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• Arbitrary Lagrangian-Eulerian finite element analysis of strain localization in transient problems

  G. Pijaudier-Cabot, L. Bodé, A. Huerta

  (1994). Research Report, Nº PI56

  
  

  Abstract

  Nonlocal models guaranty that finite element computations on strain materials remain sound up to failure from a theoretical and computational viewpoint. The non-locality prevents strain localization with zero global dissipation of energy, and consequently finite element calculations converge upon mesh refinements. One of the major drawbacks of these models is that the element size needed in order to capture the localization zone, must be smaller than the internal length. Hence, the total number of degrees of freedom becomes rapidly prohibitive for most engineering applications and there is an obvious need for mesh adaptivity. This paper deals with the application of the arbitrary Lagrangian-Eulerian (ALE) formulation, well known in hydrodynamics and fluid-structure interaction problems, to transient strain localization in a nonlocal damageable material. It is shown that the ALE formulation which is employed in large boundary motion problems, can also be well suited for nonlinear transient analysis of softening materials where localization bands appear. The remeshing strategy is based on the equi-distribution of an indicator that quantifies the interelement jump of a selected state variable. Two well-known one-dimensional examples illustrate the capabilities of this technique: the first one deals with localization due to a propagating wave in a bar, and the second one studies the wave propagation in a hollow sphere.  

  Abstract
  Nonlocal models guaranty that finite element computations on strain materials remain sound up to failure from a theoretical and computational viewpoint. The non-locality prevents [...]

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• Reliability and cost-efficiency of finite methods for non-linear structural analysis

  R. Codina, O. Soto

  (1994). Research Report, Nº PI58

  
  

  Abstract

  The objective of this paper is to present a finite element formulation to solve the Stokes problem with Coriolis force. This force results in a skew-symmetric term in the weak formulation of the problem that deteriorates the stability of the standard Galerkin finite element method when the viscosity is small. We show that the stability is worsened due to the presence of the pressure gradient to enforce the incompressibility of the flow. The relevance of this effect depends on the relative importance of the viscous force and the Coriolis force, which measured by the Ekman number. When it is small, oscillations occur using the Galerkin approach. To overcome them, we propose two different methods based on a consistent modification of the basic Galerkin formulation. Both methods eliminate oscillations, keeping the accuracy of the formulation and enhancing its numerical stability.

  Abstract
  The objective of this paper is to present a finite element formulation to solve the Stokes problem with Coriolis force. This force results in a skew-symmetric term in the [...]

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• Adaptive finite element computations of hypersonic inviscid flows around a double ellipsoid.

  T. Fischer, E. Oñate

  (1995). Research Report, Nº PI60

  
  

  Abstract

  This report documents the potential capabilities of adaptive inviscid flow calculations on unstructured meshes in three dimensions using the finite element method. The finite element formulation of the compressible Euler and Navier-Stokes equations is based on a two-step explicit Taylor-Galerkin scheme. Adaptive remeshing is applied to enhance the numerical solution in the vicinity the shocks. Particular emphasis is put on the generation of unstructured tetrahedral meshes as well as in the discussion of estimating the error in the numerical solution. Finally, an application to a well-known 3D high speed flow problem is shown where adaptive remeshing techniques become essential to keep the computational cost within reasonable limits. Its results are compared to some seemingly best reference solutions using other algorithms.    

  Abstract
  This report documents the potential capabilities of adaptive inviscid flow calculations on unstructured meshes in three dimensions using the finite element method. The finite [...]

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• PARAMESH. Two dimensional unstructured parallel mesh generation program

  J. Mestres, E. Oñate, G. Bugeda

  (1995). Research Report, Nº PI61

  
  

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• A fractional-step method for the incompressible navier-stokes equations related to a predictor-multicorrector algorithm

  J. Blasco, R. Codina, A. Huerta

  (1995). Research Report, Nº PI63

  
  

  Abstract

  An implicit fractional-step method for the numerical solution of the time-dependent incompressible Naiver-Stokes equations in primitive variables is developed and studied in this paper. The method, which is first order accurate in the time-step, is shown to convergence to an exact solution of the equations. By adequately splitting the viscous term, it allows to enforce full Dirichlet boundary conditions on the velocity in all substeps of the scheme, while needing no boundary condition at all for the pressure. It is also shown to be related to an iterative predictor-multicorrector algorithm for evolution equations, when this is applied to the incompressible Naiver-Stokes system. A new derivation of the algorithm in a general setting is provided. Two different finite element interpolations are considered for the implementation of the algorithm; numerical results obtained with them for standard benchmark cases are presented.

  Abstract
  An implicit fractional-step method for the numerical solution of the time-dependent incompressible Naiver-Stokes equations in primitive variables is developed and studied [...]

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• A finite element formulation for Stokes proble allowing equal velocity-pressure interpolation

  R. Codina, J. Blasco

  (1995). Research Report, Nº PI66

  
  

  Abstract

  In this paper we study a variational formulation of the Stokes problem that accommodates the use of equal velocity-pressure finite element interpolations. The motivation of this method relies on the analysis of a class of fractional-step methods for the Navier-Stokes equations for which it is known that equal interpolations yield good numerical results. The reason for this turns out to be the difference between two discrete Laplacian operators computed in a different manner. The formulation of the Stokes problem considered here aims to reproduce this effect. From the analysis of the finite element approximation of the problem we obtain stability and optimal error estimates using velocity-pressure interpolations satisfying of the standard formulation. In particular, this condition is fulfilled by the most common equal order interpolations.

  Abstract
  In this paper we study a variational formulation of the Stokes problem that accommodates the use of equal velocity-pressure finite element interpolations. The motivation of [...]

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• Finite point methods in computational mechanics

  E. Oñate, S. Idelsohn, O. Zienkiewicz

  (1995). Research Report, Nº PI67

  
  

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• Numerical simulation of wear phenomena

  M. Chiumenti, C. Agelet de Saracibar

  (1995). Research Report, Nº PI68

  
  

  Abstract

  Over the last few years a remarkable progress has been achieved in the field of computational contact mechanics. The formulation by means of variational inequalities, as well as the use of return mapping algorithms and tools of mathematical programming have provided efficient frameworks for the numerical treatment of such problems. The objective is the numerical simulation of the frictional behavior of steel sheets subjected to large sliding distances and variables normal pressures. A simple phenomenological model for frictional contact accounting for wear effects is proposed with a view to its prediction and consequent minimization. Within the context of thermodynamics with internal variables, the coefficient of friction is assumed to be a function of the density of frictional work resulting in a theory analogous to classical work hardening elastoplasticity. The finite element simulation of a series of sliding test is carried out and the results are compared with experiment. The calculation presented in the following in the following have been performed at the Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE) in Barcelona, Spain with the program for finite element analysis FEAP.  

  Abstract
  Over the last few years a remarkable progress has been achieved in the field of computational contact mechanics. The formulation by means of variational inequalities, as [...]

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• A new frictional time integration algorithm for large slip multi-body frictional contact problems

  C. Agelet de Saracibar

  (1995). Research Report, Nº PI69

  
  

  Abstract

  In this paper a new frictional time integration algorithm suitable for large slip multibody frictional contact problems is presented. The algorithm is introduced within the simple context of a model problem: the sliding motion of a particle onto a rough surface. Time integration of frictional traction is performed introducing a new slip path parametrization, which is defined independently traction is performed introducing element parametrization used in the spatial triangularization. The key point of the algorithm is that now, in presence of large slips, problems associated with slip motions such that a full incremental slip path is not within a single surface element, are completed bypassed. Remarkably, the algorithm is defined on the solely basis of the unit outward normal field to the surface without any appeal to the underlying local surface finite element triangularization. Geometrically, the assumed slip path can be viewed as an approximation to the geodesic passing throughout the initial and final points of each incremental slip path. The algorithm is amenable to exact linearization and asymptotic quadratic rate of convergence can be achieved within a Newton-Raphson iterative solution scheme. The algorithm can easily be extended to large slip multi-body frictional contact problems, involving finite strains.  

  Abstract
  In this paper a new frictional time integration algorithm suitable for large slip multibody frictional contact problems is presented. The algorithm is introduced within the [...]

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• Numerical analysis of frictional wear contact problems computational model and applications

  C. Agelet de Saracibar, M. Chiumenti

  (1995). Research Report, Nº PI70

  
  

  Abstract

  In this paper a numerical model for the analysis of multi-body frictional wear contact problems at finite deformations is presented. Wear phenomena are analysed and the main wear mechanics are identified. Archard’s wear law provides an estimate of the amount of wear volume produced during forming operations. Wear phenomena are incorporated into the Coulomb frictional model by considering a friction coefficient as function of an internal variable to be defined as the frictional dissipation or the slip amount. Within the context of a displacement-driven formulation of frictional contact problems, i.e. penalty or augmented Lagrangian methods, and exploiting the computational framework developed for plasticity, two methods are considered for the time integration of the constrained frictional evolution problems: the lowest Backward Difference (BD) method, Backward Euler (BE) algorithm, and an Implicit Runge-Kutta (IRK) method, the generalized Projected Mid-Point (PMP) algorithm. The constrained frictional algebraic problem arising from the application of these time integration algorithms to the constrained frictional evolution problem, is amenable to exact linearization leading to an asymptotic quadratic rate of convergence when used within a Newton-Raphson solution scheme. The numerical model has been implemented into an enhanced version of the computational finite element program FEAP. Numerical examples and simulation of industrial metal forming processes show the performance of the numerical model in the analysis of frictional wear contact problems.     

  Abstract
  In this paper a numerical model for the analysis of multi-body frictional wear contact problems at finite deformations is presented. Wear phenomena are analysed and the main [...]

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