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Finite Element Implementation (finite + element_implementation)
Selected AbstractsMicromechanical viscoelasto-plastic models and finite element implementation for rate-independent and rate-dependent permanent deformation of stone-based materialsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2010Qingli Dai Abstract This paper presents parallel and serial viscoelasto-plastic models to simulate the rate-independent and the rate-dependent permanent deformation of stone-based materials, respectively. The generalized Maxwell viscoelastic and Chaboche's plastic models were employed to formulate the proposed parallel and serial viscoelasto-plastic constitutive laws. The finite element (FE) implementation of the parallel model used a displacement-based incremental formulation for the viscoelastic part and an elastic predictor,plastic corrector scheme for the elastoplastic component. The FE framework of the serial viscoelasto-plastic model employed a viscoelastic predictor,plastic corrector algorithm. The stone-based materials are consisted of irregular aggregates, matrix and air voids. This study used asphalt mixtures as an example. A digital sample was generated with imaging analysis from an optically scanned surface image of an asphalt mixture specimen. The modeling scheme employed continuum elements to mesh the effective matrix, and rigid bodies for aggregates. The ABAQUS user material subroutines defined with the proposed viscoelasto-plastic matrix models were employed. The micromechanical FE simulations were conducted on the digital mixture sample with the viscoelasto-plastic matrix models. The simulation results showed that the serial viscoelasto-plastic matrix model generated more permanent deformation than the parallel one by using the identical material parameters and displacement loadings. The effect of loading rates on the material viscoelastic and viscoelasto-plastic mixture behaviors was investigated. Permanent deformations under cyclic loadings were determined with FE simulations. The comparison studies showed that the simulation results correctly predicted the rate-independent and rate-dependent viscoelasto-plastic constitutive properties of the proposed matrix models. Overall, these studies indicated that the developed micromechanical FE models have the abilities to predict the global viscoelasto-plastic behaviors of the stone-based materials. Copyright © 2009 John Wiley & Sons, Ltd. [source] Dynamics of unsaturated soils using various finite element formulationsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2009Nadarajah Ravichandran Abstract Unsaturated soils are three-phase porous media consisting of a solid skeleton, pore liquid, and pore gas. The coupled mathematical equations representing the dynamics of unsaturated soils can be derived based on the theory of mixtures. Solution of these fully coupled governing equations for unsaturated soils requires tremendous computational resources because three individual phases and interactions between them have to be taken into account. The fully coupled equations governing the dynamics of unsaturated soils are first presented and then two finite element formulations of the governing equations are presented and implemented within a finite element framework. The finite element implementation of all the terms in the governing equations results in the complete formulation and is solved for the first time in this paper. A computationally efficient reduced formulation is obtained by neglecting the relative accelerations and velocities of liquid and gas in the governing equations to investigate the effects of fluid flow in the overall behavior. These two formulations are used to simulate the behavior of an unsaturated silty soil embankment subjected to base shaking and compared with the results from another commonly used partially reduced formulation that neglects the relative accelerations, but takes into account the relative velocities. The stress,strain response of the solid skeleton is modeled as both elastic and elastoplastic in all three analyses. In the elastic analyses no permanent deformations are predicted and the displacements of the partially reduced formulation are in between those of the reduced and complete formulations. The frequency of vibration of the complete formulation in the elastic analysis is closer to the predominant frequency of the base motion and smaller than the frequencies of vibration of the other two analyses. Proper consideration of damping due to fluid flows in the complete formulation is the likely reason for this difference. Permanent deformations are predicted by all three formulations for the elastoplastic analyses. The complete formulation, however, predicts reductions in pore fluid pressures following strong shaking resulting in somewhat smaller displacements than the reduced formulation. The results from complete and reduced formulations are otherwise comparable for elastoplastic analyses. For the elastoplastic analysis, the partially reduced formulation leads to stiffer response than the other two formulations. The likely reason for this stiffer response in the elastoplastic analysis is the interpolation scheme (linear displacement and linear pore fluid pressures) used in the finite element implementation of the partially reduced formulation. Copyright © 2008 John Wiley & Sons, Ltd. [source] Elastoplastic multiphase model for simulating the response of piled raft foundations subject to combined loadingsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2006G. Hassen Abstract A multiphase model and corresponding computational time-saving finite element code is proposed in this paper for predicting the settlements experienced by a piled raft foundation when subject to the combined action of vertical and lateral loadings. This model, which is formulated in the framework of an elastoplastic behaviour for the soil and the reinforcing piles as well, explicitly accounts for the shear and flexural behaviour of the latter. Starting from a simple analytical example where all the concepts attached to this model are clearly illustrated, the main stages leading to its finite element implementation are then presented. The numerical tool thus elaborated, is applied to the simulation of a pile-reinforced strip foundation submitted to a horizontally applied seismic load in addition to a permanent vertical load. One of the key results of such a simulation in terms of design recommendation, lies in the conclusion that, while the shear and flexural contributions of the reinforcement play quite a negligible role in the case of a vertical load (as compared with their axial resistance), they remain absolutely essential for withstanding the seismic lateral loading. Copyright © 2006 John Wiley & Sons, Ltd. [source] Minimum principle and related numerical scheme for simulating initial flow and subsequent propagation of liquefied groundINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2005Sami Montassar Abstract The problem of predicting the evolution of liquefied ground, modelled as a viscoplastic material, is addressed by combining a minimum principle for the velocity field, which characterizes such an evolution, and a time step integration procedure. Two different numerical schemes are then presented for the finite element implementation of this minimum principle, namely, the regularization technique and the decomposition-co-ordination method by augmented Lagrangian. The second method, which proves more accurate and efficient than the first, is finally applied to simulate the incipient flow failure and subsequent spreading of a liquefied soil embankment subject to gravity. The strong influence of liquefied soil residual shear strength on reducing the maximum amplitude of the ground displacement is particularly emphasized in such an analysis. Copyright © 2005 John Wiley & Sons, Ltd. [source] Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010C. Miehe Abstract The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies. This can be overcome by a diffusive crack modeling based on the introduction of a crack phase-field. In this paper, we outline a thermodynamically consistent framework for phase-field models of crack propagation in elastic solids, develop incremental variational principles and consider their numerical implementations by multi-field finite element methods. We start our investigation with an intuitive and descriptive derivation of a regularized crack surface functional that ,-converges for vanishing length-scale parameter to a sharp crack topology functional. This functional provides the basis for the definition of suitable convex dissipation functions that govern the evolution of the crack phase-field. Here, we propose alternative rate-independent and viscous over-force models that ensure the local growth of the phase-field. Next, we define an energy storage function whose positive tensile part degrades with increasing phase-field. With these constitutive functionals at hand, we derive the coupled balances of quasi-static stress equilibrium and gradient-type phase-field evolution in the solid from the argument of virtual power. Here, we consider a canonical two-field setting for rate-independent response and a time-regularized three-field formulation with viscous over-force response. It is then shown that these balances follow as the Euler equations of incremental variational principles that govern the multi-field problems. These principles make the proposed formulation extremely compact and provide a perfect base for the finite element implementation, including features such as the symmetry of the monolithic tangent matrices. We demonstrate the performance of the proposed phase-field formulations of fracture by means of representative numerical examples. Copyright © 2010 John Wiley & Sons, Ltd. [source] A geometrically and materially non-linear piezoelectric three-dimensional-beam finite element formulation including warping effectsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008A. Butz Abstract This paper is concerned with a three-dimensional piezoelectric beam formulation and its finite element implementation. The developed model considers geometrically and materially non-linear effects. An eccentric beam formulation is derived based on the Timoshenko kinematics. The kinematic assumptions are extended by three additional warping functions of the cross section. These functions follow from torsion and piezoelectrically induced shear deformations. The presented beam formulation incorporates large displacements and finite rotations and allows the investigation of stability problems. The finite element model has two nodes with nine mechanical and five electrical degrees of freedom. It provides an accurate approximation of the electric potential, which is assumed to be linear in the direction of the beam axis and quadratic within the cross section. The mechanical degrees of freedom are three displacements, three rotations and three scaling factors for the warping functions. The latter are computed in a preprocess by solving a two-dimensional in-plane equilibrium condition with the finite element method. The gained warping patterns are considered within the integration through the cross section of the beam formulation. With respect to material non-linearities, which arise in ferroelectric materials, the scalar Preisach model is embedded in the formulation. This model is a mathematical model for the general description of hysteresis phenomena. Its application to piezoelectric materials leads to a phenomenological model for ferroelectric hysteresis effects. Here, the polarization direction is assumed to be constant, which leads to unidirectional constitutive equations. Some examples demonstrate the capability of the proposed model. Copyright © 2008 John Wiley & Sons, Ltd. [source] On the differentiation of the Rodrigues formula and its significance for the vector-like parameterization of Reissner,Simo beam theoryINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2002M. Ritto-Corrêa Abstract In this paper we present a systematic way of differentiating, up to the second directional derivative, (i) the Rodrigues formula and (ii) the spin-rotation vector variation relationship. To achieve this goal, several trigonometric functions are grouped into a family of scalar quantities, which can be expressed in terms of a single power series. These results are then applied to the vector-like parameterization of Reissner,Simo beam theory, enabling a straightforward derivation and leading to a clearer formulation. In particular, and in contrast with previous formulations, a relatively compact and obviously symmetric form of the tangent operator is obtained. The paper also discusses several relevant issues concerning a beam finite element implementation and concludes with the presentation of a few selected illustrative examples. Copyright © 2002 John Wiley & Sons, Ltd. [source] Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfacesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2005Anton Smolianski Abstract The present work is devoted to the study on unsteady flows of two immiscible viscous fluids separated by free moving interface. Our goal is to elaborate a unified strategy for numerical modelling of two-fluid interfacial flows, having in mind possible interface topology changes (like merger or break-up) and realistically wide ranges for physical parameters of the problem. The proposed computational approach essentially relies on three basic components: the finite element method for spatial approximation, the operator-splitting for temporal discretization and the level-set method for interface representation. We show that the finite element implementation of the level-set approach brings some additional benefits as compared to the standard, finite difference level-set realizations. In particular, the use of finite elements permits to localize the interface precisely, without introducing any artificial parameters like the interface thickness; it also allows to maintain the second-order accuracy of the interface normal, curvature and mass conservation. The operator-splitting makes it possible to separate all major difficulties of the problem and enables us to implement the equal-order interpolation for the velocity and pressure. Diverse numerical examples including simulations of bubble dynamics, bifurcating jet flow and Rayleigh,Taylor instability are presented to validate the computational method. Copyright © 2004 John Wiley & Sons, Ltd. [source] Engineering investigations on the potentiality of the thermoformability of HDPE charged by wood flours in the thermoforming partPOLYMER ENGINEERING & SCIENCE, Issue 8 2009F. Erchiqui A dynamic finite element method is used to analyze the thermoformability of composites containing wood and a thermoplastic matrix for five different proportions of wood flour. Linear viscoelastic properties can be obtained by small amplitude oscillatory shear tests and the viscoelastic behavior is characterized using the Lodge model. To account for enclosed gas volume, which inflates the thermoplastic composite membrane, a thermodynamic approach is used to express the external work in terms of a closed volume. Pressure load is deduced by thermodynamic law using the Redlich,Kwong gas equation. The Lagrangian method together with the assumption of membrane theory is used in the finite element implementation. In addition, the influence of air flow on thickness and stress and the energy required to form a thin polymeric part in the thermoforming process are analyzed for five different proportions of wood flour in the HDPE material. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers [source] | ||||||||||