  A formal analogy between the equations of pure plastic and viscoplastic flow theory for void containing metals and those of standard non linear elasticity is presented. It is shown how by direct simplifications of the general equations, the standard incompressible flow expressions for non voided metals are obtained. The general formulation is particularized for the analysis of sheet metal forming problems and details of the viscous voided shell and membrane formulations for dealing with the axisymmetric case are given. Finally, some examples of applications of pure and hemispherical stretching and deep drawing of a circular sheet axe presented.

  Abstract
  A formal analogy between the equations of pure plastic and viscoplastic flow theory for void containing metals and those of standard non linear elasticity is presented. It [...]

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• Stabilization techniques for finite element analysis of convection-diffusion problems

  E. Oñate, M. Manzan

  (2000). Convection Heat Transfer, B. Sundén and G. Comini (Eds.), WIT Press, Southampton, United Kingdom

  
  

  Abstract

  The accurate solution of convection type problems on practical grids has been ever a challenging issue, and invariably some sort of stabilization is needed in order to get a physical solution. This has pushed researchers to develop various stabilization algorithms used in every day practice by numerical analysts. In this chapter some methods are presented along with a new finite increment calculus approach to obtain the different algorithms using higher order conservation equations.

  Abstract
  The accurate solution of convection type problems on practical grids has been ever a challenging issue, and invariably some sort of stabilization is needed in order to get [...]

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• An alpha-adaptive approach for stabilized finite element solution of advective-diffusive problems with sharp gradients

  E. Oñate, J. García-Espinosa, S. Idelsohn

  (1998). New Advances in Adaptive Computational Methods in Mechanics, P. Ladeveze and J.T. Oden (Eds.), Elsevier

  
  

  Abstract

  In this paper the FIC method is used as the basis for a new “alpha-adaptive” procedure (where alpha denotes the stabilization parameters) for obtaining stable solution in advective-diffusive problems where arbitrary sharp transverse gradients are present. The new stabilization thechnique can be viewed as an alternative class of adaptive methods where the numerical solution is enhanced by searching “adaptively” the optimal value of the streamline and transverse (crosswing) stabilization parameters while keeping the mesh and the finite element approximation unchanged. Indeed the basic alpha-adaptive process can be enhanced by combining it with standard h, p or hp adaptive schemes. In the first part of the paper the basis of the FIC stabilized method for advectivediffusive problems are explained. Next the algorithm for computing the streamline and transverse stabilization parameters via the new “alpha-adaptive” procedure is described. Finally, the efficiency and accuracy of the new approach are shown in two examples of application.

  Abstract
  In this paper the FIC method is used as the basis for a new “alpha-adaptive” procedure (where alpha denotes the stabilization parameters) for obtaining stable [...]

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• Possibilities of parallel computing in the finite element analysis of industrial forming processes

  E. Oñate

  (1997). Vector and Parallel Processing - VECPAR'96, Palma J.M.L.M., Dongarra J. (eds) Vector and Parallel Processing — VECPAR'96. VECPAR Lecture Notes in Computer Science, vol. 1215, pp 258-294, Springer, Berlin, Heidelberg

  
  

  Abstract

  The paper presents an overview of the possibilities of parallel computing for the analysis of industrial forming processes using the finite element method. The theoretical and computational aspects of the various finite element formulations are presented in some detail as well as the different strategies for parallehzation of the solver, the mesh generation, the error simulation and the mesh adaption modules. Some examples of parallel analysis of powder compaction and sheet stamping processes using parallel finite element codes developed at CIMNE are finally presented.

  Abstract
  The paper presents an overview of the possibilities of parallel computing for the analysis of industrial forming processes using the finite element method. The theoretical [...]

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• Discrete Volume Method. A variational approach for brittle fracture

  V. Cardoso, E. Oñate, S. Botello

  Monograph CIMNE (2019). M184

  
  

  Abstract

  The Discrete Element Method has been used to simulate fracture dynamics beacuse its inherent capacity to reproduce multi-body interaction, but in the case of elasticity mechanics the microparameters of the numerical model, required to replicate the properties of the material, are difficult to calibrate. On the other hand, damage models based on finite element strategies can easily reproduce the properties of the media but they can not simulate the dynamics of multiple fractures. We propose a numerical approach, the Discrete Volume Method, to simulate fracture of brittle materials without the disadvantages mentioned, by combining the benefits of variational formulations and the numerical convenience of discrete element method to capture the dynamics of cracks. The Discrete Volume Method does not have microparameters, since the displacements are computed using the material properties and the fracture mechanism is controlled by an auxiliary damage field. Within this work we discuss a numerical strategy to solve the elasticity problem upon unstructured and non conforming meshes, allowing all kinds of flat-faced elements (polygons in 2D and polyhedra in 3D). The core of the formulation relies on two numerical procedures the Control Volume Function Approximation (CVFA), and the polynomial interpolation in the neighborhood of the control volumes, which is used to solve the surface integrals resulting from applying the divergence theorem. By comparing the estimated stress against the analytical stress field of the well known test of an infinite plate with a hole, we show that this conservative approach is robust and accurate. A similar strategy is used to get the damage field solution. In order to coupling both fields, displacement and damage, we use a finite increment arrangement for reducing the resdidual of elastic equation within each time step. We develop a numerical formulation for time discretization based on the analytical solution of the differential equation resulting from assuming a continuous variation of internal forces of the system between time steps. Finally, we show the effectiveness of the methodology by performing numerical experiments and comparing the solutions with published results. 

  Abstract
  The Discrete Element Method has been used to simulate fracture dynamics beacuse its inherent capacity to reproduce multi-body interaction, but in the case of elasticity mechanics [...]

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• Finite volume for stress analysis upon polygonal, unstructured and non conforming meshes

  V. Cardoso Nungaray, S. Botello, F. Zarate, E. Oñate

  Rev. int. métodos numér. cálc. diseño ing. (2019). Vol. 35, (4), 47

  
  

  Abstract

  Within this paper we discuss a numerical strategy to solve the elasticity problem upon unstructured and non conforming meshes, allowing all kinds of flat-faced elements (polygons in 2D and polyhedra in 3D). The core of the formulation relies on two numerical procedures 1) the Control Volume Function Approximation (CVFA), and 2) the polynomial interpolation in the neighborhood of the control volumes, which is used to solve the surface integrals resulting from applying the divergence theorem. By comparing the estimated stress against the analytical stress field of the well known test of an infinite plate with a hole, we show that this conservative approach is robust and accurate.

  Abstract
  Within this paper we discuss a numerical strategy to solve the elasticity problem upon unstructured and non conforming meshes, allowing all kinds of flat-faced elements (polygons [...]

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• Ship hydrodynamics

  E. Oñate, J. García-Espinosa, S. Idelsohn

  (2004). Encyclopedia of Computational Mechanics, E. Stein, R. de Borst and T.J.R. Hughes (Eds.), John Wiley & Sons Ltd, Vol. 3, Chapter 18, pp. 579 - 607

  
  

  Abstract

  This chapter presents an overview of some computational methods for analysis of ship hydrodynamics problems. Attention is focused on the description of a stabilized finite element formulation derived via a finite calculus procedure. Both arbitrary Lagrangian-Eulerian (ALE) and fully Lagrangian forms are presented. Details of the treatment of the free-surface waves and the interaction between the ship structure and the sea water are also given. Examples of application to a variety of ship hydrodynamics problems are shown.

  Abstract
  This chapter presents an overview of some computational methods for analysis of ship hydrodynamics problems. Attention is focused on the description of a stabilized finite [...]

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• Meshless analysis of incompressible flows using the Finite Point Method

  E. Oñate, C. Sacco, S. Idelsohn

  (2001). Innovative Tools for Scientific Computation in Aeronautical Engineering, J. Periaux, P. Joly, O. Pironneau and E. Oñate (Eds.), pp. 208-232, CIMNE, Barcelona, Spain

  
  

  Abstract

  A stabilized finite point method (FPM) for the meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite calculus (FIC) procedure. An enhanced fractional step procedure allowing the semi-implicit numerical solution of incompressible fluids using the FPM is described. Examples of application of the stabilized FPM to the solution of incompressible flow problems are presented.

  Abstract
  A stabilized finite point method (FPM) for the meshless analysis of incompressible fluid flow problems is presented. The stabilization approach is based in the finite calculus [...]

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• The Particle Finite Element Method (PFEM). An effective numerical technique for solving marine, naval and harbour engineering problems

  E. Oñate, S. Idelsohn, M. Celigueta, B. Suarez

  (2013). Marine 2011, IV Int. Conference on Computational Methods in Marine Engineering. Selected papers, L. Eça, E. Oñate, J. García-Espinosa, T. Kvamsdal and P. Bergan (Eds.), pp. 65-81, Springer (preprint)

  
  

  Abstract

  We present some developments in the Particle Finite Element Method (PFEM) for the solution of complex coupled problems in marine, naval and harbour engineering involving fluid-soil-structure interaction (FSSI). The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in a continuum domain containing fluid, soil/rock and structures subdomains. A mesh connects the nodes defining the discretized domain where the governing equations for each of the constituent materials are solved with the FEM. The stabilization for dealing with an incompressibility material is introduced via the finite calculus (FIC) method. An incremental iterative scheme for solving the non linear transient 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 examples of application of the PFEM to solve FSSI problems in marine, naval and harbour engineering such as the motion of rocks by water streams, the stability of breakwaters and constructions under sea waves, the sinking of ships and the collision of a ship with ice blocks.

  Abstract
  We present some developments in the Particle Finite Element Method (PFEM) for the solution of complex coupled problems in marine, naval and harbour engineering involving fluid-soil-structure [...]

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• Advances in the particle finite element method (PFEM) for solving coupled problems in engineering

  E. Oñate, S. Idelsohn, M. Celigueta, R. Rossi, J. Marti, J. Carbonell, P. Ryzhakov, B. Suárez

  (2011). Particle-Based Methods, Computational Methods in Applied Sciences, Springer, E. Oñate and R. Owen (Eds.), Vol. 25, pp. 1-48

  
  

  Abstract

  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 solid-solid 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.

  Abstract
  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 [...]

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