Papers by Antonio Carrasco Huerta
International Journal of Solids and Structures, 2000
Nonlocal damage models are typically used to model failure of quasi-brittle materials. Due to bri... more Nonlocal damage models are typically used to model failure of quasi-brittle materials. Due to brittleness, the choice of a particular model or set of parameters can have a crucial in¯uence on the structural response. To assess this inuence, it is essential to keep ®nite element discretization errors under control. If not, the eect of these errors on the result of a computation could be erroneously interpreted from a constitutive viewpoint. To ensure the quality of the FE solution, an adaptive strategy based on error estimation is proposed here. It is based on the combination of a residualtype error estimator and quadrilateral h-remeshing. Another important consequence of brittleness is that it leads to structural responses of the snap-through or snap-back type. This requires the use of arc-length control, with a de®nition of the arc parameter that accounts for the localized nature of quasi-brittle failure. All these aspects are discussed for two particular nonlocal damage models (Mazars and modi®ed von Mises) and for two tests: the Brazilian tensile splitting test and the single-edge notched beam test. For the latter test, the capability of the Mazars model to capture the curved crack pattern observed in experiments ± a topic of debate in the literature ± is con®rmed. Ó
A new least-squares approximation of affine mappings for sweep algorithms
Proceedings of the 14th International Meshing Roundtable, 2005
This paper presents a new algorithm to generate hexahedral meshes in extrusion geometries. Severa... more This paper presents a new algorithm to generate hexahedral meshes in extrusion geometries. Several algorithms have been devised to generate hexahedral meshes by projecting the cap surfaces along a sweep path. In all of these algorithms the crucial step is the placement of the inner layer of nodes. That is, the projection of the source surface mesh along the sweep
Comparing Two Algorithms to Add Large Strains to Small-Strain FE Code
Journal of Engineering Mechanics, 1998
ABSTRACT
Accuracy of Two Stress Update Algorithms for Shear-Free Large Deformation Paths
Journal of Engineering Mechanics, 1999
ABSTRACT
International Journal for Numerical Methods in Fluids, 2005
Numerical modelling of void inclusions in porous media
International Journal for Numerical Methods in Engineering, 2004
... E-mail: [email protected] Website: www-lacan.upc.es Contract/grant sponsor: Mi... more ... E-mail: [email protected] Website: www-lacan.upc.es Contract/grant sponsor: Ministerio de Ciencia y Tecnología; contract/grant number: REN2001-0925-C03-01/CLI Contract/grant sponsor: Expert Components SA ...
International Journal for Numerical Methods in Engineering, 2000
This work is devoted to the description of an algorithm for automatic quadrilateral mesh generati... more This work is devoted to the description of an algorithm for automatic quadrilateral mesh generation. The technique is based on a recursive decomposition of the domain into quadrilateral elements. This automatically generates meshes composed entirely by quadrilaterals over complex geometries (there is no need for a previous step where triangles are generated). A background mesh with the desired element sizes allows to obtain the preferred sizes anywhere in the domain. The ÿnal mesh can be viewed as the optimal one given the objective function is deÿned. The recursive algorithm induces an e cient data structure which optimizes the computer cost. Several examples are presented to show the e ciency of this algorithm. E cient automated meshing techniques are expected to have certain features in order to ensure its applicability in a wide scope of cases, which can range from regular domains with uniform element sizes to non-singly connected domains with large boundary curvatures and non-uniform element sizes. Haber et al. present an excellent discussion of such features: precise modelling of the boundaries; good correlation between the interior mesh and the information prescribed at the boundary; minimal input e ort; broad range of applicability; general topology; automatic topology generation; and favorable element shapes. Some of these features can be easily implemented; for instance, BÃ ezier or B-splines interpolation curves allow a precise modelling of the boundaries. Others, such as minimal input e ort and broad range of applicability are much more di cult to obtain. Therefore, all the developed techniques for mesh generation should include most of the previous features and this is the goal of the proposed algorithm.
International Journal for Numerical Methods in Engineering, 1997
Two algorithms for the stress update (i.e., time integration of the constitutive equation) in lar... more Two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are compared from an analytical point of view. The order of the truncation error associated to the numerical integration is deduced for each algorithm a priori, using standard numerical analysis. This accuracy analysis has been performed by means of a convected frame formalism, which also allows a uniÿed derivation of both algorithms in spite of their inherent di erences. Then the two algorithms are adapted from convected frames to a ÿxed Cartesian frame and implemented in a small-strain ÿnite element code. The implementation is validated by means of a set of simple deformation paths (simple shear, extension, extension and compression, extension and rotation) and two benchmark tests in non-linear mechanics (the necking of a circular bar and a shell under ring loads). In these numerical tests, the observed order of convergence is in very good agreement with the theoretical order of convergence, thus corroborating the accuracy analysis.
International Journal for Numerical Methods in Engineering, 2000
In Reference [1] the authors have shown that numerical differentiation is a competitive alternati... more In Reference [1] the authors have shown that numerical differentiation is a competitive alternative to analytical derivatives for the computation of consistent tangent matrices. Relatively simple models were treated in that reference. The approach is extended here to a complex model: the MRS-Lade model . This plastic model has a cone-cap yield surface and exhibits strong coupling between the flow vector and the hardening moduli. Because of this, derivating these quantities with respect to stresses and internal variables -the crucial step in obtaining consistent tangent matrices-is rather involved. Numerical differentiation is used here to approximate these derivatives. The approximated derivatives are then used 1) to compute consistent tangent matrices (global problem) and 2) to integrate the constitutive equation at each Gauss point (local problem) with the Newton-Raphson method. The choice of the stepsize (i.e. the perturbation in the approximation schemes), based on the concept of relative stepsize, poses no difficulties. In contrast to previous approaches for the MRS-Lade model, quadratic convergence is achieved, for both the local and the global problems. The computational efficiency (CPU time) and robustness of the proposed approach is illustrated by means of several numerical examples, where the major relevant topics are discussed in detail.
ALE stress update for transient and quasistatic processes
International Journal for Numerical Methods in Engineering, 1998
ALE STRESS UPDATE FOR TRANSIENT AND QUASISTATIC PROCESSES Antonio Rodríguez-Ferran,1 Folco Casade... more ALE STRESS UPDATE FOR TRANSIENT AND QUASISTATIC PROCESSES Antonio Rodríguez-Ferran,1 Folco Casadei,2 and Antonio Huerta *t To appear in International Journal for Numerical Methods in Engineering Departamento de Matemática Aplicada III, ETS de ...
International Journal for Numerical Methods in Engineering, 2002
When fluid simulation has to deal with moving boundary domains there is a problem when one wants ... more When fluid simulation has to deal with moving boundary domains there is a problem when one wants to make finite differences in time at points where the fluid is not always present. One solution for this is to transport the equation on a fixed domain. We present here the ALE derived formulation consisting to fix the domain only for one time step. We give the derivations allowing to reformulate the Euler equation with obvious extensions to a wide range of PDE.
A NOTE ON A NUMERICAL BENCHMARK TEST: AN AXISYMMETRIC SHELL UNDER RING LOADS
Communications in Numerical Methods in Engineering, 1997
ABSTRACT
International Journal for Numerical and Analytical Methods in Geomechanics, 2001
The consistent tangent matrix for density-dependent plastic models within the theory of isotropic... more The consistent tangent matrix for density-dependent plastic models within the theory of isotropic multiplicative hyperelastoplasticity is presented here. Plastic equations expressed as general functions of the Kirchho! stresses and density are considered. They include the Cauchy-based plastic models as a particular case. The standard exponential return-mapping algorithm is applied, with the density playing the role of a "xed parameter during the nonlinear plastic corrector problem. The consistent tangent matrix has the same structure as in the usual density-independent plastic models. A simple additional term takes into account the in#uence of the density on the plastic corrector problem. Quadratic convergence results are shown for several representative examples involving geomaterial and powder constitutive models. Figure 6. Powder-A isostatic test. Convergence results for di!erent load levels.
International Journal for Numerical and Analytical Methods in Geomechanics, 2005
es web page: www-lacan.upc.es key words: nonlocal damage models; nonlocal displacements; gradient... more es web page: www-lacan.upc.es key words: nonlocal damage models; nonlocal displacements; gradient models; consistent tangent matrix; quadratic convergence SUMMARY A new nonlocal damage model is presented. Nonlocality (of integral or gradient type) is incorporated into the model by means of nonlocal displacements. This contrasts with existing damage models, where a nonlocal 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.
Computers & Structures, 2005
This paper proposes a methodology for the continuous blending of the finite element method and Sm... more 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.
Computer Methods in Applied Mechanics and Engineering, 2001
The consistent tangent matrix for density-dependent plastic models within the theory of isotropic... more The consistent tangent matrix for density-dependent plastic models within the theory of isotropic multiplicative hyperelastoplasticity is presented here. Plastic equations expressed as general functions of the Kirchho! stresses and density are considered. They include the Cauchy-based plastic models as a particular case. The standard exponential return-mapping algorithm is applied, with the density playing the role of a "xed parameter during the nonlinear plastic corrector problem. The consistent tangent matrix has the same structure as in the usual density-independent plastic models. A simple additional term takes into account the in#uence of the density on the plastic corrector problem. Quadratic convergence results are shown for several representative examples involving geomaterial and powder constitutive models. Figure 6. Powder-A isostatic test. Convergence results for di!erent load levels.
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Papers by Antonio Carrasco Huerta