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• Extraction of a crack opening from a continuous approach using regularized damage models

  F. Dufour, G. Pijaudier, M. Choinska, A. Huerta

  Computers and concrete (2008). Vol. 5 (4), pp. 375-388

  
  

  Abstract

  Crack opening governs many transfer properties that play a pivotal role in durability analyses. Instead of trying to combine continuum and discrete models in computational analyses, it would be attractive to derive from the continuum approach an estimate of crack opening, without considering the explicit description of a discontinuous displacement field in the computational model. This is the prime objective of this contribution. The derivation is based on the comparison between two continuous variables: the distribution if the effective non local strain that controls damage and an analytical distribution of the effective non local variable that derives from a strong discontinuity analysis. Close to complete failure, these distributions should be very close to each other. Their comparison provides two quantities: the displacement jump across the crack [U] and the distance between the two profiles. This distance is an error indicator defining how close the damage distribution is from that corresponding to a crack surrounded by a fracture process zone. It may subsequently serve in continuous/discrete models in order to define the threshold below which the continuum approach is close enough to the discrete one in order to switch descriptions. The estimation of the crack opening is illustrated on a one-dimensional example and the error between the profiles issued from discontinuous and FE analyses is found to be of a few percents close to complete failure.

  Abstract
  Crack opening governs many transfer properties that play a pivotal role in durability analyses. Instead of trying to combine continuum and discrete models in computational [...]

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• NURBS-enhanced finite element method (NEFEM)

  R. Sevilla, S. Fernández-Méndez, A. Huerta

  Int. J. Numer. Meth. Engng. (2008). Vol. 76 (1), pp. 56-83

  
  

  Abstract

  An improvement to the classical finite element (FE) method is proposed. It is able to exactly represent the geometry by means of the usual CAD description of the boundary with non-uniform rational B-splines (NURBS). Here, the 2D case is presented. For elements not intersecting the boundary, a standard FE interpolation and numerical integration are used. But elements intersecting the NURBS boundary need a specifically designed piecewise polynomial interpolation and numerical integration. A priori error estimates are also presented. Finally, some examples demonstrate the applicability and benefits of the proposed methodology. NURBS-enhanced finite element method (NEFEM) is at least one order of magnitude more precise than the corresponding isoparametric FE in every numerical example shown. This is the case for both continuous and discontinuous Galerkin formulations. Moreover, for a desired precision, NEFEM is also more computationally efficient, as shown in the numerical examples. The use of NEFEM is strongly recommended in the presence of curved boundaries and/or when the boundary of the domain has complex geometric details. The possibility of computing an accurate solution with coarse meshes and high-order interpolations makes NEFEM a more efficient strategy than classical isoparametric FE. 

  Abstract
  An improvement to the classical finite element (FE) method is proposed. It is able to exactly represent the geometry by means of the usual CAD description of the boundary [...]

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• Upper and lower bounds in limit analysis: adaptive meshing strategies and discontinuous loading

  J. Muñoz, J. Bonet, A. Huerta, J. Peraire

  Int. J. Numer. Meth. Engng. (2008). Vol. 77 (4), pp. 471-501

  
  

  Abstract

  Upper and lower bounds of the collapse load factor are here obtained as the optimum values of two discrete constrained optimization problems. The membership constraints for Von Mises and Mohr–Coulomb plasticity criteria are written as a set of quadratic constraints, which permits one to solve the optimization problem using specific algorithms for Second‐Order Conic Program (SOCP). From the stress field at the lower bound and the velocities at the upper bound, we construct a novel error estimate based on elemental and edge contributions to the bound gap. These contributions are employed in an adaptive remeshing strategy that is able to reproduce fan‐type mesh patterns around points with discontinuous surface loading. The solution of this type of problems is analysed in detail, and from this study some additional meshing strategies are also described. We particularise the resulting formulation and strategies to two‐dimensional problems in plane strain and we demonstrate the effectiveness of the method with a set of numerical examples extracted from the literature.

  Abstract
  Upper and lower bounds of the collapse load factor are here obtained as the optimum values of two discrete constrained optimization problems. The membership constraints for [...]

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• NURBS-enhanced finite element method for Euler equations

  R. Sevilla, S. Fernández-Méndez, A. Huerta

  Int. J. Numer. Meth. Engng. (2008). Vol. 57 (9), pp. 1051-1069

  
  

  Abstract

  In this work, the NURBS-enhanced finite element method (NEFEM) is combined with a discontinuous Galerkin (DG) formulation for the numerical solution of Euler equations of gas dynamics. With NEFEM, numerical fluxes along curved boundaries are computed much more accurately due to the exact geometric representation of the computational domain. The proper implementation of the wall boundary condition and the exact geometry provide accurate results even with a linear approximation of the solution. A detailed comparison of NEFEM in front of isoparametric finite elements is presented, demonstrating the superiority of NEFEM approach for both linear and higher-order computations

  Abstract
  In this work, the NURBS-enhanced finite element method (NEFEM) is combined with a discontinuous Galerkin (DG) formulation for the numerical solution of Euler equations of [...]

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• Discontinuous Galerkin methods for the Stokes equations using divergence-free approximations

  A. Montlaur, S. Fernández-Méndez, A. Huerta

  Int. J. Numer. Meth. Engng. (2008). Vol. 57 (9), pp. 1071-1092

  
  

  Abstract

  A discontinuous Galerkin (DG) method with solenoidal approximation for the simulation of incompressible flow is proposed. It is applied to the solution of the Stokes equations. The interior penalty method is employed to construct the DG weak form. For every element, the approximation space for the velocity field is decomposed as the direct sum of a solenoidal space and an irrotational space. This allows to split the DG weak form into two uncoupled problems: the first one solves for the velocity and the hybrid pressure (pressure along the mesh edges) and the second one allows the computation of the pressure in the element interior. Furthermore, the introduction of an extra penalty term leads to an alternative DG formulation for the computation of solenoidal velocities with no presence of pressure terms. Pressure can then be computed as a post-process of the velocity solution. Numerical examples demonstrate the applicability of the proposed methodologies.

  Abstract
  A discontinuous Galerkin (DG) method with solenoidal approximation for the simulation of incompressible flow is proposed. It is applied to the solution of the Stokes equations. [...]

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• Stability of incompressible formulations enriched with X-FEM

  G. Legrain, N. Moës, A. Huerta

  Comput. Methods Appl. Mech. Engrg., (2008). Vol. 197 (21-24), pp. 1835-1849

  
  

  Abstract

  The treatment of (near-)incompressibility is a major concern for applications involving rubber-like materials, or when important plastic ows occurs as in forming processes. The use of mixed nite element methods is known to prevent the locking of the nite element approximation in the incompressible limit. However, it also introduces a critical condition for the stability of the formulation, called the infsup or LBB condition. Recently, the nite element method has evolved with the introduction of the partition of unity. The eXtended Finite Element Method (XFEM) uses the partition of unity to remove the need to mesh physical surfaces or to remesh them as they evolve. The enrichment of the displacement eld makes it possible to treat surfaces of discontinuity inside nite elements. In this paper, some strategies are proposed for the enrichment of mixed nite element approximations in the incompressible setting. The case of holes, material interfaces and cracks are considered. Numerical examples show that for well chosen enrichment strategies, the nite element convergence rate is preserved and the inf-sup condition is passed.

  Abstract
  The treatment of (near-)incompressibility is a major concern for applications involving rubber-like materials, or when important plastic ows occurs as in forming processes. [...]

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• Mathematical e-Learning: state of the art and experiences at the Open University of Catalonia

  A. Juan, A. Huerta, C. Steegmann, C. Corcoles, C. Serrat

  Int. J. Math. Education in Science and Technology (2008). Vol. 39 (4), pp. 455-471

  
  

  Abstract

  In this article we present a review of the state of the art in mathematical e-learning and some personal experiences on this area developed during the last eleven years at the Open University of Catalonia (UOC), a completely online university located in Spain. The article discusses important aspects related to online mathematics courses offered in higher education programs, including: benefits and challenges, universities offering this type of education, methodological considerations, emergent technologies, learning projects and environments, etc. Also, key aspects of the UOC mathematical e-learning model and its historical evolution are described and analysed. Special attention is paid to mathematical curricula in computer sciences degrees, where a lot of work needs to be done in order to adapt mathematics courses to the continuously changing educational necessities of students. A curricula design proposal, based on a top-down approach, is presented as a best practice. Finally, some trends and future perspectives on the subject are suggested.

  Abstract
  In this article we present a review of the state of the art in mathematical e-learning and some personal experiences on this area developed during the last eleven years at [...]

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• Hydraulic behaviour of a representative structural volume for containment buildings

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

  Nuclear Engineering and Design (2007). Vol. 237 (12-13), pp. 1259-1274

  
  

  Abstract

  For particular structures like containment buildings of nuclear power plants, the study of the hydraulic behaviour is of great concern. These structures are indeed the third barrier used to protect the environment in case of accidents. The evolution of the leaking rate through the porous medium is closely related to the changes in the permeability during the ageing process of the structure. It is thus essential to know the relation between concrete degradation and the transfer property when the consequences of a mechanical loading on the hydraulic behaviour have to be evaluated. A chained approach is designed for this purpose. The mechanical behaviour is described by an elastic plastic damage formulation, where damage is responsible for the softening evolution while plasticity accounts for the development of irreversible strains. The drying process is evaluated according to a non-linear equation of diffusion. From the knowledge of the damage and the degree of saturation, a relation is proposed to calculate the permeability of concrete. Finally, the non-homogeneous distribution of the hydraulic conductivity is included in the hydraulic problem which is in fact the association of the mass balance equation for gas phase and Darcy law. From this methodology, it is shown how an indicator for the hydraulic flows can be deduced.

  Abstract
  For particular structures like containment buildings of nuclear power plants, the study of the hydraulic behaviour is of great concern. These structures are indeed the third [...]

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• Goal oriented error estimation for the element free Galerkin method

  Y. Vidal, A. Huerta

  Lecture Notes in Computational Sciences and Engineering (2007). Vol. 57, pp. 265-282

  
  

  Abstract

  A novel approach for implicit residual-type error estimation in meshfree methods is presented. This allows to compute upper and lower bounds of the error in energy norm with the ultimate goal of obtaining bounds for outputs of interest. The proposed approach precludes the main drawbacks of standard residual type estimators circumventing the need of flux-equilibration and resulting in a simple implementation that avoids integrals on edges/sides of a domain decomposition (mesh). This is especially interesting for mesh-free methods.

  Abstract
  A novel approach for implicit residual-type error estimation in meshfree methods is presented. This allows to compute upper and lower bounds of the error in energy norm with [...]

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• Stabilized updated Lagrangian corrected SPH for explicit dynamic problems

  Y. Vidal, J. Bonet, A. Huerta

  Int. J. Numer. Meth. Engng. (2007). Vol. 69 (13), pp. 2687-2710

  
  

  Abstract

  Smooth Particle Hydrodynamics with a total Lagrangian formulation are, in general, more robust than nite elements for large distortion problems. Nevertheless, updating the reference con¯guration may still be necessary in some problems involving extremely large distortions. However, as discussed here a standard updated formulation suffers the presence of zero energy modes that are activated and may spoil completely the solution. It is important to note that, unlike an Eulerian formulation,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 and capable to solve problems with extremely large distortions.

  Abstract
  Smooth Particle Hydrodynamics with a total Lagrangian formulation are, in general, more robust than nite elements for large distortion problems. Nevertheless, updating the [...]

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