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Self-poling of ferroelectric films, i.e., a preferred, uniform direction of the ferroelectric polarization in as-grown samples is often observed yet poorly understood despite its importance for device applications. The multiferroic perovskite BiFeO3, which crystallizes in two distinct structural polymorphs depending on applied epitaxial strain, is well known to exhibit self-poling. This study investigates the effect of self-poling on the monoclinic domain configuration and the switching properties of the two polymorphs of BiFeO3 (R′ and T′) in thin films grown on LaAlO3 substrates with slightly different La0.3Sr0.7MnO3 buffer layers. This study shows that the polarization state formed during the growth acts as “imprint” on the polarization and that switching the polarization away from this self-poled direction can only be done at the expense of the sample's monoclinic domain configuration. The observed reduction of the monoclinic domain size is largely reversible; hence, the domain size is restored when the polarization is switched back to its original orientation. This is a direct consequence of the growth taking place in the polar phase (below Tc). Switching the polarization away from the preferred configuration, in which defects and domain patterns synergistically minimize the system's energy, leads to a domain state with smaller (and more highly strained and distorted) monoclinic domains.

This work is motivated by the current numerical limitation in multiscale simulation of ductile fracture processes at scale down to the microstructure size and aims to overcome the difficulties in 3D complicated mesh generation and locally extremely large strain analysis (local mesh distortion). The proposed 'conforming local meshfree approximation' directly and exactly satisfies displacement compatibility on a non-conforming assembly mesh. Local meshfree nodes, which can be freely placed and move on a finite element mesh, describe local large deformation. The improved accuracy on non-conforming mesh, the exactness in geometry representation on a structured mesh, and the good tolerance to mesh distortion are demonstrated by numerical examples.

Recent development in the multiscale method based on the bridging scale concept is presented with an emphasis on complex material systems. The bridging scale method (BSM) was originally proposed by Wagner and Liu (J. Comput. Phys. 2003; 190:249–274) as an effective way of treating the interface in coupled atomistic/continuum simulation. Since its publication, the BSM has become a very useful paradigm that has been applied to solve a host of problems in mechanical sciences of complex material systems. In this paper, we present a review on the recent developments. We first describe the application of BSM to the coupled atomistic/continuum simulation of dynamic fracture. The important extensions within the framework of space–time method and multiscale non-equilibrium molecular dynamics are then presented. We then focus on the multiresolution continuum theory that inherits the BSM concept in the analysis of heterogeneous material structures. Recent work of incorporating statistical factors into this model based on the concurrent nested homogenization of randomness of the material structures is highlighted. Finally, we present the use of the bridging scale concept in resolving the electron-mechanical coupling mechanism. The robustness of the BSM is demonstrated through many benchmark problems and application examples. Copyright © 2010 John Wiley & Sons, Ltd.

New technological advances today allow for a range of advanced composite materials, including multilayer materials and nanofiber-matrix composites. In this context, the key to developing advanced materials is the understanding of the interplay between the various physical scales present, from the atomic level interactions to the microstructural composition and the macroscale behavior. Using the developing ‘multiresolution data sets mechanics’, the ‘predictive science-based governing laws of the materials microstructure evolutions’ are derived and melted into a ‘stochastic multiresolution design framework.’ Under such a framework, the governing laws of the materials microstructure evolution will be essential to assess, across multiple scales, the impact of multiscale material design, geometry design of a structure, and the manufacturing process conditions, by following the cause–effect relationships from structure to property and then to performance. The future integrated multiscale analysis system will be constructed based on a probabilistic complexity science-based mathematical framework. Its verification, validation and uncertainty quantification are done through carefully designed experiments, and the life-cycled materials design for products design and manufacturing is performed through the use of petascale computing. The various techniques of microstructure reconstruction result in the generation of model microstructures that, at some level, has the same statistical properties as the real heterogeneous media. Having reconstructed the heterogeneous medium, one can then evaluate its effective properties via direct numerical simulation and compare these values with experimentally measured properties of the actual medium. The proposed analysis will be dynamic in nature to capture the multi-stage historical evolvement of material/structure performance over the life span of a product. In addition to providing more accurate assessment of structure performance with stochastic multiscale analysis, our development will provide the capability of predicting structure failures and system reliability to enable more reliable design and manufacturing decisions in product development. Copyright © 2009 John Wiley & Sons, Ltd.

This paper focuses on the non-linear responses in thin cylindrical structures subjected to combined mechanical and thermal loads. The coupling effects of mechanical deformation and temperature in the material are considered through the development of a thermo-elasto-viscoplastic constitutive model at finite strain. A meshfree Galerkin approach is used to discretize the weak forms of the energy and momentum equations. Due to the different time scales involved in thermal conduction and failure development, an explicit–implicit time integration scheme is developed to link the time scale differences between the two key mechanisms. We apply the developed approach to the analysis of the failure of cylindrical shell subjected to both heat sources and internal pressure. The numerical results show four different failure modes: dynamic fragmentation, single crack with branch, thermally induced cracks and cracks due to the combined effects of pressure and temperature. These results illustrate the important roles of thermal and mechanical loads with different time scales. Copyright © 2008 John Wiley & Sons, Ltd.

A novel white-beam microdiffraction analysis of defects, strains and tilts in a free standing m -plane GaN film grown via hydride vapor phase epitaxy is presented. It is shown that misfit dislocations are grouped within cell boundaries creating local lattice rotations (tilts) between the growing cells. Distribution of lattice rotations in the film is not homogeneous. Regions of large rotations are separated by low rotations regions. The dominating rotation axis is parallel [110] direction. High in plane shear stress component is observed along [0001]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A weak form and an implementation are given for fluid-structure interaction by the immersed/fictitious element method for compressible fluids. The weak form is applicable to models where the fluid is described by Eulerian coordinates while the solid is described by Lagrangian coordinates, which suits their intrinsic characteristics. A unique feature of the method is the treatment of the fictitious fluid by a Lagrangian description, which simplifies the interface conditions. Methods for enforcing volumetric consistency between the fluid and solid and treating thin members are given. Although a compressible viscous fluid is considered here, the new developments can be applied to incompressible fluids.

The major purpose of this work is to investigate the performance of the bridging scale method (BSM), a multiscale simulation framework for the dynamic, concurrent coupling of atomistics to continua, in capturing shear-dominant failure. The shear-dominant failure process considered in this work is intersonic crack propagation along a weak plane in an elastic material, similar to the seminal molecular dynamics (MD) simulations by Abraham and Gao (Phys. Rev. Lett. 2000; 84(14):3113–3116). We show that the BSM simulations accurately capture the essential physics of the intersonic crack propagation, including the formation of a daughter crack and the sudden acceleration of the crack to a velocity exceeding the material shear wave speed. It is also demonstrated that the non-reflecting boundary condition can adequately dissipate the strongly localized wave formed by the Mach cone after the crack accelerates beyond the material shear wave speed. Finally, we provide the algorithm for our implementation of the BSM, as well as the code used to determine the damping kernels via a newly adopted technique which is less expensive than previous methods. Copyright © 2007 John Wiley & Sons, Ltd.

We present a novel approach to numerical modelling of the crystalline solid as a heat bath. The approach allows bringing together a small and a large crystalline domain, and model accurately the resultant interface, using harmonic assumptions for the larger domain, which is excluded from the explicit model and viewed only as a hypothetic heat bath. Such an interface is non-reflective for the elastic waves, as well as providing thermostatting conditions for the small domain. The small domain can be modelled with a standard molecular dynamics approach, and its interior may accommodate arbitrary non-linearities. The formulation involves a normal decomposition for the random thermal motion term R(t) in the generalized Langevin equation for solid–solid interfaces. Heat bath temperature serves as a parameter for the distribution of the normal mode amplitudes found from the Gibbs canonical distribution for the phonon gas. Spectral properties of the normal modes (polarization vectors and normal frequencies) are derived from the interatomic potential. Approach results in a physically motivated random force term R(t) derived consistently to represent the correlated thermal motion of lattice atoms. We describe the method in detail, and demonstrate applications to one- and two-dimensional lattice structures. Copyright © 2006 John Wiley & Sons, Ltd.

A new method is proposed for modelling the electrokinetic-induced mechanical motion of particles in a fluid domain under an applied electric field. In this method, independent solid meshes move in a fixed background field mesh that models the fluid and the electric field. This simple strategy removes the need for expensive mesh updates. Furthermore, the reproducing kernel particle functions enable efficient coupling of various immersed deformable solids with the surrounding viscous fluid in the presence of an applied electric field. The electric force on a particle is calculated by the Maxwell stress tensor method. For the first time, three-dimensional assembly of nano/biomaterials of various geometries and electrical properties have been comprehensively studied using the new method. Simulation of the dynamic process of electro-manipulation of individual and multiple cells agrees well with experimental data. Preliminary results for selective deposition of viruses and stretching of a DNA molecule are also presented. Copyright © 2006 John Wiley & Sons, Ltd.

In this paper, we present a mathematical framework of the bridging scale method (BSM), recently proposed by Liu et al. Under certain conditions, it had been designed for accurately and efficiently simulating complex dynamics with different spatial scales. From a clear and consistent derivation, we identify two error sources in this method. First, we use a linear finite element interpolation, and derive the coarse grid equations directly from Newton's second law. Numerical error in this length scale exists mainly due to inadequate approximation for the effects of the fine scale fluctuations. An modified linear element (MLE) scheme is developed to improve the accuracy. Secondly, we derive an exact multiscale interfacial condition to treat the interfaces between the molecular dynamics region ΩD and the complementary domain ΩC, using a time history kernel technique. The interfacial condition proposed in the original BSM may be regarded as a leading order approximation to the exact one (with respect to the coarsening ratio). This approximation is responsible for minor reflections across the interfaces, with a dependency on the choice of ΩD. We further illustrate the framework and analysis with linear and non-linear lattices in one-dimensional space. Copyright © 2005 John Wiley & Sons, Ltd.

SUMMARY We present a method to numerically calculate a non-reflecting boundary condition which is applicable to atomistic, continuum and coupled multiscale atomistic/continuum simulations. The method is based on the assumption that the forces near the domain boundary can be well represented as a linear function of the displacements, and utilizes standard Laplace and Fourier transform techniques to eliminate the unnecessary degrees of freedom. The eliminated degrees of freedom are accounted for in a time-history kernel that can be calculated for arbitrary crystal lattices and interatomic potentials, or regular finite element meshes using an automated numerical procedure. The new theoretical developments presented in this work allow the application of the method to non-nearest neighbour atomic interactions; it is also demonstrated that the identical procedure can be used for finite element and mesh-free simulations. We illustrate the effectiveness of the method on a one-dimensional model problem, and calculate the time-history kernel for FCC gold using the embedded atom method (EAM). Copyright ! 2005 John Wiley & Sons, Ltd.

Computer simulations of atomic scale processes in solids are often associated with the issue of spurious reflection of elastic waves at the boundaries of a molecular dynamics domain. In this paper, we propose an approach to emulate non-reflecting boundary conditions in atomistic simulations of crystalline solids. Harmonic response of the outer, non-simulated, region is accurately represented by a memory function, related to the lattice dynamics Green's function. The outward wave flow is cancelled due to work done by the corresponding response forces. Performance of method, dependent on a series of method parameters, is illustrated on a benchmark problem. Copyright © 2004 John Wiley & Sons, Ltd.

A discontinuous reproducing kernel element approximation is proposed in the case where weak discontinuity exists over an interface in the physical domain. The proposed method can effectively take care of the discontinuity of the derivative by truncating the window function and global partition polynomials. This new approximation keeps the advantage of both finite element methods and meshfree methods as in the reproducing kernel element method. The approximation has the interpolation property if the support of the window function is contained in the union of the elements associated with the corresponding node; therefore, the continuity of the primitive variables at nodes on the interface is ensured. Furthermore, it is smooth on each subregion (or each material) separated by the interface. The major advantage of the method is its simplicity in implementation and it is computationally efficient compared to other methods treating discontinuity. The convergence of the numerical solution is validated through calculations of some material discontinuity problems. Copyright © 2005 John Wiley & Sons, Ltd.

A finite element model is presented for mixed lubrication of journal-bearing systems operating in adverse conditions. The asperity effects on contact and lubrication at large eccentricity ratios are modelled. The elastic deformation due to both hydrodynamic and contact pressure, and the cavitation of the lubricant film are considered in the model system. Two verification problems with both theoretical and experimental comparisons are given to show the effectiveness of this model. Finally, a new example is presented which discusses the influence of waviness depth, secondary roughness, external force and shaft speed on the mixed lubrication. Copyright © 2004 John Wiley & Sons, Ltd.

We describe a new version of the moving particle finite element method (MPFEM) that provides solutions within a C 0 finite element framework. The finite elements determine the weighting for the moving partition of unity. A concept of 'General Shape Function' is proposed which extends regular finite element shape functions to a larger domain. These are combined with Shepard functions to obtain a smooth approximation. The Moving Particle Finite Element Method combines desirable features of finite element and meshfree methods. The proposed approach, in fact, can be interpreted as a 'moving partition of unity finite element method' or 'moving kernel finite element method'. This method possesses the robustness and efficiency of the C 0 finite element method while providing at least C 1 continuity.

SUMMARY The red blood cell (RBC) aggregation plays an important role in many physiological phenomena, in particular the atherosclerosis and thrombotic processes. In this research, we introduce a new modelling technique that couples Navier-Stokes equations with protein molecular dynamics to investigate the behaviours of RBC aggregates and their eects on the blood rheology. In essence, the Lagrangian solid mesh, which represents the immersed deformable cells, is set to move on top of a background Eulerian mesh. The eects of cell-cell interaction (adhesive =repulsive) and hydrody- namic forces on RBC aggregates are studied by introducing equivalent protein molecular potentials into the immersednite element method. The aggregation of red blood cells in quiescentuids is simulated. The de-aggregation of a RBC cluster at dierent shear rates is also investigated to pro- vide an explanation of the shear-rate-dependence of the blood viscoelastic properties. Finally, the in- �uences of cell-cell interaction, RBC rigidity, and vessel geometry are addressed in a series of test cases with deformable cells (normal and sickle RBCs) passing through micro- and capillary vessels. Copyright ? 2004 John Wiley & Sons, Ltd.

In this paper, the implementation of a 3-D parallel CFD code using the meshless method. Reproducing Kernel Particle Method (RKPM) is described. A novel procedure for implementing the essential boundary condition using the hierarchical enrichment method is presented. The Total Arbitrary Lagrangian Eulerian (ALE) formulations using Finite Element Method are developed and implemented in the parallel code. The flow past a cylinder problem served as examples throughout the paper. Both methods have shown promising results compared with analytical solution. Copyright © 2003 John Wiley & Sons, Ltd.

A technique for the numerical simulation of suspensions of particles in fluid based on the extended finite element method (X-FEM) is developed. In this method, the particle surfaces need not conform to the finite element boundaries, so that moving particles can be simulated without remeshing. The finite element basis is enriched with the Stokes flow solution for flow past a single particle and the lubrication theory solution for flow between particles. The latter enrichment allows the simulation of particles that come arbitrarily close together without refining the mesh in the gap between them. Example problems illustrating both types of enrichment are shown, along with a study of a 50% solution in channel flow. Copyright © 2003 John Wiley & Sons, Ltd.

This paper presents the fundamental concepts behind the moving particle finite element method, which combines salient features of finite element and meshfree methods. The proposed method alleviates certain problems that plague meshfree techniques, such as essential boundary condition enforcement and the use of a separate background mesh to integrate the weak form. The method is illustrated via two-dimensional linear elastic problems. Numerical examples are provided to show the capability of the method in benchmark problems. Copyright © 2001 John Wiley & Sons, Ltd.

The finite-element method, when used with a basis made up of piecewise polynomials, often requires the generation of a very fine computational mesh in order to capture localized solution phenomena such as boundary layers or near-singularities. Enrichment of the basis with additional functions, obtained through analytical or experimental means, can allow for a coarser mesh and more accurate solution. We introduce an enrichment scheme in which an interaction or ‘bridging’ scale term is used to separate the basis formed by the enrichment functions from the original set of basis functions, in effect making the enrichment hierarchical. This separation of scales allows the simple application of essential boundary conditions. It also allows a quantification of the effects of the enrichment, leading to strategies for error estimation and control of the stiffness matrix condition number. We also find that this formulation allows for the simple application of essential boundary conditions for mesh-free shape functions, which are notoriously problematic. We find that for multiple dimensions, care must be taken to derive a weak form which is truly consistent with the strong form on the essential boundary. Copyright © 2001 John Wiley & Sons, Ltd.

Implementation of Dirichlet boundary conditions in mesh-free methods is problematic. In Wagner and Liu (International Journal for Numerical Methods in Engineering 2001; 50:507), a hierarchical enrichment technique is introduced that allows a simple implementation of the Dirichlet boundary conditions. In this paper, we provide some error analysis for the hierarchical enrichment mesh-free technique. We derive optimal order error estimates for the hierarchical enrichment mesh-free interpolants. For one-dimensional elliptic boundary value problems, we can directly apply the interpolation error estimates to obtain error estimates for the mesh-free solutions. For higher-dimensional problems, derivation of error estimates for the mesh-free solutions depends on the availability of an inverse inequality. Numerical examples in 1D and 2D are included showing the convergence behaviour of mesh-free interpolants and mesh-free solutions when the hierarchical enrichment mesh-free technique is employed. Copyright © 2001 John Wiley & Sons, Ltd.

In this paper four multiple scale methods are proposed. The meshless hierarchical partition of unity is used as a multiple scale basis. The multiple scale analysis with the introduction of a dilation parameter to perform multiresolution analysis is discussed. The multiple field based on a 1-D gradient plasticity theory with material length scale is also proposed to remove the mesh dependency difficulty in softening/localization problems. A non-local (smoothing) particle integration procedure with its multiple scale analysis are then developed. These techniques are described in the context of the reproducing kernel particle method. Results are presented for elastic-plastic one-dimensional problems and 2-D large deformation strain localization problems to illustrate the effectiveness of these methods. Copyright © 2000 John Wiley & Sons, Ltd.

A parallel computational implementation of modern meshless methods is presented for explicit dynamic analysis. The procedures are demonstrated by application of the Reproducing Kernel Particle Method (RKPM). Aspects of a coarse grain parallel paradigm are detailed for a Lagrangian formulation using model partitioning. Integration points are uniquely defined on separate processors and particle definitions are duplicated, as necessary, so that all support particles for each point are defined locally on the corresponding processor. Several partitioning schemes are considered and a reduced graph-based procedure is presented. Partitioning issues are discussed and procedures to accommodate essential boundary conditions in parallel are presented. Explicit MPI message passing statements are used for all communications among partitions on different processors. The effectiveness of the procedure is demonstrated by highly deformable inelastic example problems.

In this paper, a comprehensive account on using mesh-free methods to simulate strain localization in inelastic solids is presented. Using an explicit displacement-based formulation in mesh-free computations, high-resolution shear-band formations are obtained in both two-dimensional (2-D) and three-dimensional (3-D) simulations without recourse to any mixed formulation, discontinuous/incompatible element or special mesh design. The numerical solutions obtained here are insensitive to the orientation of the particle distributions if the local particle distribution is quasi-uniform, which, to a large extent, relieves the mesh alignment sensitivity that finite element methods suffer. Moreover, a simple h-adaptivity procedure is implemented in the explicit calculation, and by utilizing a mesh-free hierarchical partition of unity a spectral (wavelet) adaptivity procedure is developed to seek high-resolution shear-band formations. Moreover, the phenomenon of multiple shear band and mode switching are observed in numerical computations with a relatively coarse particle distribution in contrast to the costly fine-scale finite element simulations. Copyright © 2000 John Wiley & Sons, Ltd.

A uni ed stability analysis of meshless methods with Eulerian and Lagrangian kernels is presented. Three types of instabilities were identi ed in one dimension: an instability due to rank de ciency, a tensile instability and a material instability which is also found in continua. The stability of particle methods with Eulerian and Lagrangian kernels is markedly di erent: Lagrangian kernels do not exhibit the tensile instability. In both kernels, the instability due to rank de ciency can be suppressed by stress points. In two dimensions the stabilizing e ect of stress points is dependent on their locations. It was found that the best approach to stable particle discretizations is to use Lagrangian kernels with stress points. The stability of the least-squares stabilization was also studied. Copyright ? 2000 John Wiley & Sons, Ltd.

In this part of the work, the meshless hierarchical partition of unity proposed in [1], referred here as Part I, is used as a multiple scale basis in numerical computations to solve practical problems. The applications discussed in the present work fall into two categories: (1) a wavelet adaptivity refinement procedure; and (2) a so-called wavelet Petrov–Galerkin procedure. In the applications of wavelet adaptivity, the hierarchical reproducing kernels are used as a multiple scale basis to compute the numerical solutions of the Helmholtz equation, a model equation of wave propagation problems, and to simulate shear band formation in an elasto-viscoplastic material, a problem dictated by the presence of the high gradient deformation. In both numerical experiments, numerical solutions with high resolution are obtained by inserting the wavelet-like basis into the primary interpolation function basis, a process that may be viewed as a spectral p-type refinement. By using the interpolant that has synchronized convergence property as a weighting function, a wavelet Petrov–Galerkin procedure is proposed to stabilize computations of some pathological problems in numerical computations, such as advection–diffusion problems and Stokes' flow problem; it offers an alternative procedure in stablized methods and also provides some insight, or new interpretation of the method. Detailed analysis has been carried out on the stability and convergence of the wavelet Petrov–Galerkin method. Copyright © 1999 John Wiley & Sons, Ltd.

Multiresolution analysis based on the reproducing kernel particle method (RKPM) is developed for computational fluid dynamics. An algorithm incorporating multiple-scale adaptive refinement is introduced. The concept of using a wavelet solution as an error indicator is also presented. A few representative numerical examples are solved to illustrate the performance of this new meshless method.

Multiple scale methods based on reproducing kernel and wavelet analysis are developed. These permit the response of a system to be separated into different scales. These scales can be either the wave numbers corresponding to spatial variables or the frequencies corresponding to temporal variables, and each scale response can be examined separately. This complete characterization of the unknown response is performed through the integral window transform, and a space-scale and time-frequency localization process is achieved by dilating the flexible multiple scale window function. An error estimation technique based on this decomposition algorithm is developed which is especially useful for local mesh refinement and convergence studies. This flexible space-scale window function can be constructed to resemble the well-known unstructured multigrid and hp-adaptive finite element methods. However, the multiple scale adaptive refinements are performed simply by inserting nodes into the highest wavelet scale solution region and at the same time narrowing the window function. Hence hp-like adaptive refinements can be performed without a mesh.

This paper explores a Reproducing Kernel Particle Method (RKPM) which incorporates several attractive features. The emphasis is away from classical mesh generated elements in favour of a mesh free system which only requires a set of nodes or particles in space. Using a Gaussian function or a cubic spline function, flexible window functions are implemented to provide refinement in the solution process. It also creates the ability to analyse a specific frequency range in dynamic problems reducing the computer time required. This advantage is achieved through an increase in the critical time step when the frequency range is low and a large window is used. The stability of the window function as well as the critical time step formula are investigated to provide insight into RKPMs. The predictions of the theories are confirmed through numerical experiments by performing reconstructions of given functions and solving elastic and elastic–plastic one-dimensional (1-D) bar problems for both small and large deformation as well as three 2-D large deformation non-linear elastic problems. Numerical and theoretical results show the proposed reproducing kernel interpolation functions satisfy the consistency conditions and the critical time step prediction; furthermore, the RKPM provides better stability than Smooth Particle Hydrodynamics (SPH) methods. In contrast with what has been reported in SPH literature, we do not find any tensile instability with RKPMs.

A new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time-frequency and space-wave number localization of a window function is developed. This method is motivated by the theory of wavelets and also has the desirable attributes of the recently proposed smooth particle hydrodynamics (SPH) methods, moving least squares methods (MLSM), diffuse element methods (DEM) and element-free Galerkin methods (EFGM). The proposed method maintains the advantages of the free Lagrange or SPH methods; however, because of the addition of a correction function, it gives much more accurate results. Therefore it is called the reproducing kernel particle method (RKPM). In computer implementation RKPM is shown to be more efficient than DEM and EFGM. Moreover, if the window function is C∞, the solution and its derivatives are also C∞ in the entire domain. Theoretical analysis and numerical experiments on the 1D diffusion equation reveal the stability conditions and the effect of the dilation parameter on the unusually high convergence rates of the proposed method. Two-dimensional examples of advection-diffusion equations and compressible Euler equations are also presented together with 2D multiple-scale decompositions.

The complex contact conditions on the three-dimensional (3-D) tooling-workpiece interface, such as non-penetrations, slip–stick phenomena and friction forces due to the relative motion of contacting surfaces, are of vital importance in metal forming operations. Usually, a lubricant is provided as an interface medium between the tool and the workpiece to avoid strain localization, wear and surface damage. Hence, a simple friction law such as Coulomb friction, involving only a constant friction coefficient, cannot model the contact phenomena accurately. In this research, a realistic friction model, which accounts for the tribological behaviour, and most importantly, the effect of surface roughness on the lubricated contact, is developed. This model has been implemented in a 3-D arbitrary Lagrangian Fulerian finite element code for metal forming analysis. The applicability of the proposed model is demonstrated by the simulation of fluid-lubricated thrust bearing and sheet metal stretch forming.

In this paper, the stochastic boundary element method, which combines the mixed boundary integral equations method explored in Reference 1 with the first-order reliability method, is developed to study probabilistic fatigue crack growth. Due to the high degree of complexity and non-linearity of the response, direct differentiation coupied with the response-surface method is employed to determine the response gradient. Three random processes, the mode I and mode II. stress intensity factors and the crack direction angle, are included in the expression of the response gradient. The sensitivity of these random processes is determined using a first-order response model. An iteration scheme based on the HL-RF method2 is applied to locate the most probable failure point on the limit-state surface. The accuracy and efficiency of the stochastic boundary element method are evaluated by comparing the cumulative distribution function of the fatigue life obtained with Monte Carlo simulation. The reliability index and the corresponding probability of failure are calculated for a fatigue crack growth problem with randomness in the crack geometry, defect geometry, fatigue parameters and external loads. The response sensitivity of each primary random variable at the design point is determined to show its role in the fatigue failure. The variation of each primary random variable at the design point with the change of probability of failure is also presented in numerical examples.

In this paper, the mixed boundary integral equation method is developed to study the elastic interactions of a fatigue crack and a micro-defect such as a void, a rigid inclusion or a transformation inclusion. The method of pseudo-tractions is employed to study the effect of a transformation inclusion. An enriched element which incorporates the mixed-mode stress intensity factors is applied to characterize the singularity at a moving crack tip. In order to evaluate the accuracy of the numerical procedure, the analysis of a crack emanating from a circular hole in a finite plate is performed and the results are compared with the available numerical solution. The effects of various micro-defects on the crack path and fatigue life are investigated. The results agree with the experimental observations.

A method that incorporates the hydrodynamic lubrication analysis into the arbitrary Lagrangian Eulerian (ALE) finite element analysis is developed for steady-state strip rolling simulation. By employing the ALE formulation, only part of the workpiece, which is subjected to large plastic deformation within the roll-bite region, is modelled, so that the computational cost is substantially reduced. In the hydrodynamic lubrication formulation, the effect of surface roughness on the lubricant flow is taken into consideration by the use of an average flow model. The friction stress is expressed in terms of forming variables such as surface roughness, lubricant and workpiece properties, film thickness, forming speed and process geometry. Furthermore, the elastic deformation of rolls is also analysed by the boundary element method to avoid the finite element discretization inside the rolls. Two numerical examples, aluminium and steel strip rolling processes, are presented to demonstrate the merits of the proposed method.

In this paper, a ring rolling process is analysed by the Arbitrary Lagrangian Eulerian (ALE) finite element method. Phenomena associated with the process, such as large deformations, elastoplastic material behaviour and the friction on the interface, are included in the analysis. Special modelling on driven, idle and guide rolls is given. Results which include the overall shape of the formed ring, the time histories of roll separating force and driving torque, the distribution of the normal pressure on the ring–roll interface as well as the distribution of effective stresses in the formed ring, are also presented.

New temporal and spatial discretization methods are developed for multiple scale structural dynamic problems. The concept of fast and slow time scales is introduced for the temporal discretization. The required time step is shown to be dependent only on the slow time scale, and therefore, large time steps can be used for high frequency problems. To satisfy the spatial counterpart of the requirement on time step constraint, finite-spectral elements and finite wave elements are developed. Finite-spectral element methods combine the usual finite elements with the fast convergent spectral functions to obtain a faster convergence rate; whereas, finite wave elements are developed in parallel to the temporal shifting technique. Therefore, the spatial resolution is increased substantially. These methods are especially applicable to structural acoustics and linear space structures. Numerical examples are presented to illustrate the effectiveness of these methods.

A Galerkin Finite Element formulation for the dynamic stability analysis of liquid-filled shells is given in this paper. The coupling among the axial and circumferential modes is investigated. The dynamic stability characteristics of two liquid-filled storage tanks subjected to vertical, horizontal and rocking seismic excitations are presented. It is shown that a tall tank tends to buckle at distinct frequencies; and for cos θ-type ground excitation, cos 2θ, cos 3θ and cos 4θ are the dominant modes of failure. On the other hand, in a broad tank, buckling regions overlap each other. In particular, for cos θ-type ground excitation, the dominant buckling modes are cos 6θ to cos 9θ, and also cos 12θ to cos 14θ.

A convergence analysis is performed for an element-partitioned subcycling algorithm for the semi-discrete heat equation. It is shown that the algorithm generally attains first-order rate-of-convergence.

A method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one-point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2 and 1 for the normalized stabilization parameter lead to the 5-point finite difference, 9-point finite difference and fully integrated finite element operators, respectively, for rectangular meshes; numerical experiments reported here show that the three have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.

The probabilistic finite element method (PFEM) is formulated for linear and non-linear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in non-linear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem and a two-dimensional plane-stress beam bending problem. The moments calculated compare favourably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

The computational methods used to predict and optimize the thermal-structural behaviour of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a difficult yet critical factor in the efficient solution of such problems. Therefore mixed time integration methods for transient thermal analysis of structures are being developed. This proposed methodology would be readily adaptable to existing computer programs for structural thermal analysis.