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• Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems

  E. Oñate, J. Rojek

  Comput. Methods Appl. Mech. Engrg., (2004). Vol 193, 3087-3128

  
  

  Abstract

  The paper presents combination of Discrete Element Method (DEM) and Finite Element Method (FEM) for dynamic analysis of geomechanics problems. Combined models can employ spherical (or cylindrical in 2D) rigid elements and finite elements in the discretization of different parts of the system. The DEM is a suitable tool to model soil/rock materials while the FEM in many cases can be a better choice to model other parts of the system considered. A typical example can be an idealization of rock cutting with a tool discretized with finite elements and rock or soil samples modelled with discrete elements. The FEM presented in the paper allows large elasto-plastic deformations in the solid regions. Such problems require the use of stabilized FEM to deal with the incompressibility constraint in order to eliminate the volumetric locking defect, especially when using triangular and tetrahedra elements with equal order interpolation for the displacement and the pressure variables. In the paper a stabilization based on the Finite Calculus (FIC) approach is used. Both theoretical algorithms of DEM and stabilized FEM are implemented in an explicit dynamic code. The paper presents some details of both formulations. A combined numerical algorithm is described finally. Selected numerical results illustrate the possibilities and performance of discrete/finite element analysis in geomechanics problems.

  Abstract
  The paper presents combination of Discrete Element Method (DEM) and Finite Element Method (FEM) for dynamic analysis of geomechanics problems. Combined models can employ spherical [...]

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• Advances in the formulation of the rotation-free basic shell triangle

  E. Oñate, F. Flores

  Comput. Methods Appl. Mech. Engrg., (2005). Vol. 194 (21-24), pp. 2406-2443

  
  

  Abstract

  A family of rotation-free three node triangular shell elements is presented. The simplest element of the family is based on an assumed constant curvature field expressed in terms of the nodal deflections of a patch of four elements and a constant membrane field computed from the standard linear interpolation of the displacements within each triangle. An enhanced version of the element is obtained by using a quadratic interpolation of the geometry in terms of the six patch nodes. This allows to compute an assumed linear membrane strain field which improves the in-plane behaviour of the original element. A simple and economic version of the element using a single integration point is presented. The efficiency of the different rotation-free shell triangles is demonstrated in many examples of application including linear and non linear analysis of shells under static and dynamic loads, the inflation and de-inflation of membranes and a sheet stamping problem.

  Abstract
  A family of rotation-free three node triangular shell elements is presented. The simplest element of the family is based on an assumed constant curvature field expressed in [...]

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• Improvements in the membrane behaviour of the three node rotation-free BST shell triangle using an assumed strain approach

  F. Flores, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (2005). Vol. 194, pp. 907-932

  
  

  Abstract

  In this paper an assumed strain approach is presented in order to improve the membrane behaviour of a thin shell triangular element. The so called Basic Shell Triangle (BST) has three nodes with only translational degrees of freedom and is based on a Total Lagrangian Formulation. As in the original BST element the curvatures are computed resorting to the surrounding elements (patch of four elements). Membrane strains are now also computed from the same patch of elements which leads to a non-conforming membrane behaviour. Despite this non-conformity the element passes the patch test. Large strain plasticity is considered using a logarithmic strain-stress pair. A plane stress behaviour with an additive decomposition of elastic and plastic strains is assumed. A hyperplastic law is considered for the elastic part while for the plastic part an anisotropic quadratic (Hill) yield function with non-linear isotropic hardening is adopted. The element, termed CBST, has been implemented in an explicit (hydro-)code adequate to simulate sheet-stamping processes and in an implicit static/dynamic code. Several examples are given showing the good performance of the enhnaced rotation-free shell triangle.

  Abstract
  In this paper an assumed strain approach is presented in order to improve the membrane behaviour of a thin shell triangular element. The so called Basic Shell Triangle (BST) [...]

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• Advances in stabilized finite element and particle methods for bulk forming processes

  E. Oñate, J. Rojek, M. Chiumenti, S. Idelsohn, F. Pin, R. Aubry

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 6750-6777

  
  

  Abstract

  The paper describes some recent developments in finite element and particle methods for analysis of a wide range of bulk forming processes. The developments include new stabilized linear triangles and tetrahedra using finite calculus and a new procedure combining particle methods and finite element methods. Applications of the new numerical methods to casting, forging and other bulk metal forming problems and mixing processes are shown.

  Abstract
  The paper describes some recent developments in finite element and particle methods for analysis of a wide range of bulk forming processes. The developments include new stabilized [...]

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• Rotation-free finite element for the non-linear analysis of beams and axisymmetric shells

  F. Flores, E. Oñate

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 5297–5315

  
  

  Abstract

  In this paper a finite element for the non-linear analysis of two dimensional beams and axisymmetric shells is presented. The element uses classical thin shell assumptions (no transverse shear strains). The main feature of the element is that it has no rotational degrees of freedom. Curvatures are computed using geometrical information from the patch of three elements formed by the main element and the two neighbour (adjacent) elements. Special attention is devoted to non-smooth geometries and branching shells. An elastic-plastic material law is considered. Large strains are treated using a logarithmic strain measure and a through-the-thickness numerical integration of the constitutive equations. Several examples are presented including linear problems to study convergence properties, and non-linear problems for both elastic and elastic-plastic materials and large strains.

  Abstract
  In this paper a finite element for the non-linear analysis of two dimensional beams and axisymmetric shells is presented. The element uses classical thin shell assumptions [...]

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• A unified monolithic approach for multi-fluid flows and Fluid-Structure Interaction using the Particle Finite Element Method with fixed mesh

  P. Becker, S. Idelsohn, E. Oñate

  Computational Mechanics (2015). (preprint) Vol. 55, pp. 1091–1104

  
  

  Abstract

  This paper describes a strategy to solve multi-fluid and Fluid-Structure Interaction (FSI) problems using Lagrangian particles combined with a fixed Finite Element (FE) mesh . Our approach is an extension of the fluid-only PFEM-2 [1,2] which uses explicit integration over the streamlines to improve accuracy. As a result, the convective term does not appear in the set of equations solved on the fixed mesh. Enrichments in the pressure field are used to improve the description of the interface between phases.

  Abstract
  This paper describes a strategy to solve multi-fluid and Fluid-Structure Interaction (FSI) problems using Lagrangian particles combined with a fixed Finite Element (FE) mesh [...]

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• Finite element formulation for convective-diffusive problems with sharp gradients using finite calculus

  E. Oñate, F. Zarate, S. Idelsohn

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195 (13-16), pp. 1793–1825

  
  

  Abstract

  A finite element method (FEM) for steady-state convective-diffusive problems presenting sharp gradients of the solution both in the interior of the domain and in boundary layers is presented. The necessary stabilization of the numerical solution is provided by the Finite Calculus (FIC) approach. The FIC method is based in the solution by the Galerkin FEM of a modified set of governing equations which include characteristic length parameters. It is shown that the FIC balance equation for the multidimensional convection-diffusion problem written in the principal curvature axes of the solution, introduces an orthotropic diffusion which stabilizes the numerical solution both in smooth regions as well in the vicinity of sharp gradients. The dependence of the stabilization terms with the principal curvature directions of the solution makes the method non linear. Details of the iterative scheme to obtain stabilized results are presented together with examples of application which show the efficiency and accuracy of the approach.

  Abstract
  A finite element method (FEM) for steady-state convective-diffusive problems presenting sharp gradients of the solution both in the interior of the domain and in boundary [...]

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• Stabilized formulation for the advection-diffusion-absorption equation using finite calculus and linear finite elements

  E. Oñate, J. Miquel, G. Hauke

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195, pp. 3926–3946

  
  

  Abstract

  A stabilized finite element method (FEM) for the steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on the modified governing differential equations derived via the Finite Calculus (FIC) method. The basis of the method is detailed for the 1D problem. It is shown that the stabilization terms act as a non linear additional diffusion governed by a single stabilization parameter. A critical constant value of this parameter ensuring a stabilized solution using two node linear elements is given. More accurate numerical results can be obtained by using a simple expression of the non linear stabilization parameter depending on the signs of the numerical solution and of its derivatives. A straightforward two steps algorithm yielding a stable and accurate solution for all the range of physical parameters and boundary conditions is described. The extension to the multi-dimensional case is briefly described. Numerical results for 1D and 2D problems are presented showing the efficiency and accuracy of the new stabilized formulation.

  Abstract
  A stabilized finite element method (FEM) for the steady state advection-diffusion-absorption equation is presented. The stabilized formulation is based on the modified governing [...]

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• Modelling the vertical UL 94 test: competition and collaboration between melt dripping, gasification and combustion

  F. Kempel, B. Schartel, J. Marti, K. Butler, R. Rossi, S. Idelsohn, E. Oñate

  Fire and Materials (2015). Vol. 39 (6), pp. 570-584

  
  

  Abstract

  An experimental and numerical investigation of the effect of bisphenol A bis(diphenyl phosphate) (BDP) and polytetrafluoroethylene (PTFE) on the fire behaviour of bisphenol A polycarbonate/acrylonitrile butadiene styrene (PC/ABS) in the vertical UL 94 scenario is presented. Four PC/ABS blends were discussed, which satisfy different UL 94 classifi cations d ue to the  competing ef fects of gasifica ti on, charring, flame inhibition and melt flow/dripping. For numerical investigation, the particle finite element method (PFEM) is used. Its capability to model the complex fire behaviour of polymers in the UL 94 is analysed. The materials’ properties are characterised, in particular the additives impact on the dripping behaviour during thermal exposure. BDP is an efficie nt p lasticiser; adding PTFE p reve nts dripping  by causing a flo w limit. P FEM simulation s reproduce the dripping and burning behaviour, in particular the competition between gasification and dripping. The thermal impact of both the burner and the flame is approximated taking into account flame inhibition, charring and effective heat of combustion. PFEM is a promising numerical tool for the investigation of the fire behaviour of polymers, particularly when large deformations are involved. Not only the principal phenomena but also the different UL 94 classi fi cations and t he exti nc tion times are well predicted.

  Abstract
  An experimental and numerical investigation of the effect of bisphenol A bis(diphenyl phosphate) (BDP) and polytetrafluoroethylene (PTFE) on the fire behaviour of bisphenol [...]

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• Fluid-structure interaction using the Particle Finite Element Method

  S. Idelsohn, E. Oñate, F. Pin, N. Calvo

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195 (17-18), pp. 2100-2123

  
  

  Abstract

  In the present work a new approach to solve fluid-structure interaction problems is described. Both, the equations of motion for fluids and for solids have been approximated using a material (lagrangian) formulation. To approximate the partial differential equations representing the fluid motion, the shape functions introduced by the Meshless Finite Element Method (MFEM) have been used. Thus, the continuum is discretized into particles that move under body forces (gravity) and surface forces (due to the interaction with neighboring particles). All the physical properties such as density, viscosity, conductivity, etc., as well as the variables that define the temporal state such as velocity and position and also other variables like temperature are assigned to the particles and are transported with the particle motion. The so called Particle Finite Element Method (PFEM) provides a very advantageous and efficient way for solving contact and free-surface problems, highly simplifying the treatment of fluid-structure interactions. '''Key words: '''Fluid-Structure interaction, Particle methods, Lagrange formulations, Incompressible Fluid Flows, Meshless Methods, Finite Element Method.

  Abstract
  In the present work a new approach to solve fluid-structure interaction problems is described. Both, the equations of motion for fluids and for solids have been approximated [...]

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