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• Updated Lagrangian formulation for corrected smooth particle hydrodynamics

  A. Huerta, Y. Vidal, J. Bonet

  Int. J. Numer. Meth. Engng. (2006). Vol. 3 (4), pp. 383-399

  
  

  Abstract

  Smooth Particle Hydrodynamics (SPH) are, in general, more robust than finite elements for large distortion problems. Nevertheless, updating the reference configuration may be necessary in some problems involving extremely large distortions. If a standard updated formulation is implemented in SPH zero energy modes are activated and spoil the solution. It is important to note that the updated Lagrangian does not present tension instability but only zero energy modes. Here an stabilization technique is incorporated to the updated formulation to obtain an improved method without mechanisms.

  Abstract
  Smooth Particle Hydrodynamics (SPH) are, in general, more robust than finite elements for large distortion problems. Nevertheless, updating the reference configuration may [...]

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• An elastic plastic damage formulation for concrete: application to elementary and structural tests

  L. Jason, A. Huerta, G. Pijaudier, S. Ghavamian

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195 (52), pp. 7077-7092

  
  

  Abstract

  Pure elastic damage models or pure elastic plastic constitutive laws are not totally satisfactory to describe the behaviour of concrete. They indeed fail to reproduce the unloading slopes during cyclic loading which define experimentally the value of the damage in the material. When coupled effects are considered, in particular in hydro-mechanical problems, the capability of numerical models to reproduce the unloading behaviour is essential, because an accurate value of the damage, which controls the material permeability, is needed. In the context of very large size calculations that are needed for 3D massive structures heavily reinforced and pre-stressed (such as containment vessels), constitutive relations ought also to be as simple as possible. Here an elastic plastic damage formulation is proposed to circumvent the disadvantages of pure plastic and pure damage approaches. It is based on an isotropic damage model combined with a hardening yield plastic surface in order to reach a compromise as far as simplicity is concerned. Three elementary tests are first considered for validation. A tension test, a cyclic compression test and triaxial tests illustrate the improvements achieved by the coupled law compared to a simple damage model (plastic strains, change of volumetric behaviour, decrease in the elastic slope under hydrostatic pressures). Finally, one structural application is also considered: a concrete column wrapped in a steel tube.

  Abstract
  Pure elastic damage models or pure elastic plastic constitutive laws are not totally satisfactory to describe the behaviour of concrete. They indeed fail to reproduce the [...]

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• Étude de la stabilité d'une formulation incompressible traitée par X-FEM

  G. Legrain, N. Moës, A. Huerta

  European Journal of Computational Mechanics (2006). Vol. 15 (1, 2, 3), pp. 257-268

  
  

  Abstract

  The treatment of (near-)incompressibility is a major concern for the simulation of rubber-like parts, or forming processes. The use of mixed finite element methods is known to prevent the locking of the F.E. approximation in the incompressible limit. However, the stability of these formulations is conditionned by the fullfilment of the inf-sup condition. Recently, finite elements method has evolved with the introduction of the partition of unity. The X-FEM uses it to remove the need to mesh (and remesh) physical surfaces. In this paper, a strategy is proposed for the treatment of holes within X-FEM in the incompressible setting. Numerical examples show that F.E. convergence rate is preserved and that the inf-sup condition is passed.

  Abstract
  The treatment of (near-)incompressibility is a major concern for the simulation of rubber-like parts, or forming processes. The use of mixed finite element methods is known [...]

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• Mesh projection between parametric surfaces

  X. Roca, J. Sarrate, A. Huerta

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 22 (6), pp. 591-603

  
  

  Abstract

    This paper presents a new algorithm to map a given mesh over a source surface onto a target surface. This projection is determined by means of a least-squares approximation of a transformation defined between the loops of boundary nodes of the cap surfaces in the parametric spaces. Once the new mesh is obtained on the parametric space of the target surface, it is mapped to the target surface according to its parameterization. Therefore, in contrast with the usual techniques, the developed algorithm does not require solving any root finding problem to ensure that the projected nodes are on the target surface. Finally, this projection algorithm is extended to three-dimensional cases and included in a sweep meshing tool in order to generate the inner layers of elements in the physical space.

  Abstract
    This paper presents a new algorithm to map a given mesh over a source surface onto a target surface. This projection is determined by means of a least-squares approximation [...]

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• The computation of bounds for linear-functional outputs of weak solutions to the two-dimensional elasticity equations

  N. Parés, I. Riera, A. Huerta, J. Peraire

  Comput. Methods Appl. Mech. Engrg., (2006). Vol. 195 (4-6), pp. 406-429

  
  

  Abstract

  We present a method for the computation of upper and lower bounds for linear-functional outputs of the exact solutions to the two dimensional elasticity equations. The method can be regarded as a generalization of the well known complementary energy principle. The desired output is cast as the supremum of a quadratic-linear convex functional over an infinite dimensional domain. Using duality the computation of an upper bound for the output of interest is reduced to a feasibility problem for the complementary, or dual, problem. In order to make the problem tractable from a computational perspective two additional relaxations that preserve the bounding properties are introduced. First, the domain is triangulated and a domain decomposition strategy is used to generate a sequence of independent problems to be solved over each triangle. The Lagrange multipliers enforcing continuity are approximated using piecewise linear functions over the edges of the triangulation. Second, the solution of the adjoint problem is approximated over the triangulation using a standard Galerkin finite element approach. A lower bound for the output of interest is computed by repeating the process for the negative of the output. Reversing the sign of the computed upper bound for the negative of the output yields a lower bound for the actual output. The method can be easily generalized to three dimensions. However, a constructive proof for the existence of feasible solutions for the outputs of interest is only given in two dimensions. The computed bound gaps are found to converge optimally, that is, at the same rate as the finite element approximation. An attractive feature of the proposed approach is that it allows for a data set to be generated that can be used to certify and document the computed bounds. Using this data set and a simple algorithm, the correctness of the computed bounds can be established without recourse to the original code used to compute them. In the present paper, only computational domains whose boundary is made up of straight sided segments and polynomially varying loads are considered. Two examples are given to illustrate the proposed methodology.

  Abstract
  We present a method for the computation of upper and lower bounds for linear-functional outputs of the exact solutions to the two dimensional elasticity equations. The method [...]

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• Continuous blending of SPH with finite elements

  S. Fernández-Méndez, J. Bonet, A. Huerta

  Computers and Structures (2005). Vol. 83 (17-18), pp. 1448-1459

  
  

  Abstract

  This paper proposes a methodology for the continuous blending of the finite element method and smooth particle hydrodynamics. The coupled approximation with finite elements and particles, and the discretization of the boundary value problem with a coupled integration, are described. An integration correction is also proposed to stabilize the solution. Some numerical examples demonstrate the applicability of the method.

  Abstract
  This paper proposes a methodology for the continuous blending of the finite element method and smooth particle hydrodynamics. The coupled approximation with finite elements [...]

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• A new damage model based on non-local displacements

  A. Rodríguez-Ferran, I. Morata, A. Huerta

  Int. J. Numer. Anal. Meth. Geomech. (2005). Vol. 29 (5), pp. 473-493

  
  

  Abstract

  A new non-local damage model is presented. Non-locality (of integral or gradient type) is incorporated into the model by means of non-local displacements. This contrasts with existing damage models, where a non-local strain or strain-related state variable is used. The new model is very attractive from a computational viewpoint, especially regarding the computation of the consistent tangent matrix needed to achieve quadratic convergence in Newton iterations. At the same time, its physical response is very similar to that of the standard models, including its regularization capabilities. All these aspects are discussed in detail and illustrated by means of numerical examples.

  Abstract
  A new non-local damage model is presented. Non-locality (of integral or gradient type) is incorporated into the model by means of non-local displacements. This contrasts with [...]

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• Benchmarks for the validation of a non local model

  L. Jason, S. Ghavamian, G. Pijaudier, A. Huerta

  Revue française de génie civil (2004). Vol. 8 (2-3), pp. 303-328

  
  

  Abstract

  The aim of this contribution is to present a series of organised benchmarks that helps at validating the robustness of the FE implementation of a constitutive relation, its pertinence with respect to experiments, and quantitative and qualitative comparisons of structural elements. It is applied to an isotropic damage model used for concrete, coupled with a non local gradient formulation to avoid a spurious description of strain localisation. After the elementary (uniaxial monotonic, cyclic or triaxial loading) and structural (three point bending tests) simulations, an industrial application is presented in the form of a representative structural volume of a containment building for French nuclear power plants.

  Abstract
  The aim of this contribution is to present a series of organised benchmarks that helps at validating the robustness of the FE implementation of a constitutive relation, its [...]

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• Efficient and reliable nonlocal damage models

  A. Rodríguez-Ferran, I. Morata, A. Huerta

  Comput. Methods Appl. Mech. Engrg., (2004). Vol. 193 (30-32), pp. 3431-3455

  
  

  Abstract

  We present an efficient and reliable approach for the numerical modelling of failure with nonlocal damage models. The two major numerical challenges––the strongly nonlinear, highly localized and parameter-dependent structural response of quasi-brittle materials, and the interaction between nonadjacent finite elements associated to nonlocality––are addressed in detail. Reliability of the numerical results is ensured by an h-adaptive strategy based on error estimation. We use a residual-type error estimator for nonlinear FE analysis based on local computations, which, at the same time, accounts for the nonlocality of the damage model. Efficiency is achieved by a proper combination of load-stepping control technique and iterative solver for the nonlinear equilibrium equations. A major issue is the computation of the consistent tangent matrix, which is nontrivial due to nonlocal interaction between Gauss points. With computational efficiency in mind, we also present a new nonlocal damage model based on the nonlocal average of displacements. For this new model, the consistent tangent matrix is considerably simpler to compute than for current models. The various ideas discussed in the paper are illustrated by means of three application examples: the uniaxial tension test, the three-point bending test and the single-edge notched beam test.

  Abstract
  We present an efficient and reliable approach for the numerical modelling of failure with nonlocal damage models. The two major numerical challenges––the strongly [...]

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• A comparison of two formulations to blend finite elements and mesh-free methods

  A. Huerta, S. Fernández-Méndez, W. Liu

  Comput. Methods Appl. Mech. Engrg., (2004). Vol. 193 (12-14), pp. 1105-1117

  
  

  Abstract

  Mesh-free methods have since their early developments been blended to the finite element formulation in order to benefit from the advantages of both numerical techniques. In this paper, two recently proposed formulations to couple mesh-free and finite element methods are discussed and compared.

  Abstract
  Mesh-free methods have since their early developments been blended to the finite element formulation in order to benefit from the advantages of both numerical techniques. [...]

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