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Large Deformations (large + deformation)
Terms modified by Large Deformations Selected AbstractsThe Energetics of Large Deformations of a Single Polyimide Molecular Chain: DFT and MO CalculationsMACROMOLECULAR THEORY AND SIMULATIONS, Issue 9 2008Akinori Fujinami Abstract The large-deformation energetics of a single molecular chain of the rod-like polyimide PMDA-PDA was investigated using DFT, ab initio MO and semi-empirical MO methods. The force/displacement curves were calculated from tensile testing simulations along the axis of the molecular chain, allowing a discussion of the distribution and change of local strain of the molecular chain. The deformation behavior of a single PMDA-PDA molecular chain under finite deformations as functions of bending angle and dihedral angle between PMDA and PDA groups are compared. It is found that the semi-empirical MO calculations provide sufficient accuracy to express the energetics of large deformations except for compressive deformation. [source] Highly Conductive Sheets from Millimeter-Long Single-Walled Carbon Nanotubes and Ionic Liquids: Application to Fast-Moving, Low-Voltage Electromechanical Actuators Operable in AirADVANCED MATERIALS, Issue 16 2009Ken Mukai Ionic liquids allow millimeter-long single-walled carbon nanotubes to associate tightly, forming a free-standing sheet with superb mechanical and electrical properties. An actuator strip, fabricated by sandwiching an ionic-liquid-gel electrolyte layer with the nanotubes sheets obtained exhibits a large deformation in quick response (4,mm per 0.05 s) to low applied voltages, and a high durability upon 10 000 times continuous operations. [source] Arbitrary Lagrangian,Eulerian method for large-strain consolidation problemsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2008Majidreza Nazem Abstract In this paper, an arbitrary Lagrangian,Eulerian (ALE) method is generalized to solve consolidation problems involving large deformation. Special issues such as pore-water pressure convection, permeability and void ratio updates due to rotation and convection, mesh refinement and equilibrium checks are discussed. A simple and effective mesh refinement scheme is presented for the ALE method. The ALE method as well as an updated-Lagrangian method is then used to solve some classical consolidation problems involving large deformations with different constitutive laws. The results clearly show the advantage and efficiency of the ALE method for these examples. Copyright © 2007 John Wiley & Sons, Ltd. [source] An operator-split ALE model for large deformation analysis of geomaterialsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2007Y. Di Abstract Analysis of large deformation of geomaterials subjected to time-varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator-split arbitrary Lagrangian,Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid,fluid coupling and strong material non-linearity. Each time step of the operator-split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one-dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading. Copyright © 2007 John Wiley & Sons, Ltd. [source] Discrete element modelling of deep penetration in granular soilsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2006M. J. Jiang Abstract This paper presents a numerical study on deep penetration mechanisms in granular materials with the focus on the effect of soil,penetrometer interface friction. A two-dimensional discrete element method has been used to carry out simulation of deep penetration tests on a granular ground that is under an amplified gravity with a K0 lateral stress boundary. The numerical results show that the deep penetration makes the soil near the penetrometer move in a complex displacement path, undergo an evident loading and unloading process, and a rotation of principal stresses as large as 180°. In addition, the penetration leads to significant changes in displacement and velocity fields as well as the magnitude and direction of stresses. In general, during the whole penetration process, the granular ground undergoes several kinds of failure mechanisms in sequence, and the soil of large deformation may reach a stress state slightly over the strength envelope obtained from conventional compression tests. Soil,penetrometer interface friction has clear effects on the actual penetration mechanisms. Copyright © 2005 John Wiley & Sons, Ltd. [source] Robust adaptive remeshing strategy for large deformation, transient impact simulationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2006Tobias Erhart Abstract In this paper, an adaptive approach, with remeshing as essential ingredient, towards robust and efficient simulation techniques for fast transient, highly non-linear processes including contact is discussed. The necessity for remeshing stems from two sources: the capability to deal with large deformations that might even require topological changes of the mesh and the desire for an error driven distribution of computational resources. The overall computational approach is sketched, the adaptive remeshing strategy is presented and the crucial aspect, the choice of suitable error indicator(s), is discussed in more detail. Several numerical examples demonstrate the performance of the approach. Copyright © 2005 John Wiley & Sons, Ltd. [source] Optimal solid shell element for large deformable composite structures with piezoelectric layers and active vibration controlINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2005X. G. Tan Abstract In this paper, we present an optimal low-order accurate piezoelectric solid-shell element formulation to model active composite shell structures that can undergo large deformation and large overall motion. This element has only displacement and electric degrees of freedom (dofs), with no rotational dofs, and an optimal number of enhancing assumed strain (EAS) parameters to pass the patch tests (both membrane and out-of-plane bending). The combination of the present optimal piezoelectric solid-shell element and the optimal solid-shell element previously developed allows for efficient and accurate analyses of large deformable composite multilayer shell structures with piezoelectric layers. To make the 3-D analysis of active composite shells containing discrete piezoelectric sensors and actuators even more efficient, the composite solid-shell element is further developed here. Based on the mixed Fraeijs de Veubeke,Hu,Washizu (FHW) variational principle, the in-plane and out-of-plane bending behaviours are improved via a new and efficient enhancement of the strain tensor. Shear-locking and curvature thickness locking are resolved effectively by using the assumed natural strain (ANS) method. We also present an optimal-control design for vibration suppression of a large deformable structure based on the general finite element approach. The linear-quadratic regulator control scheme with output feedback is used as a control law on the basis of the state space model of the system. Numerical examples involving static analyses and dynamic analyses of active shell structures having a large range of element aspect ratios are presented. Active vibration control of a composite multilayer shell with distributed piezoelectric sensors and actuators is performed to test the present element and the control design procedure. Copyright © 2005 John Wiley & Sons, Ltd. [source] A-scalability and an integrated computational technology and framework for non-linear structural dynamics.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2003Part 2: Implementation aspects, parallel performance results Abstract An integrated framework and computational technology is described that addresses the issues to foster absolute scalability (A-scalability) of the entire transient duration of the simulations of implicit non-linear structural dynamics of large scale practical applications on a large number of parallel processors. Whereas the theoretical developments and parallel formulations were presented in Part 1, the implementation, validation and parallel performance assessments and results are presented here in Part 2 of the paper. Relatively simple numerical examples involving large deformation and elastic and elastoplastic non-linear dynamic behaviour are first presented via the proposed framework for demonstrating the comparative accuracy of methods in comparison to available experimental results and/or results available in the literature. For practical geometrically complex meshes, the A-scalability of non-linear implicit dynamic computations is then illustrated by employing scalable optimal dissipative zero-order displacement and velocity overshoot behaviour time operators which are a subset of the generalized framework in conjunction with numerically scalable spatial domain decomposition methods and scalable graph partitioning techniques. The constant run times of the entire simulation of ,fixed-memory-use-per-processor' scaling of complex finite element mesh geometries is demonstrated for large scale problems and large processor counts on at least 1024 processors. Copyright © 2003 John Wiley & Sons, Ltd. [source] Numerical analysis of deformed free surface under AC magnetic fieldsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2004Haruhiko Kohno Abstract A novel numerical scheme for the analysis of large deformation of electrically conducting liquid under alternating current magnetic fields is presented. The main features are characterized by two numerical tools; the level set method to calculate deformed free surface stably and the hybrid finite element method and boundary element method to discretize the electromagnetic field efficiently. Two-dimensional numerical simulation of conducting drop deformation is carried out to demonstrate the effectiveness of the present scheme, and the oscillatory behaviour, which depends on the magnitude of surface tension and Lorentz force, is investigated. Copyright © 2004 John Wiley & Sons, Ltd. [source] Contribution of Cellular Structure to the Large and Small Deformation Rheological Behavior of KiwifruitJOURNAL OF FOOD SCIENCE, Issue 6 2002A.M. Rojas ABSTRACT: The relative contribution of turgor pressure, cell wall and middle lamellae to the rheology of kiwifruit was studied by performing large deformation assays and using an empirical model proposed by our group. Results were compared with those obtained previously through dynamic testing. Initial (,0) and residual relaxation (,,) stresses determined under 14% constant deformation correlated significantly with complex moduli (G*) and they allowed to detect incipient plasmolysis but not to determine the individual contributions of cell wall and middle lamellae to tissue elasticity. Firmness (Fm) showed no correlation with G* because measurement of failure stress required tissue damage but it was affected by ripening allowing to determine the individual contributions of cell wall and middle lamellae to its value. [source] A Discrete, Space Variation Model for Studying the Kinetics of Shape Deformation of Vesicles Coupled with Phase SeparationMACROMOLECULAR THEORY AND SIMULATIONS, Issue 5 2006Jianfeng Li Abstract Summary: The evolution dynamics of phase separation, coupled with shape deformation of vesicles is described by using dissipative dynamic equations, specifically the time-dependent Ginzburg-Landau (TDGL) equations. In order to improve the numerical stability and thus to efficiently deal with a large deformation of vesicles, a new algorithm, namely the discrete space variation model (DSVM) has been developed for the first time. The algorithm is based on the variation of the discretized free-energy functional, which is constructed in discrete membrane space, in contrast to the commonly used continuous free-energy functional. For the sake of numerical tractability, only the cylindrical vesicles (2D), with two components, are taken into consideration to illustrate the efficiency and validity of new algorithm. The simulation results, based on the DSVM algorithm have been compared with those from both linear analysis and strong segregation theory using the continuous space free-energy functional. It is found that the DSVM algorithm can correctly describe the coupling between the lateral phase-separation on the vesicle membrane and the vesicle shape deformation, both for early and late stages. A flower-like vesicle obtained by DSVM simulation. [source] Superplasticity and high temperature deformation behaviour in nano grain Tungsten compactsMATERIALWISSENSCHAFT UND WERKSTOFFTECHNIK, Issue 4-5 2008K. Ameyama Abstract Nano grain tungsten is fabricated by Mechanical Milling (MM) process, and its grain growth behavior and high temperature deformability is investigated. As a result, a nano grain structure, whose grain size is approximately 20 nm or less, is obtained after MM for 360ks. Those nano grains demonstrate an irregular grain boundary structure, i.e., "non-equilibrium grain boundary", and they change to a smooth grain boundary structure by annealing at 1023 K for 3.6 ks. Compacts with nano grain structure indicate superior sintering property even at 1273 K (0.35 Tm). Rhenium addition prevents grain growth during sintering and thus the compacts indicate a further improvement in deformability. The compact is composed of equiaxed grain, whose grain size is 420 nm, and has low dislocation density even after the large deformation. The strain rate sensitivity, i.e., m-value, of 0.41 is obtained in the W-Re compact at 1473 K. Those results strongly imply that the nano grain W-Re compacts show superplasticity at less than half of the melting temperature, i.e., 1473 K (0.42 of the solidus temperature). [source] Local and non-local ductile damage and failure modelling at large deformation with applications to engineeringPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Bob Svendsen Prof. Dr. The numerical analysis of ductile damage and failure in engineering materials is often based on the micromechanical model of Gurson [1]. Numerical studies in the context of the finite-element method demonstrate that, as with other such types of local damage models, the numerical simulation of the initiation and propagation of damage zones is strongly mesh-dependent and thus unreliable. The numerical problems concern the global load-displacement response as well as the onset, size and orientation of damage zones. From a mathematical point of view, this problem is caused by the loss of ellipticity of the set of partial di.erential equations determining the (rate of) deformation field. One possible way to overcome these problems with and shortcomings of the local modelling is the application of so-called non-local damage models. In particular, these are based on the introduction of a gradient type evolution equation of the damage variable regarding the spatial distribution of damage. In this work, we investigate the (material) stability behaviour of local Gurson-based damage modelling and a gradient-extension of this modelling at large deformation in order to be able to model the width and other physical aspects of the localization of the damage and failure process in metallic materials. [source] Description for smooth contact conditions based on the internal geometry of contact surfacesPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Alexander Konyukhov Dr. A kinematical approach, based on the consideration of the contact conditions in the local coordinate system, is proposed for the contact description and for consistent linearization. This leads to a simple structure of the tangent matrix, which is subdivided into main, rotational and curvature parts. Various alternatives neglecting parts of the contact tangent matrix are considered. Representative examples show the effectiveness of the proposed approach for contact problems with arbitrary large deformation. [source] Restraint of fire-exposed concrete floor systemsFIRE AND MATERIALS, Issue 2-4 2004Linus Lim Abstract This paper describes the numerical analyses of restrained concrete floor slabs exposed to fire. The analyses of the slabs were carried out with the SAFIR finite element program considering a 200 mm thick slab, spanning 5 m between two end supports. The slabs were exposed to the ISO standard fire for up to 4 h and were analysed with pinned and rotationally restrained supports. Different heights of the line of thrust at the supports and different levels of axial restraint were also investigated. The analyses show that fully restrained pin-supported slabs can survive the 4 h ISO fire without collapse if the position of the line of thrust is located near the soffit of the slab. If the position of the line of thrust is located much above the soffit of the slab, the slabs will rapidly undergo large deformations and sag into a catenary, imposing axial tensile forces at the supports. The analyses have shown that even if the line of thrust is located close to the soffit, the slab can still deform into a catenary if there is insufficient horizontal axial restraint. In this study, rotationally restrained slabs experience much smaller vertical deflections than pin-supported slabs when exposed to fires. Rotationally restrained slabs with low levels of horizontal restraint do not collapse, due to the beneficial effects of moment redistribution. However, high levels of horizontal restraint can be detrimental, causing slabs to collapse at advanced stages of the fire. Copyright © 2004 John Wiley & Sons, Ltd. [source] Plastic Dissipation Mechanisms in Periodic Microframe-Structured PolymersADVANCED FUNCTIONAL MATERIALS, Issue 9 2009Lifeng Wang Abstract Novel lightweight micro- and nanostructured materials are being used as constituents in hierarchically structured composites for providing high stiffness, high strength, and energy absorbing capability at low weight. Three dimensional SU-8 periodic microframe materials with submicrometer elements exhibit unusual large plastic deformations. Here, the plastic dissipation and mechanical response of polymeric microframe structures is investigated using micromechanical modeling of large deformations. Finite element analysis shows that multiple deformation domains initiate, stabilize, and then spread plasticity through the structure; simulated deformation mechanisms and deformation progression are found to be in excellent agreement with experimental observation. Furthermore, the geometry can be used to tailor aspects of 3D behavior such as effective lateral contraction ratios (elastic and plastic) during tensile loading as well as negative normal stress during simple shear deformation. The effects of structural geometry on mechanical response are also studied to tailor and optimize mechanical performance at a given density. These quantitative investigations enable simulation-based design of optimal lightweight material microstructures for dissipating energy. [source] Arbitrary Lagrangian,Eulerian method for large-strain consolidation problemsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2008Majidreza Nazem Abstract In this paper, an arbitrary Lagrangian,Eulerian (ALE) method is generalized to solve consolidation problems involving large deformation. Special issues such as pore-water pressure convection, permeability and void ratio updates due to rotation and convection, mesh refinement and equilibrium checks are discussed. A simple and effective mesh refinement scheme is presented for the ALE method. The ALE method as well as an updated-Lagrangian method is then used to solve some classical consolidation problems involving large deformations with different constitutive laws. The results clearly show the advantage and efficiency of the ALE method for these examples. Copyright © 2007 John Wiley & Sons, Ltd. [source] A numerical study of flexural buckling of foliated rock slopesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2001D. P. Adhikary Abstract The occurrence of foliated rock masses is common in mining environment. Methods employing continuum approximation in describing the deformation of such rock masses possess a clear advantage over methods where each rock layer and each inter-layer interface (joint) is explicitly modelled. In devising such a continuum model it is imperative that moment (couple) stresses and internal rotations associated with the bending of the rock layers be properly incorporated in the model formulation. Such an approach will lead to a Cosserat-type theory. In the present model, the behaviour of the intact rock layer is assumed to be linearly elastic and the joints are assumed to be elastic,perfectly plastic. Condition of slip at the interfaces are determined by a Mohr,Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformations. The model is incorporated into the finite element program AFENA and validated against an analytical solution of elementary buckling problems of a layered medium under gravity loading. A design chart suitable for assessing the stability of slopes in foliated rock masses against flexural buckling failure has been developed. The design chart is easy to use and provides a quick estimate of critical loading factors for slopes in foliated rock masses. It is shown that the model based on Euler's buckling theory as proposed by Cavers (Rock Mechanics and Rock Engineering 1981; 14:87,104) substantially overestimates the critical heights for a vertical slope and underestimates the same for sub-vertical slopes. Copyright © 2001 John Wiley & Sons, Ltd. [source] Non-stationary plane problem of the successive origination of stress concentrators in a loaded body.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2008Finite deformations, their superposition Abstract The first (for the given class of problems) results of solving non-stationary plane problems of non-simultaneous origination of holes and inclusions in a preliminary loaded solid with initial finite strains are presented and discussed. It is taken into account that the origination of a hole or an inclusion produces additional finite deformations (at least, at the vicinity of the hole) superimposed ,physically' on the finite initial ones. The problem is solved using the theory of repeated superposition of large deformations. It is supposed that the shape of stress concentrators is given at the moment of their origination. Calculations were made with the use of the specialized computer package ,Superposition' based on finite-element method. Stress fields are presented at different times. The change of maximal stresses in time is also presented. Copyright © 2008 John Wiley & Sons, Ltd. [source] An efficient hourglass control implementation for the uniform strain hexahedron using the Total Lagrangian formulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2008Grand Roman Joldes Abstract The under-integrated hexahedron is one of the best candidates for use in real-time surgical simulations, because of its computational efficiency. This element requires a very efficient method of controlling the zero energy (hourglass) modes that arise from one-point integration. An efficient implementation of the perturbation hourglass control method proposed by Flanagan and Belytschko for the uniform strain hexahedron is presented. The implementation uses the Total Lagrangian formulation and takes into consideration large deformations and rigid body motions. By using the Total Lagrangian formulation most of the necessary components for calculating the hourglass forces can be pre-computed, leading to a significant reduction of the additional computation time required for hourglass control. The performance evaluation results show the very good accuracy and computational efficiency of the presented algorithm. Copyright © 2007 John Wiley & Sons, Ltd. [source] Coupling of mesh-free methods with finite elements: basic concepts and test resultsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2006T. Rabczuk Abstract This paper reviews several novel and older methods for coupling mesh-free particle methods, particularly the element-free Galerkin (EFG) method and the smooth particle hydrodynamics (SPH), with finite elements (FEs). We study master,slave couplings where particles are fixed across the FE boundary, coupling via interface shape functions such that consistency conditions are satisfied, bridging domain coupling, compatibility coupling with Lagrange multipliers and hybrid coupling methods where forces from the particles are applied via their shape functions on the FE nodes and vice versa. The hybrid coupling methods are well suited for large deformations and adaptivity and the coupling procedure is independent of the particle distance and nodal arrangement. We will study the methods for several static and dynamic applications, compare the results to analytical and experimental data and show advantages and drawbacks of the methods. Copyright © 2006 John Wiley & Sons, Ltd. [source] Decoupling and balancing of space and time errors in the material point method (MPM)INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010Michael Steffen Abstract The material point method (MPM) is a computationally effective particle method with mathematical roots in both particle-in-cell and finite element-type methods. The method has proven to be extremely useful in solving solid mechanics problems involving large deformations and/or fragmentation of structures, problem domains that are sometimes problematic for finite element-type methods. Recently, the MPM community has focused significant attention on understanding the basic mathematical error properties of the method. Complementary to this thrust, in this paper we show how spatial and temporal errors are typically coupled within the MPM framework. In an attempt to overcome the challenge to analysis that this coupling poses, we take advantage of MPM's connection to finite element methods by developing a ,moving-mesh' variant of MPM that allows us to use finite element-type error analysis to demonstrate and understand the spatial and temporal error behaviors of MPM. We then provide an analysis and demonstration of various spatial and temporal errors in MPM and in simplified MPM-type simulations. Our analysis allows us to anticipate the global error behavior in MPM-type methods and allows us to estimate the time-step where spatial and temporal errors are balanced. Larger time-steps result in solutions dominated by temporal errors and show second-order temporal error convergence. Smaller time-steps result in solutions dominated by spatial errors, and hence temporal refinement produces no appreciative change in the solution. Based upon our understanding of MPM from both analysis and numerical experimentation, we are able to provide to MPM practitioners a collection of guidelines to be used in the selection of simulation parameters that respect the interplay between spatial (grid) resolution, number of particles and time-step. Copyright © 2009 John Wiley & Sons, Ltd. [source] A mesh adaptation framework for dealing with large deforming meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2010Gaëtan Compère Abstract In this paper, we identify and propose solutions for several issues encountered when designing a mesh adaptation package, such as mesh-to-mesh projections and mesh database design, and we describe an algorithm to integrate a mesh adaptation procedure in a physics solver. The open-source MAdLib package is presented as an example of such a mesh adaptation library. A new technique combining global node repositioning and mesh optimization in order to perform arbitrarily large deformations is also proposed. We then present several test cases to evaluate the performances of the proposed techniques and to show their applicability to fluid,structure interaction problems with arbitrarily large deformations. Copyright © 2009 John Wiley & Sons, Ltd. [source] Energy,momentum consistent finite element discretization of dynamic finite viscoelasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010M. Groß Abstract This paper is concerned with energy,momentum consistent time discretizations of dynamic finite viscoelasticity. Energy consistency means that the total energy is conserved or dissipated by the fully discretized system in agreement with the laws of thermodynamics. The discretization is energy,momentum consistent if also momentum maps are conserved when group motions are superimposed to deformations. The performed approximation is based on a three-field formulation, in which the deformation field, the velocity field and a strain-like viscous internal variable field are treated as independent quantities. The new non-linear viscous evolution equation satisfies a non-negative viscous dissipation not only in the continuous case, but also in the fully discretized system. The initial boundary value problem is discretized by using finite elements in space and time. Thereby, the temporal approximation is performed prior to the spatial approximation in order to preserve the stress objectivity for finite rotation increments (incremental objectivity). Although the present approach makes possible to design schemes of arbitrary order, the focus is on finite elements relying on linear Lagrange polynomials for the sake of clearness. The discrete energy,momentum consistency is based on the collocation property and an enhanced second Piola,Kirchhoff stress tensor. The obtained coupled non-linear algebraic equations are consistently linearized. The corresponding iterative solution procedure is associated with newly proposed convergence criteria, which take the discrete energy consistency into account. The iterative solution procedure is therefore not complicated by different scalings in the independent variables, since the motion of the element is taken into account for solving the viscous evolution equation. Representative numerical simulations with various boundary conditions show the superior stability of the new time-integration algorithm in comparison with the ordinary midpoint rule. Both the quasi-rigid deformations during a free flight, and large deformations arising in a dynamic tensile test are considered. Copyright © 2009 John Wiley & Sons, Ltd. [source] Robust adaptive remeshing strategy for large deformation, transient impact simulationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2006Tobias Erhart Abstract In this paper, an adaptive approach, with remeshing as essential ingredient, towards robust and efficient simulation techniques for fast transient, highly non-linear processes including contact is discussed. The necessity for remeshing stems from two sources: the capability to deal with large deformations that might even require topological changes of the mesh and the desire for an error driven distribution of computational resources. The overall computational approach is sketched, the adaptive remeshing strategy is presented and the crucial aspect, the choice of suitable error indicator(s), is discussed in more detail. Several numerical examples demonstrate the performance of the approach. Copyright © 2005 John Wiley & Sons, Ltd. [source] Assessment of conservative load transfer for fluid,solid interface with non-matching meshesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2005R. K. Jaiman Abstract We present a detailed comparative study of three conservative schemes used to transfer interface loads in fluid,solid interaction simulations involving non-matching meshes. The three load transfer schemes investigated are the node-projection scheme, the quadrature-projection scheme and the common-refinement based scheme. The accuracy associated with these schemes is assessed with the aid of 2-D fluid,solid interaction problems of increasing complexity. This includes a static load transfer and three transient problems, namely, elastic piston, superseismic shock and flexible inhibitor involving large deformations. We show how the load transfer schemes may affect the accuracy of the solutions along the fluid,solid interface and in the fluid and solid domains. We introduce a grid mismatching function which correlates well with the errors of the traditional load transfer schemes. We also compare the computational costs of these load transfer schemes. Copyright © 2005 John Wiley & Sons, Ltd. [source] Finite element formulation for modelling large deformations in elasto-viscoplastic polycrystalsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2004Karel Matou Abstract Anisotropic, elasto-viscoplastic behaviour in polycrystalline materials is modelled using a new, updated Lagrangian formulation based on a three-field form of the Hu-Washizu variational principle to create a stable finite element method in the context of nearly incompressible behaviour. The meso-scale is characterized by a representative volume element, which contains grains governed by single crystal behaviour. A new, fully implicit, two-level, backward Euler integration scheme together with an efficient finite element formulation, including consistent linearization, is presented. The proposed finite element model is capable of predicting non-homogeneous meso-fields, which, for example, may impact subsequent recrystallization. Finally, simple deformations involving an aluminium alloy are considered in order to demonstrate the algorithm. Copyright © 2004 John Wiley & Sons, Ltd. [source] A low-order, hexahedral finite element for modelling shells,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2004Samuel W. Key Abstract A thin, eight-node, tri-linear displacement, hexahedral finite element is the starting point for the derivation of a constant membrane stress resultant, constant bending stress resultant shell finite element. The derivation begins by introducing a Taylor series expansion for the stress distribution in the isoparametric co-ordinates of the element. The effect of the Taylor series expansion for the stress distribution is to explicitly identify those strain modes of the element that are conjugate to the mean or average stress and the linear variation in stress. The constant membrane stress resultants are identified with the mean stress components, and the constant bending stress resultants are identified with the linear variation in stress through the thickness along with in-plane linear variations of selected components of the transverse shear stress. Further, a plane-stress constitutive assumption is introduced, and an explicit treatment of the finite element's thickness is introduced. A number of elastic simulations show the useful results that can be obtained (tip-loaded twisted beam, point-loaded hemisphere, point-loaded sphere, tip-loaded Raasch hook, and a beam bent into a ring). All of the gradient/divergence operators are evaluated in closed form providing unequivocal evaluations of membrane and bending strain rates along with the appropriate divergence calculations involving the membrane stress and bending stress resultants. The fact that a hexahedral shell finite element has two distinct surfaces aids sliding interface algorithms when a shell folds back on itself when subjected to large deformations. Published in 2004 by John Wiley & Sons, Ltd. [source] A 3D mortar method for solid mechanics,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004Michael A. Puso Abstract A version of the mortar method is developed for tying arbitrary dissimilar 3D meshes with a focus on issues related to large deformation solid mechanics. Issues regarding momentum conservation, large deformations, computational efficiency and bending are considered. In particular, a mortar method formulation that is invariant to rigid body rotations is introduced. A scheme is presented for the numerical integration of the mortar surface projection integrals applicable to arbitrary 3D curved dissimilar interfaces. Here, integration need only be performed at problem initialization such that coefficients can be stored and used throughout a quasi-static time stepping process even for large deformation problems. A degree of freedom reduction scheme exploiting the dual space interpolation method such that direct linear solution techniques can be applied without Lagrange multipliers is proposed. This provided a significant reduction in factorization times. Example problems which touch on the aforementioned solid mechanics related issues are presented. Published in 2003 by John Wiley & Sons, Ltd. [source] Improvements and algorithmical considerations on a recent three-dimensional model describing stress-induced solid phase transformationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002Ferdinando Auricchio Abstract During mechanical loading,unloading cycles shape-memory alloys (SMA) are able to undergo large deformations without showing residual strains (pseudoelasticity) or recovering them through thermal cycles (shape memory effect). Motivated by stress-induced solid phase transformations, these unique behaviours induce the SMA exploitation in innovative and commercially valuable applications, stimulating, consequently, the interest in the development of constitutive models. Also if many models are now available in the literature, effective three-dimensional proposals are still few and limited in several aspects. In this paper, a three-dimensional thermomechanical model recently proposed by Souza et al. (European Journal of Mechanics,A/Solids, 1998; 17: 789,806.) is taken into consideration; such a model is of particular interest for its effectiveness and flexibility, but it also shows some limitations and missing links in the algorithmical counterparts. This work discusses some improvements to the original model as well as the development and the implementation of a robust integration algorithm to be adopted in a numerical scheme, such as a finite-element framework. Copyright © 2002 John Wiley & Sons, Ltd. [source] | ||||||||||||||||