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• Accuracy of two stress update algorithms for shear-free large deformations paths

  A. Rodríguez-Ferran, A. Huerta

  Journal of Engineering Mechanics (1999). Vol. 125 (6), pp. 715-717

  
  

  Abstract

  The behavior of two stress update algorithms for shear-free large deformation paths is analyzed. The first algorithm has a truncation error of order 1. The second algorithm has a truncation error of order 2. As a consequence, the global performance of the second algorithm is clearly superior. However, for the particular case of shear-free deformation paths, the first algorithm correctly predicts null shear stresses, while the second one does not. This behavior was reported in a previous paper for an extension-rotation test. In this note a general shear-free deformation path is considered in full detail.

  Abstract
  The behavior of two stress update algorithms for shear-free large deformation paths is analyzed. The first algorithm has a truncation error of order 1. The second algorithm [...]

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• Analysis of the vane test considering size and time effects

  A. Pérez-Foguet, A. Ledesma, A. Huerta

  Int. J. Numer. Anal. Meth. Geomech. (1999). Vol. 23 (5), pp. 383-412

  
  

  Abstract

  An analysis of the vane test using an Arbitrary Lagrangian-Eulerian formulation within a finite element framework is presented. This is suitable for soft clays for which the test is commonly used to measure in situ undrained shear strength. Constitutive laws are expressed in terms of shear stress-shear strain rates, and that permits the study of time effects in a natural manner. An analysis of the shear stress distributions on the failure surface according to the material model is presented. The effect of the constitutive law on the shear band amplitude and on the position of the failure surface is shown. In general, the failure surface is found at 1-1·01 times the vane radius, which is consistent with some experimental results. The problem depends on two dimensionless parameters that represent inertial and viscous forces. For usual vane tests, viscous forces are predominant, and the measured shear strength depends mainly on the angular velocity applied. That can explain some of the comparisons reported when using different vane sizes. Finally, the range of the shear strain rate applied to the soil is shown to be fundamental when comparing experimental results from vane, triaxial and viscosimeter tests. Appart from that, an experimental relation between undrained shear strength and vane angular velocity has been reproduced by this simulation.

  Abstract
  An analysis of the vane test using an Arbitrary Lagrangian-Eulerian formulation within a finite element framework is presented. This is suitable for soft clays for which the [...]

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• Plastic flow potential for cone region on the MRS-Lade model

  A. Pérez-Foguet, A. Huerta

  Journal of Engineering Mechanics (1999). Vol. 125 (3), pp. 364-367

  
  

  Abstract

  The original formulation of the MRS-Lade model, with nonassociated flow rule on the meridian plane in the cone region, has a corner. In order to reduce the computational effort of corner solution algorithms, a modified plastic flow potential for the cone part is found in the literature. This modification may have a nonadmissible flip over of the flow vector in the cone-cap intersection if the plastic flow potential is not correctly defined. Here a corrected plastic flow potential for the cone region is defined to obtain a continuous transition of the flow vector.

  Abstract
  The original formulation of the MRS-Lade model, with nonassociated flow rule on the meridian plane in the cone region, has a corner. In order to reduce the computational effort [...]

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• Adaptive analysis of yield line patterns in plates with the Arbitrary Lagrangian-Eulerian method

  H. Askes, A. Rodríguez-Ferran, A. Huerta

  Computers and Structures (1999). Vol. 70 (3), pp. 257-271

  
  

  Abstract

  Plasticity models provide suitable tools to describe the so-called yield line pattern that occurs with the failure of plates. However, in a Lagrangian description a huge number of finite elements are needed for accurate solutions. Accuracy can be combined with low computer costs by means of the arbitrary Lagrangian–Eulerian (ALE) method. With the ALE method, the finite element mesh is automatically refined in the yield lines. A new remesh indicator is proposed that captures newly appearing yield lines as well as already formed yield lines. Numerical examples show the effectiveness of this approach.

  Abstract
  Plasticity models provide suitable tools to describe the so-called yield line pattern that occurs with the failure of plates. However, in a Lagrangian description a huge number [...]

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• ALE stress update for transient and quasistatic processes

  A. Rodríguez-Ferran, F. Casadei, A. Huerta

  Int. J. Numer. Meth. Engng. (1998). Vol. 43 (2), pp. 241-262

  
  

  Abstract

  A key issue in Arbitrary Lagrangian-Eulerian (ALE) non-linear solid mechanics is the correct treatment of the convection terms in the constitutive equation. These convection terms, which reflect the relative motion between the finite element mesh and the material, are found for both transient and quasistatic ALE analyses. It is shown in this paper that the same explicit algorithms can be employed to handle the convection terms of the constitutive equation for both types of analyses. The most attractive consequence of this fact is that a quasistatic simulation can be upgraded from Updated Lagrangian (UL) to ALE without significant extra computational cost. These ideas are illustrated by means of two numerical examples.

  Abstract
  A key issue in Arbitrary Lagrangian-Eulerian (ALE) non-linear solid mechanics is the correct treatment of the convection terms in the constitutive equation. These convection [...]

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• Comparing two algorithms to add large strains to small-strain FE code

  A. Rodríguez-Ferran, A. Huerta

  Journal of Engineering Mechanics (1998). Vol. 124 (9), pp. 939-948

  
  

  Abstract

  Two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are discussed, with particular emphasis on two issues: (1) The incremental objectivity; and (2) the implementation aspects. It is shown that both algorithms are incrementally objective (i.e., they treat rigid rotations properly) and that they can be employed to add large-strain capabilities to a small-strain finite element (FE) code in a simple way. A set of benchmark tests, consisting of simple large deformation paths, have been used to test and compare the two algorithms, both for elastic and plastic analyses. These tests evidence different time-integration accuracy for each algorithm. However, it is also shown that the algorithm that is less accurate in general gives exact results for shear-free deformation paths.

  Abstract
  Two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are discussed, with particular emphasis on two issues: [...]

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• Two stress update algorithms for large strains: accuracy analysis and numerical implementation

  A. Rodríguez-Ferran, P. Pegon, A. Huerta

  Int. J. Numer. Meth. Engng. (1997). Vol. 40 (23), pp. 4363-4404

  
  

  Abstract

  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 unified derivation of both algorithms in spite of their inherent differences. Then the two algorithms are adapted from convected frames to a fixed Cartesian frame and implemented in a small-strain finite 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.

  Abstract
  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 [...]

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• A note on a numerical benchmark test: an axisymmetric shell under ring loads

  A. Vila, A. Rodríguez-Ferran, A. Huerta

  Comput. Methods Appl. Mech. Engrg., (1997). Vol. 13 (3), pp. 181-192

  
  

  Abstract

  In this paper, a well-known numerical benchmark test which is usually solved with displacement control for low values of the load eccentricity is examined for a complete range of eccentricities of the ring load. For a certain range of the eccentricity the response shows either snap-through or snap-back, depending on the controlled variable. Thus, in this range of eccentricities, the test can be used to verify implementations of arc-length algorithms, using the displacement controlled solution as a reference. Moreover, results are presented for large eccentricities beyond the applicability of displacement-controlled strategies.

  Abstract
  In this paper, a well-known numerical benchmark test which is usually solved with displacement control for low values of the load eccentricity is examined for a complete range [...]

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• Arbitrary lagrangian-eulerian finite element analysis of strain localization in transient problems

  A. Huerta, G. Pijaudier, L. Bodé

  Int. J. Numer. Meth. Engng. (1995). Vol. 38 (24), pp. 4171-4191

  
  

  Abstract

  Non-local models guaranty that finite element computations on strain softening 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 to non-zero width localization zones. 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 intemallength. 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 non-local damageable material. It is shown that the ALE formulation which is employed in large boundary motion problems can also be well suited for non-linear transient analysis of softening materials where localization bands appear. The remeshing strategy is based on the equidistribution 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
  Non-local models guaranty that finite element computations on strain softening materials remain sound up to failure from a theoretical and computational viewpoint. The non-locality [...]

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• New ALE applications in non-linear fast-transient solid dynamics

  A. Huerta, F. Casadei

  Engineering Computations (1994). Vol. 11 (4), pp. 317-345

  
  

  Abstract

  The arbitrary Lagrangian—Eulerian (ALE) formulation, which is already well established in the hydrodynamics and fluid-structure interaction fields, is extended to materials with memory, namely, non- linear path-dependent materials. Previous attempts to treat non- linear solid mechanics with the ALE description have, in common, the implicit interpolation technique employed. Obviously, this implies a numerical burden which may be uneconomical and may induce to give up this formulation, particularly in fast-transient dynamics where explicit algorithms are usually employed. Here, several applications are presented to show that if adequate stress updating techniques are implemented, the ALE formulation could be much more competitive than classical Lagrangian computations when large deformations are present. Moreover, if the ALE technique is interpreted as a simple interpolation enrichment, adequate—in opposition to distorted or locally coarse—meshes are employed. Notice also that impossible computations (or at least very involved numerically) with a Lagrangian code are easily implementable in an ALE analysis. Finally, it is important to observe that the numerical examples shown range from a purely academic test to real engineering simulations. They show the effective applicability of this formulation to non-linear solid mechanics and, in particular, to impact, coining or forming analysis.

  Abstract
  The arbitrary Lagrangian—Eulerian (ALE) formulation, which is already well established in the hydrodynamics and fluid-structure interaction fields, is extended to materials [...]

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