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• Discretization influence on regularization by two localization limiters

  A. Huerta, G. Pijaudier

  Journal of Engineering Mechanics (1994). Vol. 120 (6), pp. 1198-1218

  
  

  Abstract

  In materials with a strain‐softening characteristic behavior, classical continuum mechanics favors uncontrolled strain localization in numerical analyses. Several methods have been proposed to regularize the problem. Two such localization limiters developed to overcome spurious instabilities in computational failure analysis are examined and compared. A disturbance analysis, on both models, is performed to obtain the closed‐form solution of propagating wave velocities as well as the velocities at which the energy travels. It also shows that in spite of forcing the same stress‐strain response, the wave equation does not yield similar results. Both propagations of waves are dispersive, but the internal length of each model is different when equivalent behavior is desired. In fact, the previously suggested derivations of gradient models from nonlocal integral models were not completely rigorous. The perturbation analysis is pursued in the discrete space where computations are done, and the closed form solutions are also obtained. The finite‐element discretization introduces an added dispersion associated to the regularization technique. Therefore, the influence of the discretization on the localization limiters can be evaluated. The element size must be smaller than the internal length of the models in order to obtain sufficient accuracy.

  Abstract
  In materials with a strain‐softening characteristic behavior, classical continuum mechanics favors uncontrolled strain localization in numerical analyses. Several methods [...]

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• Numerical analysis of nonlinear large-strain consolidation and filling

  A. Huerta, A. Rodríguez-Ferran

  Computers and Structures (1992). Vol. 44 (1-2), pp. 357-365

  
  

  Abstract

  Finite strain consolidation and filling of soft sediments at high water level is a challenging problem because of its highly non-linear physical and mathematical aspects. Several numerical schemes designed for this problem are presented as well as simple numerical improvements for a better handling of the extremely high variations of the material properties with depth. The numerical algorithms developed are robust and verify convergence of the iterative schemes instead of the more classical approaches based on choosing time increments ‘sufficiently’ small and assuming convergence at every step. A set of computer programs has been developed to predict magnitude and rate of large-strain self-weight one-dimensional and pseudo bi-dimensional (i.e. one-dimensional deformation, bi-dimensional flux) consolidation during and after deposition, that is, coupling filling and consolidation phenomena. The actual life of the deposit can be numerically simulated combining filling periods and quiescent periods where surcharges (or capping) can exist. Consequently, they are a basic technique for the design of disposal ponds.

  Abstract
  Finite strain consolidation and filling of soft sediments at high water level is a challenging problem because of its highly non-linear physical and mathematical aspects. [...]

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• Finite element analysis of bifurcation in nonlocal strain softening solids

  G. Pijaudier, A. Huerta

  Comput. Methods Appl. Mech. Engrg. (1991). Vol. 90 (1-3), pp. 905-919

  
  

  Abstract

  Progressive damage in brittle heterogeneous materials produces at the macroscopic level strain softening from which theoretical difficulties arise (e.g. ill-posedness and multiple bifurcation points). This characteristics behavior favours spurious strain localization in numerical analyses and calls for the implementation of localization limiters, for instance nonlocal damage constitutive relations. The issue of possible (stable or unstable) equilibrium paths, multiple localization zones, and of the detection of bifurcation points has, however, never been addressed in the context of nonlocal constitutive laws. We extend here the eigenmode analysis and perturbation method proposed by De Borst to the study of the bifurcation and post-bifurcation response of discrete nonlocal strain softening solids. Numerical applications on beams show that bifurcation and instability may occur in the post-peak regime. As opposed to the case of local constitutive relations, the number of possible solutions at a bifurcation point is restricted due to the constraint introduced by the localization limiter and these solutions are shown to be mesh independent.

  Abstract
  Progressive damage in brittle heterogeneous materials produces at the macroscopic level strain softening from which theoretical difficulties arise (e.g. ill-posedness and [...]

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• Large-amplitude sloshing with submerged blocks

  A. Huerta, W. Liu

  Journal of pressure vessel technology (1990). Vol. 112 (1), pp. 104-108

  
  

  Abstract

    The computer simulation of forced vibrations induced on a water pool is presented in this paper. The complexity of the seismic fluid-structure interaction problem is accentuated by the large free surface motion. To overcome this difficulty, the arbitrary Lagrangian Eulerian (ALE) finite element formulation is employed. Moreover, the nonlinear behavior of the free surface motion is also taken into account. The results of the numerical simulation are compared with published experimental data and the effectiveness of the ALE algorithm is demonstrated

  Abstract
    The computer simulation of forced vibrations induced on a water pool is presented in this paper. The complexity of the seismic fluid-structure interaction problem [...]

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• Viscous flow with large free surface motion

  A. Huerta, W. Liu

  Comput. Methods Appl. Mech. Engrg., (1988). Vol. 69 (3), pp. 277-324

  
  

  Abstract

  An arbitrary Lagrangian-Eulerian (ALE) Petrov-Galerkin finite element technique is developed to study nonlinear viscous fluids under large free surface wave motion. A review of the kinematics and field equations from an arbitrary reference is presented and since the major challenge of the ALE description lies in the mesh rezoning algorithm, various methods, including a new mixed formulation, are developed to update the mesh and map the moving domain in a more rational manner. Moreover, the streamline-upwind/Petrov-Galerkin formulation is implemented to accurately describe highly convective free surface flows. The effectiveness of the algorithm is demonstrated on a tsunami problem, the dam-break problem where the Reynolds number is taken as high as 3000, and a large-amplitude sloshing problem.

  Abstract
  An arbitrary Lagrangian-Eulerian (ALE) Petrov-Galerkin finite element technique is developed to study nonlinear viscous fluids under large free surface wave motion. A review [...]

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• Permeability and compressibility of slurries from seepage-induced consolidation

  A. Huerta, G. Kriegsmann, R. Krizek

  Journal of geotechnical engineering (ASCE) (1988). Vol. 114 (5), pp. 614-627

  
  

  Abstract

  A one-dimensional mathematical model based on finite-strain theory is developed to solve the problem of seepage-induced consolidation in sedimented slurries or very soft clays. The direct solution employs known or assumed material property relationships to determine the final thickness of a soft sediment subjected to a constant piezometric head. It is useful for predicting the capacity of a disposal area and the time-dependent improvement in material properties. Alternatively, the inverse solution utilizes final settlement and steady-state flow data from laboratory or field tests to deduce permeability and compressibility relationships for soft sediments. This approach is especially helpful in the case of permeability determinations because it avoids some of the major problems associated with permeability testing of such materials. The resulting model shows that the coefficient of permeability influences both the time to reach the steady-state condition and the nature of the steady-state condition itself. An illustrative example is presented wherein data from a series of tests on a kaolinite slurry are used to establish material property relationships that are then used to predict the response of other tests on the same soil under different conditions

  Abstract
  A one-dimensional mathematical model based on finite-strain theory is developed to solve the problem of seepage-induced consolidation in sedimented slurries or very soft clays. [...]

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• Viscous Flow Structure Interaction

  A. Huerta, W. Liu

  Journal of pressure vessel technology (1988). Vol. 110 (1), pp. 15-21

  
  

  Abstract

  Considerable research activities in vibration and seismic analysis for various fluid-structure systems have been carried out in the past two decades. Most of the approaches are formulated within the framework of finite elements, and the majority of work deals with inviscid fluids. However, there has been little work done in the area of fluid-structure interaction problems accounting for flow separation and nonlinear phenomenon of steady streaming. In this paper, the Arbitrary Lagrangian Eulerian (ALE) finite element method is extended to address the flow separation and nonlinear phenomenon of steady streaming for arbitrarily shaped bodies undergoing large periodic motion in a viscous fluid. The results are designed to evaluate the fluid force acting on the body; thus, the coupled rigid body-viscous flow problem can be simplified to a standard structural problem using the concept of added mass and added damping. Formulas for these two constants are given for the particular case of a cylinder immersed in an infinite viscous fluid. The finite element modeling is based on a pressure-velocity mixed formulation and a streamline upwind Petrov/Galerkin technique. All computations are performed using a personal computer.

  Abstract
  Considerable research activities in vibration and seismic analysis for various fluid-structure systems have been carried out in the past two decades. Most of the approaches [...]

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• Converse flexoelectricity yields large piezoresponse force microscopy signals in non-piezoelectric materials

  A. Abdollahi, N. Domingo, I. Arias, G. Catalan

  Nature Communications (2019). Vol. 10 (1266), pp. 1-6

  
  

  Abstract

  Converse flexoelectricity is a mechanical stress induced by an electric polarization gradient. It can appear in any material, irrespective of symmetry, whenever there is an inhomogeneous electric field distribution. This situation invariably happens in piezoresponse force microscopy (PFM), which is a technique whereby a voltage is delivered to the tip of an atomic force microscope in order to stimulate and probe piezoelectricity at the nanoscale. While PFM is the premier technique for studying ferroelectricity and piezoelectricity at the nanoscale, here we show, theoretically and experimentally, that large effective piezoelectric coefficients can be measured in non-piezoelectric dielectrics due to converse flexoelectricity.

  Abstract
  Converse flexoelectricity is a mechanical stress induced by an electric polarization gradient. It can appear in any material, irrespective of symmetry, whenever there is an [...]

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• Phase-field modeling of fracture in ferroelectric materials

  A. Abdollahi, I. Arias

  Archives of Comp. Meths. Engng. (2015). Vol. 22 (2), pp. 153-181 (Preprint)

  
  

  Abstract

  This paper presents a family of phase-field models for the coupled simulation of the microstructure formation and evolution, and the nucleation and propagation of cracks in single and polycrystalline ferroelectric materials. The first objective is to introduce a phase-field model for ferroelectric single crystals. The model naturally couples two existing energetic phase-field approaches for brittle fracture and ferroelectric domain formation and evolution. Simulations show the interactions between the microstructure and the crack under mechanical and electromechanical loadings. Another objective of this paper is to encode different crack face boundary conditions into the phase-field framework since these conditions strongly affect the fracture behavior of ferroelectrics. The smeared imposition of these conditions are discussed and the results are compared with that of sharp crack models to validate the proposed approaches. Simulations show the effects of different conditions and electromechanical loadings on the crack propagation. In a third step, the model is modified by introducing a crack non-interpenetration condition in the variational approach to fracture accounting for the asymmetric behavior in tension and compression. The modified model makes it possible to explain anisotropic crack growth in ferroelectrics under the Vickers indentation loading. This model is also employed for the fracture analysis of multilayer ferroelectric actuators, which shows the potential of the model for future applications. The coupled phase-field model is also extended to polycrystals by introducing realistic polycrystalline microstructures in the model. Inter- and trans-granular crack propagation modes are observed in the simulations. Finally, and for completeness, the phase-field theory is extended to the simulation of the propagation of conducting cracks under purely electrical loading and to the three-dimensional simulation of crack propagation in ferroelectric single crystals. Salient features of the crack propagation phenomenon predicted by the simulations of this paper are directly compared with experimental observations.

  Abstract
  This paper presents a family of phase-field models for the coupled simulation of the microstructure formation and evolution, and the nucleation and propagation of cracks in [...]

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• Constructive and destructive interplay between piezoelectricity and flexoelectricity in flexural sensors and actuators

  A. Abdollahi, I. Arias

  Journal of Applied Mechanics (2015). Vol. 82 (12), pp. 121003-1/121003-4 (Preprint)

  
  

  Abstract

  Flexoelectricity is an electromechanical effect coupling polarization to strain gradients. It fundamentally differs from piezoelectricity because of its size-dependence and symmetry. Flexoelectricity is generally perceived as a small effect noticeable only at the nanoscale. Since ferroelectric ceramics have a particularly high flexoelectric coefficient, however, it may play a significant role as piezoelectric transducers shrink to the submicrometer scale. We examine this issue with a continuum model self-consistently treating piezo- and flexoelectricity. We show that in piezoelectric device configurations that induce strain gradients and at small but technologically relevant scales, the electromechanical coupling may be dominated by flexoelectricity. More importantly, depending on the device design flexoelectricity may enhance or reduce the effective piezoelectric effect. Focusing on bimorph configurations, we show that configurations that are equivalent at large scales exhibit dramatically different behavior for thicknesses below 100¿nm for typical piezoelectric materials. Our results suggest flexoelectric-aware designs for small-scale piezoelectric bimorph transducers.

  Abstract
  Flexoelectricity is an electromechanical effect coupling polarization to strain gradients. It fundamentally differs from piezoelectricity because of its size-dependence and [...]

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