Eugenio Oñate’s Book Chapters : Scipedia

Lagrangian formulation for fluid-structure interaction problems using the particle finite element method
E. Oñate, S. Idelsohn, M. Celigueta

(2006). Verification and Validation Methods for Challenging Multiphysics Problems, CIMNE, pp. 125-150

Abstract
We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use of 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 (called particles) particles 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, expressed in an integral from, 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. Examples of application of the PFEM to solve a number of fluid-structure interaction problems involving large motions of the free surface and splashing of waves are presented.
Abstract
We present a general formulation for analysis of fluid-structure interaction problems using the particle finite element method (PFEM). The key feature of the PFEM is the use [...]
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A general stabilized formulation for incompressible fluid flow using finite calculus and the finite element method
E. Oñate, J. García, G. Bugeda, S. Idelsohn

(2003). Fluid Dynamics and Aeronautics New Challenges, Périaux J., Champion M., Gagnepain J.-J., Pironneau O., Stoufflet B. and Thomas Ph.(Eds.), CIMNE, Barcelona, Spain

Abstract
We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM). The necessary stabilization for dealing with convective effects and the incompressibility condition are introduced via the so called finite calculus (FIC) method. The extension of the standard eulerian form of the equations to an arbitrary lagrangian-eulerian (ALE) frame adequate for treating fluid-structure interaction problems is presented. The fully lagrangian form is also discussed. Details of an effective mesh updating procedure are presented together with a method for dealing with free surface effects of importance for ship hydrodynamic analysis and many other fluid flow problems. Examples of application of the eulerian, the ALE and the fully lagrangian flow descriptions are presented.
Abstract
We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM). The necessary stabilization for dealing with convective effects [...]
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Finite Element Analysis of Membrane Structures
R. Taylor, E. Oñate, P. Ubach de Fuentes

(2005). Recent Advances in Textile Membranes and Inflatable Structures, Springer Verlag, pp. 47 - 68

Abstract
This paper summarizes the development for a large displacement formulation of a membrance composed of three-node triangular elements. A formulation in terms of the deformation gradient is first constructed in terms of nodal variables. In particular, the use of the right Cauchy-Green deformation tensor is shown to lead to a particulary simple representation in terms of nodal quantities. This may then be used to construct general models for use in static and transient analyses.
Abstract
This paper summarizes the development for a large displacement formulation of a membrance composed of three-node triangular elements. A formulation in terms of the deformation [...]
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Stabilization via finite calculus in finite element computations
E. Oñate

(2004). Finite Element Methods: 1970's and Beyond, Franca L.P., Tezduyar T.E. and Masud A. (Eds.),CIMNE, Barcelona, Spain

Abstract
The expression “finite calculus” refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes, forces, etc. in a space-time domain of finite size. The governing equations resulting from this approach are different from those of infinitesimal calculus theory and they incorporate new terms which depend on the dimensions of the balance domain. The new governing equations allow to derive naturally stabilized numerical schemes using any discretization procedure. The paper discusses the possibilities of the finite calculus method for the finite element solution of convection-diffusion problems with sharp gradients and incompressible fluid flow.
Abstract
The expression “finite calculus” refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes, forces, etc. in a [...]
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FE Analysis of membrane systems including wrinkling and coupling
R. Rossi, R. Vitaliani, E. Oñate

(2005). Recent Advances in Textile Membranes and Inflatable Structures, Springer Verlag, pp. 89 - 108

Abstract
Current work summarizes the experience of the writer in the modeling of membrane systems. A first subsection describes an efficient membrane model, together with a reliable solution procedure. The following section addresses the simulation of the wrinkling phenomena providing details of a new solution procedure. The last one proposes an efficient technique to obtain the solution of the fluid structural interaction problem.
Abstract
Current work summarizes the experience of the writer in the modeling of membrane systems. A first subsection describes an efficient membrane model, together with a reliable [...]
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Enhanced Rotation-Free Basic Shell Triangle. Applications to Sheet Metal Forming
E. Oñate, F. Flores, L. Neamtu

(2007). Computational Plasticity, E. Oñate and R. Owen (Eds.), pp. 239-265

Abstract
An enhanced rotation-free three node triangular shell element (termed EBST) is presented. The element formulation is based on a quadratic interpolation of the geometry in terms of the six nodes of a patch of four triangles associated to each triangular element. This allows to compute an assumed constant curvature field and an assumed linear membrane strain field which improves the in-plane behaviour of the element. A simple and economic version of the element using a single integration point is presented. The implementation of the element into an explicit dynamic scheme is described. The efficiency and accuracy of the EBST element and the explicit dynamic scheme are demonstrated in many examples of application including the analysis of a cylindrical panel under impulse loading and sheet metal stamping problems.
Abstract
An enhanced rotation-free three node triangular shell element (termed EBST) is presented. The element formulation is based on a quadratic interpolation of the geometry in [...]
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A unified symmetrical formulation for interactions between elastic solids and incompressible fluids
S. Idelsohn, E. Oñate, J. Marti

(2007). Variational Formulations in Mechanics: Theory and Applications, E. Taroco, E.A. de Souza Neto and A.A. Novotny (Eds.), CIMNE, Barcelona, Spain

Abstract
We present a general Lagrangian formulation for treating elastic solids and quasi/fully incompressible fluids in a unified form. The formulation allows to treat solid and fluid subdomains in a unified manner in fluid-structure interaction (FSI) situations. The use for both fluid and solid of a Lagrangian formulation avoid convective terms allowing to approximate the problem via a Variational Formulation. In our work the FSI problem is solved via the Particle Finite Element Method (PFEM). The PFEM is an effective technique for modeling complex interactions between floating and submerged bodies and free surface flows, accounting for splashing of waves, large motions of the bodies and frictional contact conditions. Applications of the unified Lagrangian formulation to a number of FSI problems are given.
Abstract
We present a general Lagrangian formulation for treating elastic solids and quasi/fully incompressible fluids in a unified form. The formulation allows to treat solid and [...]
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Experiences in the Design Analysis and Construction of Low Pressure Inflatable Structures
J. Marcipar, E. Oñate, J. Canet

(2005). Recent Advances in Textile Membranes and Inflatable Structures, Springer Verlag, pp. 241 - 257
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Fluid-soil-structure interaction analysis with the particle finite element method
E. Oñate, M. Celigueta, S. Idelsohn, F. Salazar, B. Suarez

(2012). Bytes and Science, G. Zavarise and D. Boso (Eds.), pp. 119 - 130, CIMNE, Barcelona Spain

Abstract
We present some developments and applications of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems in mechanics involving fluid-soil-structure interaction.
Abstract
We present some developments and applications of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems in mechanics involving fluid-soil-structure [...]
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Applications of a Rotation-Free Triangular Element for Finite Strain Analysis of Thin Shells and Membranes
F. Flores, E. Oñate

(2005). Recent Advances in Textile Membranes and Inflatable Structures, Springer Verlag, pp. 69 - 88

Abstract
This paper shows applications of a recently developed shell element to the analysis of thin shell and membrane structures. The element is a three node triangle with only translational DOFs (rotation free) that uses the configuration of the three adjacent elements to evaluate the strains. This allows to compute (constant) bending strains and (linear) membrane strains. A total Lagrangian formulation is used. Strains are defined in terms of the principal stretches. This allows to consider rubber materials and other type of materials using the Hencky stress-strain pair. An explicit central difference scheme is used to integrate the momentum equations. Several examples, including inflation and deflation of membranes show the excellent convergence properties and robustness of the element for large strain analysis of thin shells and membranes.
Abstract
This paper shows applications of a recently developed shell element to the analysis of thin shell and membrane structures. The element is a three node triangle with only translational [...]
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Membrane Structures Formed by Low Pressure Inflatable tubes. New Analysis Methods and Recent Constructions
E. Oñate, F. Flores, J. Marcipar

(2008). Textile Composites and Inflatable Structures II, E. Oñate and B. Kröplin (eds.), pp. 163-196

Abstract
This paper shows applications of a recently developed thin shell element adequate for the analysis of membrane and inflatable structures. The element is a three node triangle with only translational degrees of freedom that uses the configuration of the three adjacent elements to evaluate the strains in terms of the nodal displacements only. This allows to compute (constant) bending strains and (linear) membrane strains using a total Lagrangian formulation. Several examples, including inflation and deflation of membranes and some practical applications to the analysis, design and construction of membrane structures formed by low pressure inflatable tubes are presented.
Abstract
This paper shows applications of a recently developed thin shell element adequate for the analysis of membrane and inflatable structures. The element is a three node triangle [...]
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A finite element method for fluid-structure interaction with surface waves
E. Oñate, J. García-Espinosa

(2001). Trends in Computational Structural Mechanics. W. A. Wall, K.-U. Bletzinger and K. Schweizerhof (Eds.), CIMNE, Barcelona, Spain

Abstract
A stabilized semi-implicit fractional step finite element method for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized equations are derived at a differential level via a finite element calculus procedure. A new mesh updating technique based on solving a fictitious elastic problem on the moving mesh is described. One example of the efficiency of the stabilized semi-implicit algorithm for the coupled solution of fluid-structure interaction problems is presented.
Abstract
A stabilized semi-implicit fractional step finite element method for solving coupled fluid-structure interaction problems involving free surface waves is presented. The stabilized [...]
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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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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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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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Finite elements versus finite volumes. Is there really a choice?
O. Zienkiewicz, E. Oñate

(1992). Non linear computational mechanics. State of the art. P. Wriggers,R. Wagner and E. Stein (eds.), Chapter IV, Beam, Plate and Shell Formulations, pp. 240-254, Springer Verlag

Abstract
The finite volume method appears to be a particular case of finite elements with a non Galerkin weighting. It is course less accurate for self adjoint problems but has some computationally useful features for first order equations involving only surface integrals. For certain problems this is a substational economy and leads to computationally useful approximations.
Abstract
The finite volume method appears to be a particular case of finite elements with a non Galerkin weighting. It is course less accurate for self adjoint problems but has some [...]
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Langrangian formulation for incompressible fluids using finite calculus and the finite element method
E. Oñate, S. Idelsohn, F. Pin

(2003). Kuznetsov Y., Neittanmaki P. and Pironneau O. (Eds.),CIMNE, Barcelona, Spain

Abstract
We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM) and a lagrangian description. The necessary stabilization for dealing with the incompressibility condition is introduced via the so called finite calculus (FIC) method. Both a quasi-implicit algorithm and a fractional step scheme are described. Examples of application of the lagrangian flow description are presented.
Abstract
We present a general formulation for incompressible fluid flow analysis using the finite element method (FEM) and a lagrangian description. The necessary stabilization for [...]
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A review of some finite element families for thick and thin plate and shell analysis
E. Oñate

(1994). Recent Developments in Finite Element Analysis, Hughes J., Oñate E. and Zienkiewicz O. (Eds.), CIMNE, Barcelona

Abstract
This paper describes a number of triangular and quadrilateral plate and Shell elements derived via Reissner-Mindlin plate theory and mixed interpolation. It shown how by introducing the adequate constrains the original thick plate element evolve into DK forms adequate for this situations only. This evolution process allows to revisite some classical elements like the Morley triangle and also to derive simple plate and shell triangles and quadrilates with only translational degrees of freedom as nodal variables.
Abstract
This paper describes a number of triangular and quadrilateral plate and Shell elements derived via Reissner-Mindlin plate theory and mixed interpolation. It shown how by introducing [...]
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Analysis of the structure of gothic cathedrals. Application to Barcelona cathedral
P. Roca, L. Pellegrini, E. Oñate, A. Hanganu

(1998). Structural Analysis of Historical Constructions II, P. Roca, J.L. González, E. Oñate and P. B. Lourenço(Eds.), CIMNE, Barcelona, Spain

Abstract
The study of ancient structures composed of stone arches and vaults requires the use of specific techniques of analysis endowed with powerful procedures for the modelling of geometry, the simulation of the mechanical response of the various materials (including ashlar blocks and masonry, backings and fills) and the simulation of the structure or may have affected it through history. More specifically, those techniques must be able to reproduce the actual conditions of thrust equilibrium between the large number of curved, linear or two-dimensional members involved. The validity of several modelling techniques with a very different level of sophistication is studied through their use in the study of a particular Gothic construction: Barcelona Cathedral. The various techniques used were developed at the school of civil engineering of the technical university of Catalonia and have already been used in the analysis of a set historical constructions, including the Basilica of San Marco (Oñate et al., 1997) and the Crypt of the Colònia Güell (Roca, 1997). The present study of Barcelona Cathedral, now under development, is thus not only aimed at gaining a better understanding of various aspects of the resistance of Gothic constructions (and the southern and Catalan Gothic, in particular) but also at appraising the possibilities and limitations of various analytical techniques.
Abstract
The study of ancient structures composed of stone arches and vaults requires the use of specific techniques of analysis endowed with powerful procedures for the modelling [...]
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Ship hydrodynamics
E. Oñate, J. García-Espinosa, S. Idelsohn, B. Servan Camas

(2018). Encyclopedia of Computational Mechanics Second Edition, E. Stein, R. de Borst and T.J.R. Hughes (Eds.), John Wiley & Sons Ltd, Vol. 6, Chapter 24, pp. 1091 - 1137

Abstract
This chapter presents an overview of some computational methods for the analysis of problems in ship hydrodynamics. Attention is focused on the description of stabilized finite element formulations derived via a finite increment calculus (FIC) 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 given. Potential flow formulations for seakeeping analysis and calculation of the added resistance in waves are also described. Examples of application of the computational methods presented to a variety of ship hydrodynamics and related problems are given.
Abstract
This chapter presents an overview of some computational methods for the analysis of problems in ship hydrodynamics. Attention is focused on the description of stabilized finite [...]
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Optimizing rock cutting through computer simulation
J. Rojek, E. Oñate, C. Labra, H. Kargl, J. Akerman

(2010). Technology Innovation in Underground Construction (TUNCONSTRUCT), G. Beer (Ed.)

Abstract
This paper presents an original thermomechanical model of rock cutting with evaluation of tool wear. The model has been developed within the framework of the discrete element method, which is a suitable numerical method to study problems of multiple material fractures likes those of rock cutting. The paper presents brief overview of the theoretical formulation, calibration of the discrete element model, and a number of numerical results obtained in simulation of rock cutting processes typical for underground excavation, using both roadheaders and TBMs.
Abstract
This paper presents an original thermomechanical model of rock cutting with evaluation of tool wear. The model has been developed within the framework of the discrete element [...]
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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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Materiales compuestos - Simulación del comportamiento anisótropo
E. Car, S. Oller, E. Oñate

(2002). Análisis y Cálculo de Estructuras de Materiales Compuestos, Oller S. (Ed.), pp. 95-144, CIMNE, Barcelona, Spain
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Applying multi-objective robust design optimization procedure to the route planning of a commercial aircraft
J. Pons Prats, G. Bugeda, F. Zarate, E. Oñate, J. Periaux

(2018). Computational Methods and Models for Transport. Computational Methods in Applied Sciences. Diez, P. Neittaanmäki, P., Periaux, J., Tuovinen, T., Bräysy, O. (Eds.), Vol. 45, pp. 147-167, Springer, Cham

Abstract
Aircraft emission targets worldwide and their climatic effects have put pressure in government agencies, aircraft manufacturers and airlines to reduce water vapour, carbon dioxide (CO2CO2) and oxides of nitrogen (NOxNOx) resulting from aircraft emissions. The difficulty of reducing emissions including water vapor, carbon dioxide (CO2CO2) and oxides of nitrogen (NOxNOx) is mainly due to the fact that a commercial aircraft is usually designed for a particular optimal cruise altitude but may be requested or required to operate and deviate at different altitudes and speeds to archive a desired or commanded flight plan, resulting in increased emissions. This is a multi- disciplinary problem with multiple trade-offs such as optimizing engine efficiency, minimizing fuel burnt and emissions while maintaining prescribed aircraft trajectories, altitude profiles and air safety. There are possible attempts to solve such problems by designing new wing/aircraft shape, new efficient engine, ATM technology, or modifying the aircraft flight plan. Based on the rough data provided by an air carrier company, who was willing to assess the methodology, this paper will present the coupling of an advanced optimization technique with mathematical models and algorithms for aircraft emission, and fuel burnt reduction through flight plan optimization. Two different approaches are presented; the first one describes a deterministic optimization of the flight plan and altitude profile in order to reduce the fuel consumption while reducing time and distance. The second approach presents the robust design optimization of the previous case considering uncertainties on several parameters. Numerical results will show that the methods are able to capture a set of useful trade-offs solutions between aircraft range and fuel consumption, as well as fuel consumption and flight time.
Abstract
Aircraft emission targets worldwide and their climatic effects have put pressure in government agencies, aircraft manufacturers and airlines to reduce water vapour, carbon [...]
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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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Stochastic analysis of an impact problem
F. Zárate, J. Hurtado, E. Oñate

(1999). I. Doltsinis (Ed.), CIMNE, Barcelona, Spain
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Numerical modelling of sheet metal forming problems
E. Oñate, C. Agelet de Saracibar

(1991). Numerical Modelling of Material Deformations Processes, C. Sturgess et al (Eds.), Springer Verlag, London

Abstract
Stamping of sheet-metal parts by means of punches and dies is a standard manufacturing process. However, despite its broad application in industry, the design of forming processes is still largely based on experimental techniques, such as the use of circular grid systems (Keeler 1968) or forming limit diagrams (Hecker 1973, Keeler 1974).
Abstract
Stamping of sheet-metal parts by means of punches and dies is a standard manufacturing process. However, despite its broad application in industry, the design of forming processes [...]
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Shock control bump design optimization on natural laminar aerofoil
D. Lee, J. Periaux, K. Srinivas, L. González, N. Qin, E. Oñate

(2010). Computational Fluid Dynamics Review 2010, Part 9, 253-259, Edited by M M Hafez (University of California, Davis, USA), K Oshima (University of Tokyo, Japan), & Dochan Kwak (NASA Ames Research Center, USA)

Abstract
The chapter investigates Shock Control Bumps (SCB) on a Natural Laminar Flow (NLF) aerofoil; RAE 5243 for Active Flow Control (AFC). A SCB approach is used to decelerate supersonic flow on the suction/pressure sides of transonic aerofoil that leads delaying shock occurrence or weakening of shock strength. Such an AFC technique reduces significantly the total drag at transonic speeds. This chapter considers the SCB shape design optimisation at two boundary layer transition positions (0 and 45%) using an Euler software coupled with viscous boundary layer effects and robust Evolutionary Algorithms (EAs). The optimisation method is based on a canonical Evolution Strategy (ES) algorithm and incorporates the concepts of hierarchical topology and parallel asynchronous evaluation of candidate solution. Two test cases are considered with numerical experiments; the first test deals with a transition point occurring at the leading edge and the transition point is fixed at 45% of wing chord in the second test. Numerical results are presented and it is demonstrated that an optimal SCB design can be found to significantly reduce transonic wave drag and improves lift on drag (L/D) value when compared to the baseline aerofoil design.
Abstract
The chapter investigates Shock Control Bumps (SCB) on a Natural Laminar Flow (NLF) aerofoil; RAE 5243 for Active Flow Control (AFC). A SCB approach is used to decelerate supersonic [...]
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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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The Particle Finite Element Method for multi-fluid flows
S. Idelsohn, M. Mier-Torrecilla, J. Marti, E. Oñate

(2011). Particle-Based Methods, Computational Methods in Applied Sciences, Springer, E. Oñate and R. Owen (Eds.), Vol. 25, pp. 135-158

Abstract
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.
Abstract
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 [...]
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A finite element formulation for the geometrically non linear analysis of shells using a total lagrangian approach
J. Oliver, E. Oñate

(1988). Computational Methods for Non Linear Problems, C. Taylor (Ed.) Pineridge Press, pp. 29-55

Abstract
A total Lagrangian formulation for the large displacement large rotation: analysis of shells using finite elements is presented. Different expressions for the strain matrix obtained using various displacement interpolation forms are discussed and details of the obtention of the tangent stiffness matrix are given. Simplifications of the general 3D shell formulation for 2D shells are also presented together with some examples of applications.
Abstract
A total Lagrangian formulation for the large displacement large rotation: analysis of shells using finite elements is presented. Different expressions for the strain matrix [...]
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A multi-method approach towards understanding the pathophysiology of aortic dissections – the complementary role of in-silico, in-vitro and in-vivo information
P. Rudenick, M. Bordone, B. Bijnens, E. Soudah, E. Oñate, D. García-Dorado, A. Evangelista

(2010). Lecture Notes in Computer Science, Camara, O; Pop, M; Rhode, K; et al. (Eds.), Book Series: Lecture Notes in Computer Science, Vol. 6364, pp. 114-123

Abstract
Management and follow-up of chronic aortic dissections continues to be a clinical challenge due to progressive aortic dilatation. To predict dilatation, guidelines suggest follow-up of the aortic diameter. However, dilatation is triggered by haemodynamic parameters (pressure and wall shear stresses (WSS)), and geometry of false (FL) and true lumen (TL). We aimed at a better understanding of TL and FL haemodynamics by performing in-silico (CFD) and in-vitro studies on an idealized dissected aorta and compared this to a typical patient. We observed an increase in diastolic pressure and wall stress in the FL and the presence of diastolic retrograde flow. The inflow jet increased WSS at the proximal FL while a large variability in WSS was induced distally, all being risk factors for wall weakening. In-silico, in-vitro and in-vivo findings were very similar and complementary, showing that their combination can help in a more integrated and extensive assessment of aortic dissections, improving understanding of the haemodynamic conditions and related clinical evolution.
Abstract
Management and follow-up of chronic aortic dissections continues to be a clinical challenge due to progressive aortic dilatation. To predict dilatation, guidelines suggest [...]
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A simple method for automatic adaption of finite element meshes to changes in the boundary shape
G. Chiandussi, G. Bugeda, E. Oñate

(2001). Innovative Tools for Scientific Computation in Aeronautical Engineering, J. Periaux, P. Joly, O. Pironneau and E. Oñate (Eds.), pp. 149-167, CIMNE, Barcelona, Spain

Abstract
A simple method to automatically update the finite element mesh of the analysis domain is proposed for cases when the shape of the domain in modified. The method considers the mesh as a fictitious elastic body subjected to prescribed displacement at selected boundary points. The mechanical properties of each mesh element are appropriately selected in order to minimize the deformation and the distortion of the mesh elements. Different selection strategies have been used of remeshing in the solution of shape optimization problems and reduces the number of the remeshing step in the solution of coupled fluid-structure interaction problems
Abstract
A simple method to automatically update the finite element mesh of the analysis domain is proposed for cases when the shape of the domain in modified. The method considers [...]
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Métodos de cálculo y simulación en CAD. Diseño y simulación por computador
E. Oñate

(1986). Sistemas CAD, CAM, CAE : diseño y fabricación por computador, Boixareu Eds., Barcelona
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Development of New Lagrangian Computational Methods for Ice-Ship Interaction Problems: NICESHIP Project
J. García-Espinosa, E. Oñate, B. Servan Camas, M. Celigueta, S. Latorre, J. Colom-Cobb

(2020). Computation and Big Data for Transport. Computational Methods in Applied Sciences. In Diez P., Neittaanmäki P., Periaux J., Tuovinen T., Pons-Prats J. (eds), Vol 54, pp.121-153, Springer, Cham

Abstract
This document presents the activities carried out to date (04/2019) in the project ‘Development of new Lagrangian computational methods for ice-ship interaction problems’ (NICE-SHIP). The NICE-SHIP project aims at developing a new generation of computational methods, based on the integration of innovative Lagrangian particle-based and finite element procedures for the analysis of the operation of a vessel in an iced sea, taking into account the different possible conditions of the ice. It is expected that the computational analysis techniques to be developed in NICE-SHIP will allow ice-class vessel designers to accurately evaluate the loads acting on the structure of a ship navigating in iced-seas and, in particular, to determine the ice resistance of the ship in different ice conditions.
Abstract
This document presents the activities carried out to date (04/2019) in the project ‘Development of new Lagrangian computational methods for ice-ship interaction problems’ [...]
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Enhanced prediction of structural instability points using a critical displacement method
E. Oñate, W. Matias Silva

(1995). Advances in Finite Element Technology, N.-E. Wiberg (Ed.), CIMNE, Barcelona
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Adaptive Mesh Refinement Techniques for Structural Problems
E. Oñate, J. Castro

(1990). The Finite Element Method in the 1990's, E. Oñate et al (Eds.), CIMNE/Springer Verlag

Abstract
In this paper some adaptive mesh refinement (AMR) strategies for finite element analysis of structural problems are discussed. Two mesh optimality criteria based on the equal distribution of: (a) the global error, and (b) the specific error over the elements are studied. It is shown that the correct evaluation of the rate of convergence of the different error norms involved in the AMR procedures is essential to avoid oscillations in the refinement process. The behaviour of the different AMR strategies proposed is compared in the analysis of some structural problems.
Abstract
In this paper some adaptive mesh refinement (AMR) strategies for finite element analysis of structural problems are discussed. Two mesh optimality criteria based on the equal [...]
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Fractura elastoplástica: Modelos elastoplásticos para la simulación numérica de procesos de fractura
J. Oliver, S. Oller, E. Oñate

(1988). Métodos Numéricos Aplicados a la Mecánica de Fractura, J. Oliver et al (Eds.), CIMNE, Barcelona, pp. 27-60
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LES Turbulence models. Relation with stabilized numerical methods
A. Valls, J. García-Espinosa, E. Oñate

(2007). Models, Experiments and Computation in Turbulence, R. Castilla, E. Oñate, J. M. Redondo (Eds.), pp. 17-64

Abstract
One of the aims of this text is to show some important results in LES modelling and to identify which are main mathematical problems for the development of a complete theory. A relevant aspect of LES theory, which we will consider in our work, is the close relationship between the mathematical properties of LES models and the numerical methods used for their implementation. In last years it is more and more common the idea in the scientific community, especially in the numerical community, that turbulence models and stabilization techniques play a very similar role. Methodologies used to simulate turbulent flows, RANS or LES approaches, are based on the same concept: unability to simulate a turbulent flow using a finite discretization in time and space. Turbulence models introduce additional information (impossible to be captured by the approximation technique used in the simulation) to obtain physically coherent solutions. On the other side, numerical methods used for the integration of partial differential equations (PDE) need to be modified in order to able to reproduce solutions that present very high localized gradients. These modifications, known as stabilization techniques, make possible to capture these sharp and localized changes of the solution. According with previous paragraphs, the following natural question appears: Is it possible to reinterpret stabilization methods as turbulence models? This question suggests a possible principle of duality between turbulence modelling and numerical stabilization. More than to share certain properties, actually, it is suggested that the numerical stabilization can be understood as turbulence. The opposite will occur if turbulence models are only necessary due to discretization limitations instead of a need for reproducing the physical behaviour of the flow. Finally: can turbulence models be understood as a component of a general stabilization method?
Abstract
One of the aims of this text is to show some important results in LES modelling and to identify which are main mathematical problems for the development of a complete theory. [...]
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Mindlin finite strip and axisymmetric finite element shell analysis
E. Oñate, B. Suárez, E. Hinton

(1984). Finite Elements Software for Plates and Shells, Hinton E. y Owen D.R.J. (Eds.), Pineridge Press, 1984
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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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Efectos de los terremotos en las construcciones
E. Oñate, J. Canet

(1986). Riesgos Naturales en Ingeniería, E. Alonso et al (Eds.), Ediciones UPC
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Advanced solid elements for sheet metal forming simulation
V. Mataix Ferrándiz, R. Rossi, E. Oñate, F. flores

(2016). Journal of Physics: Conferences Series, Cesar de Sa J. M. A., Neto E. S., Cardoso R. P. R., Adetoro O. B. (eds), Vol. 734 (3), pp. 032128

Abstract
The solid-shells are an attractive kind of element for the simulation of forming processes, due to the fact that any kind of generic 3D constitutive law can be employed without any additional hypothesis. The present work consists in the improvement of a triangular prism solid-shell originally developed by Flores. The solid-shell can be used in the analysis of thin/thick shell, undergoing large deformations. The element is formulated in total Lagrangian formulation, and employs the neighbour (adjacent) elements to perform a local patch to enrich the displacement field. In the original formulation a modified right Cauchy-Green deformation tensor (C) is obtained; in the present work a modified deformation gradient (F) is obtained, which allows to generalise the methodology and allows to employ the Pull-Back and Push-Forwards operations. The element is based in three modifications: (a) a classical assumed strain approach for transverse shear strains (b) an assumed strain approach for the in-plane components using information from neighbour elements and (c) an averaging of the volumetric strain over the element. The objective is to use this type of elements for the simulation of shells avoiding transverse shear locking, improving the membrane behaviour of the in-plane triangle and to handle quasi-incompressible materials or materials with isochoric plastic flow.
Abstract
The solid-shells are an attractive kind of element for the simulation of forming processes, due to the fact that any kind of generic 3D constitutive law can be employed without [...]
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Finite Streifenmethode für Mindlinsche Platten und axialsymmetrische Schalen
E. Oñate, B. Suárez, E. Hinton

(1990). Finite Elemente Programme für Platten und Schalen, Springer-Verlag, Berlin, Germany

Abstract
Viele Konstruktionen besitzen konstante geometrische Eigenschaften entlang einer bestimmten Richtung. Derartige prismatische Strukturen sind bei Platten weit verbreitet, bei denen der Querschnitt der Platte in Längsrichtung oft konstant bleibt. Bei axialsymmetrischen Schalen bleibt der Querschnitt der Schale in Umfangsrichtung ebenfalls konstant (siehe Bild 2.1). Falls die Materialeigenschaften der Struktur ebenfalls in der gleichen Richtung konstant sind, kann die Berechnung durch eine Kombination der Methode der finiten Elemente und Fourierreihenentwicklung vereinfacht werden, um das transversale und longitudinale Verhalten zu erfassen.
Abstract
Viele Konstruktionen besitzen konstante geometrische Eigenschaften entlang einer bestimmten Richtung. Derartige prismatische Strukturen sind bei Platten weit verbreitet, bei [...]
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A variational formulation for the multilayer perceptron
R. Lopez, E. Oñate

(2006). S. Kollias et al (Eds.), ICANN 2006, Part I, LNCS 4131, pp. 19-168, Germany.

Abstract
In this work we present a theory of the multilayer perceptron from the perspective of functional analysis and variational calculus. Within this formulation, the learning problem for the multilayer perceptron lies in terms of finding a function which is an extremal for some functional. As we will see, a variational formulation for the multilayer perceptron provides a direct method for the solution of general variational problems, in any dimension and up to any degree of accuracy. In order to validate this technique we use a multilayer perceptron to solve some classical problems in the calculus of variations.
Abstract
In this work we present a theory of the multilayer perceptron from the perspective of functional analysis and variational calculus. Within this formulation, the learning problem [...]
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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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New computational challenges in fluid-structure interactions problems
S. Idelsohn, E. Oñate, R. Rossi, J. Marti, F. Del Pin

(2009). ECCOMAS Multidisciplinary Jubilee Symposium, J. Eberhardsteiner, Ch. Hellmich, H. Mang and J. Périaux (Eds.)

Abstract
In this paper the so-called added-mass effect is investigated from a different point of view of previous publications. The monolithic fluid structure problem is partitioned using a static condensation of the velocity terms. Following this procedure the classical stabilized projection method for incompressible fluid flows is introduced. The procedure allows obtaining a new pressure segregated scheme for fluid-structure interaction problems which has good convergent characteristics even for biomechanical application, where the added mass effect is strong. The procedure reveals its power when it is shown that the same projection technique must be implemented in staggered FSI methods.
Abstract
In this paper the so-called added-mass effect is investigated from a different point of view of previous publications. The monolithic fluid structure problem is partitioned [...]
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Efficient computational aspects for analyses of sheet stamping problems
G. Duffett, P. Cendonya, J. Rojek, E. Oñate

(1997). Recent Developments in Computational and Applied Mechanics. A Book in Honour of John B. Martin, B. D. Reddy (Ed.), CIMNE

Abstract
Efficiency and accuracy are vital for the acceptable simulation of large scale industrial sheet stamping problems. Two aspects, implemented within the explicit dynamic program STAMPACK, that effectively address this problem are described: an anisotropic plasticity material model combined with a thin shell element that contains only displacement degrees of freedom and an effective drawbead formulation based on an elastic-plastic analogy
Abstract
Efficiency and accuracy are vital for the acceptable simulation of large scale industrial sheet stamping problems. Two aspects, implemented within the explicit dynamic program [...]
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A finite element formulation for the geometrically non linear analysis of shells
E. Oñate, J. Oliver

(1986). Finite element methods for plate and shell structures, T.J.R. Hughes, E. Hinton (Ed.) Pineridge Press, Vol. 2: Formulations and algorithms, pp. 83-101

Abstract
A finite element formulation for the analysis of geometrically nonlinear shell problems is presented. Degenerated 3D elasticity elements are used for the finite element discretization of the shell. Large rotation effects are taken into account in the nonlinear large displacement kinematic description. The shell formulation is derived in detail using a Total Lagrangian approach and explicit forms of the relevant finite element matrices are given. In the last part of the chapter the obtention of the alternative Updated Lagrangian formulation is presented.
Abstract
A finite element formulation for the analysis of geometrically nonlinear shell problems is presented. Degenerated 3D elasticity elements are used for the finite element discretization [...]
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Prediction of elastic springback deffects in sheet stamping processes using finite element methods
E. Oñate, J. Rojek

(1997). Advanced Methods in Materials Processing Defects, Elsevier

Abstract
Undesiderable spring-back induced deformations are one of the cause for rejection of many stamped sheet parts. The paper presents the alternatives for predicting spring-back defects in the context of the most popular finite element (FE) formulations based on rigid-plastic and elasto-plastic material models, quasistatic (implicit) and explicit dynamic algorithms. Examples showing the possibilities and efficiency of the different FE procedures are also given.
Abstract
Undesiderable spring-back induced deformations are one of the cause for rejection of many stamped sheet parts. The paper presents the alternatives for predicting spring-back [...]
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Simulation of structural response to violent-free surface flows
R. Löhner, C. Yang, E. Oñate

(2008). Numerical Modeling of Coupled Phenomena in Science and Engineering, M.C. Suárez Arriaga, J. Bundschuh, F.J. Dominguez-Mota (Eds.)

Abstract
High sea states, waves breaking near shores andmoving ships, the interaction of extremewaveswith floating structures, green water on deck and sloshing (e.g. in liquid natural gas (LNG) tankers) are but a few examples of flows with violent free surface motion. The bodies exposed to these flows experience large, time-varying forces that can lead to fatigue and/or failure. It is therefore imperative to have a predictive capability in order to guarantee operability and optimize the lifespan under these conditions.
Abstract
High sea states, waves breaking near shores andmoving ships, the interaction of extremewaveswith floating structures, green water on deck and sloshing (e.g. in liquid natural [...]
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Structural analysis and durability assesment of historical constructions using a finite element damage model
E. Oñate, A. Hanganu, A. Barbat, S. Oller, R. Vitaliani, A. Saetta, R. Scotta

(1997). Structural Analysis of Historical Constructions I, P. Roca, J.L. González, A.R. Marí and E. Oñate (Eds.), CIMNE, Barcelona, Spain
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Characterization of mechanical properties of biological tissue – Application to the FEM analysis of the urinary bladder
E. Oñate, F. Bellomo, V. Monteiro, S. Oller, L. Nallim

(2014). Multiscale Simulations and Mechanics of Biological Materials, S. Li et al (Eds), Wiley

Abstract
An approach is presented for studying the mechanical behavior of soft biological tissue using the finite‐element method and a general constitutive model. The overall computational approach is used for the analysis of the mechanical behavior of the urinary bladder. Bladder tissue is modeled as a composite material formed by a soft matrix reinforced with preferentially oriented fibers. A procedure for identifying the mechanical properties of the main constituents of the bladder tissue by an inverse method is detailed. The mechanical parameters are used for the numerical simulation of the mechanical behavior of the bladder during filling within the finite‐element method.
Abstract
An approach is presented for studying the mechanical behavior of soft biological tissue using the finite‐element method and a general constitutive model. The overall computational [...]
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A total lagrangian formulation for the geometrically non-linear analysis of shells
J. Oliver, E. Oñate

(1984). Flexible Shells, E.L. Axelrad, F.A. Emmerlind (Eds.), Berlín

Abstract
The analysis of structures subjected to large displacements by means of the finite element method has attracted the attention of many researchers in recent years and different publications have been reported in the literature [1-8] In this work the authors suggest an alternative finite element formulation for the analysis of shells process of the structure is defined via a total Lagrangian approach. Stresses and strain over the shell surface are defined using a local set of Cartesian axes based on the principal curvature directions of the shell middle surface. This allows to obtain useful explicit expressions of the finite element matrices in a simple manner. Additionally, normal to the midsurface before deformation are assumed to remain straight but not necessarily to the midsurface after deformation, thus allowing for shear deformation effects. Finally, it is worth pointing out that no restrictions are made on the magnitude of the curvatures. This is of special interest for the analysis of non-shallow shells using a small number of elements. The formulation uses two dimensional finite elements for the analysis of 3-D shells. The discretization over the shell thickness is eliminates using what is usually known as “degenerated element technique” [2,4]. This allows for a substantial reduction in the number of variables and eliminates the possibility of ill-conditions of the element matrices which takes place when using 3-D elements and the thickness of the shell is small. In the first part of this work the formulation for 3-D shells is presented. Then a series of examples of shells undergoing large displacements are presented.
Abstract
The analysis of structures subjected to large displacements by means of the finite element method has attracted the attention of many researchers in recent years and different [...]
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Advances in the DEM and coupled DEM and FEM techniques in non linear solid mechanics
E. Oñate, F. Zárate, M. Celigueta, J. González, J. Canet, J. Carbonell, F. Garcia, S. Latorre, M. Santasusana

(2018). (Preprint) Advances in Computational Plasticity. Computational Methods in Applied Sciences. Oñate, E., Peric, D., de Souza Neto, E., Chiumenti, M., (Eds.), Vol. 46, pp. 309-335, Springer

Abstract
In this chapter we present recent advances on the Discrete Element Method (DEM) and on 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 on the Discrete Element Method (DEM) and on the coupling of the DEM with the Finite Element Method (FEM) for solving a variety of [...]
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Possibilities of the finite element viscous shell approach for analysis of sheet metal forming problems
E. Oñate, R. Lama

(1986). Simulation of Metal Forming Processes by the Finite Element Method (SIMOP-I). Lange K. (eds). Berichte aus dem Institut für Umformtechnik der Universität Stuttgart, vol 85. Springer, Berlin, Heidelberg

Abstract
The viscous shell approach combines the use of visco-plastic flow and classical shell theories. The paper presents the general aspects of the viscous shell formulation for axisymmetric and general 3-D shell problems using finite elements. Details of treatment of coordenate updating, friction effects, strain hardening and extensions to include the elastic deformations are also given together with some examples of application to the forming of axisymmetrical thin sheets of metal under hemispherical punches.
Abstract
The viscous shell approach combines the use of visco-plastic flow and classical shell theories. The paper presents the general aspects of the viscous shell formulation for [...]
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Posibilidades de los métodos numéricos en obras subterráneas
E. Oñate, B. Suarez, J. Canet

(2007). Avances en Mecánica de Medios Continuos. Simposium en honor al Profesor J. A. Garrido García. E. Alarcon, A. Forces, F. París (Eds.), pp. 195-210

Abstract
Se presenta un resumen de las posibilidades de diversos métodos numéricos basados en la combinación de técnicas de elementos finitos y de partículas para la simulación de problemas típicos de obras subterráneas, tales como la excavación de túneles y la inundación de cavidades.
Abstract
Se presenta un resumen de las posibilidades de diversos métodos numéricos basados en la combinación de técnicas de elementos finitos y de partículas [...]
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Possibilities of the Particle Finite Element Method in computational mechanics
E. Oñate, S. Idelsohn, M. Celigueta, R. Rossi, S. Latorre

(2010). Computer Methods in Mechanics, M. Kuzma, K. Wilmanski (Eds.), Chapter 15, pp. 271-310., Springer-Verlag, Berlin, Heidelberg

Abstract
We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems in fluid and solid mechanics accounting for fluid-structure interaction and coupled thermal effects. 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. Extensions of the PFEM to allow for frictional contact conditions at fluid-solid and solid-solid interfaces via mesh generation are described. A simple algorithm to treat erosion in the fluid bed is presented. Examples of application of the PFEM to solve a number of coupled problems such as the effect of large wave on structures, the large motions of floating and submerged bodies, bed erosion situations and melting and dripping of polymers under the effect of fire are given.
Abstract
We present some developments in the formulation of the Particle Finite Element Method (PFEM) for analysis of complex coupled problems in fluid and solid mechanics accounting [...]
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The Particle Finite Element Method. An effective numerical technique for fluid-soil-structure interaction problems
E. Oñate, M. Celigueta, S. Idelsohn, F. Salazar, B. Suarez

(2012). Issues on Mechanical and Civil Engineering. A Symposium to honour Prof. Enrique Alarcón. M. Doblaré, Ja. Domínguez, Jo. Domínguez, A. Fraile, F. García, S. Gómez, A. Martín, F. París (Eds.)

Abstract
We present some developments in the Particle Finite Element Method (PFEM) for analysis of complex coupled problems in mechanics involving fluid-soil-structure interaction (FSSI). The PFEM uses an updated Lagrangian description to model the motion of nodes (particles) in both the fluid and the solid domains (the later including soil/rock and structures). A mesh connects the particles (nodes) defining the discretized domain where the governing equations for each of the constituent materials are solved as in the standard FEM. The stabilization for dealing with an incompressibility continuum is introduced via the finite calculus (FIC) method. An incremental iterative scheme for the solution of the non linear transient coupled 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 several examples of application of the PFEM to solve FSSI problems such as the motion of rocks by water streams, the erosion of a river bed adjacent to a bridge foundation, the stability of breakwaters and constructions sea waves and the study of landslides.
Abstract
We present some developments in the Particle Finite Element Method (PFEM) for analysis of complex coupled problems in mechanics involving fluid-soil-structure interaction [...]
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A Particle Finite Element Method (PFEM) for coupled thermal analysis of quasi and fully incompressible flows and fluid-structure interaction
E. Oñate, A. Franci, J. Carbonell

(2014). (preprint) Numerical simulation of coupled problems in engineering. S. R. Idelsohn (Eds.), pp. 129-156, Springer

Abstract
We present a Lagrangian formulation for coupled thermal analysis of quasi and fully incompressible flows and fluid-structure interaction (FSI) problems that has excellent mass preservation features. The success of the formulation lays on a residual-based stabilized expression of the mass balance equation obtained using the Finite Calculus (FIC) method. The governing equations are discretized with the FEM using simplicial elements with equal linear interpolation for the velocities, the pressure and the temperature. The merits of the formulation in terms of reduced mass loss and overall accuracy are verified in the solution of 2D and 3D adiabatic and thermally-coupled quasi-incompressible free-surface flow problems using the Particle Finite Element Method (PFEM). Examples include the sloshing of water in a tank and the falling of a water sphere and a cylinder into a tank containing water.
Abstract
We present a Lagrangian formulation for coupled thermal analysis of quasi and fully incompressible flows and fluid-structure interaction (FSI) problems that has excellent [...]
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Oñate, Eugenio 2903
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