A formulation for electrostatic‐mechanical contact and its numerical solution

The progress in advanced technology fields requires more and more sophisticated formulations to consider contact problems properly. This paper is devoted to the development of a new constitutive model for electrostatic‐mechanical contacts, based on a micro–macro approach to describe the contact behaviour. The electric‐mechanical contact constitutive law is obtained considering the real microscopic shape of the contacting surfaces, the microscopic behaviour of force transmission and current flow. Some thermo‐mechanical macroscopic models based on microscopic characterizations have already been developed to compute the normal and tangential contact stiffness and the thermal contact resistance. On the basis of such macroscopic models, a similar model, suitable for the electric‐mechanical field, is developed. With reference to the thermal constriction resistance the electric contact resistance is studied, assuming a flux tube around each contacting asperity, and choosing a suitable geometry for its narrowing at the contact zone. The contact element geometry is based on well known theoretical and experimental micro‐mechanical laws, suitably adapted for the FEM formulation. The macroscopic stiffness matrix is calculated on the basis of the microscopic laws and it is continuously updated as a function of the changes in the mechanical and electric significant parameters. A consistent linearization of the set of equations is developed to improve the computational speed, within the framework of implicit methods. Copyright © 2005 John Wiley & Sons, Ltd.     

A 3D beam‐to‐beam contact finite element for coupled electric–mechanical fields

In this paper the formulation of an electric–mechanical beam‐to‐beam contact element is presented. Beams with circular cross‐sections are assumed to get in contact in a point‐wise manner and with clean metallic surfaces. The voltage distribution is influenced by the contact mechanics, since the current flow is constricted to small contacting spots. Therefore, the solution is governed by the contacting areas and hence by the contact forces. As a consequence the problem is semi‐coupled with the mechanical field influencing the electric one. The electric–mechanical contact constraints are enforced with the penalty method within the finite element technique. The virtual work equations for the mechanical and electric fields are written and consistently linearized to achieve a good level of computational efficiency with the finite element method. The set of equations is solved with a monolithic approach. Copyright © 2005 John Wiley & Sons, Ltd.     

A yield‐limited Lagrange multiplier formulation for frictional contact

An analogy with rigid plasticity is used to develop a constitutive framework for quasi‐static frictional contact between finitely deforming solids. Within this setting, a Lagrange multiplier method is used to impose a sharp distinction between stick and slip. The scope of the multipliers is limited by a constitutively defined ‘yield’ function and a finite element‐based predictor–corrector scheme is employed to efficiently determine the regions of stick and slip and the associated tractions. Selected simulations of planar quasi‐static problems are presented to validate the method and illustrate its capabilities. Copyright © 2000 John Wiley & Sons, Ltd.     

Bridging domain methods for coupled atomistic–continuum models with L2 or H1 couplings

A bridging domain method for coupled atomistic–continuum models is proposed that enables to compare various coupling terms. The approach does not require the finite element mesh to match the lattice spacing of the atomic model. It is based on an overlapping domain decomposition method that makes use of Lagrange multipliers and weight functions in the coupling zone in order to distribute the energy between the two competing models. Two couplings are investigated. The L² coupling enforces the continuity of displacements between the two models directly. The H¹ coupling involves the definition of a strain measure. For this purpose, a moving least‐square interpolant of the atomic displacement is defined. The choice of the weight functions is studied. Patch tests and a graphene sheet with a crack are studied. It is shown that both continuous and discontinuous weight functions can be used with the H¹ coupling whereas the L² coupling requires continuous weight functions. For the examples developed herein, the L² coupling produces less error in the zone of interest. The flexibility of the H¹ coupling with constant weight function may be beneficial but the results may be affected depending on the topology of the bridging zone. Copyright © 2008 John Wiley & Sons, Ltd.     

A continuum sensitivity method for finite thermo‐inelastic deformations with applications to the design of hot forming processes

A computational framework is presented to evaluate the shape as well as non‐shape (parameter) sensitivity of finite thermo‐inelastic deformations using the continuum sensitivity method (CSM). Weak sensitivity equations are developed for the large thermo‐mechanical deformation of hyperelastic thermo‐viscoplastic materials that are consistent with the kinematic, constitutive, contact and thermal analyses used in the solution of the direct deformation problem. The sensitivities are defined in a rigorous sense and the sensitivity analysis is performed in an infinite‐dimensional continuum framework. The effects of perturbation in the preform, die surface, or other process parameters are carefully considered in the CSM development for the computation of the die temperature sensitivity fields. The direct deformation and sensitivity deformation problems are solved using the finite element method. The results of the continuum sensitivity analysis are validated extensively by a comparison with those obtained by finite difference approximations (i.e. using the solution of a deformation problem with perturbed design variables). The effectiveness of the method is demonstrated with a number of applications in the design optimization of metal forming processes. Copyright © 2002 John Wiley & Sons, Ltd.     

电磁成形技术的最新进展

电磁成形是目前应用最广泛的高能率成形方法之一.综述了成形磁场力的求解方法及解决电磁成形问题的3个主要方面内容,包括磁场、磁场力及变形,阐述了电磁成形工艺的成形方法及研究现状,列举了大量的国内、外工艺应用及研究成果,介绍了电磁成形工艺的最新应用--电磁校形、粉末压实,并展望了电磁成形技术的发展前景.     

Finite element formulation for anisotropic coupled piezoelectro‐hygro‐thermo‐viscoelasto‐dynamic problems

A finite element algorithm has been developed for the efficient analysis of smart composite structures with piezoelectric polymer sensors or/and actuators based on piezoelectro‐hygro‐thermo‐viscoelasticity. Variational principles for anisotropic coupled piezoelectro‐hygro‐thermo‐viscoelasto‐dynamic problems have also been proposed in this study. As illustrative studies, dynamic responses in laminated composite beams and plates with PVDF sensors and actuators are obtained as functions of time using the present finite element procedures. The voltage feedback control scheme is utilized. The proposed numerical method can be used for analysing problems in the design of smart structures as well as smart sensors and actuators. Copyright © 1999 John Wiley & Sons, Ltd.     

An object‐oriented framework for the implementation of adjoint techniques in the design and control of complex continuum systems

Specific object‐oriented software design concepts are elaborated for a novel implementation of a class of adjoint optimization problems typical of the infinite‐dimensional design and control of continuum systems. For clarity, the design steps and ideas are elucidated using an inverse natural convection design problem. Effective application of software design concepts such as inheritance, data encapsulation, information hiding, etc., is demonstrated through instances from the example considered. Two test numerical examples are considered and the CPU statistics for one of these problems are compared with those corresponding to a procedural implementation of the same problem. The numerical examples include a three‐dimensional inverse design problem that demonstrates the effectiveness of the present object‐oriented approach in developing dimension‐independent robust design codes. Copyright © 2000 John Wiley & Sons, Ltd.     

A finite element approach to anisotropic damage of ductile materials in large deformations Part II: finite element formulation and applications

A finite element analysis model for material and geometrical non-linearities due to large plastic deformations of ductile materials is presented using the continuum damage mechanics approach. To overcome limitations of the conventional plastic analysis, a fourth-order tensor damage, defined in Part I of this paper to represent the stiffness degradation in the finite strain regime, is incorporated. General forms of an updated Lagrangian (U.L.) finite element procedure are formulated to solve the governing equations of the coupled elastic–plastic-damage analysis, and a computer program is developed for two-dimensional plane stress/strain problems. A numerical algorithm to treat the anisotropic damage is proposed in addition to the non-linear incremental solution algorithm of the U.L. formulation. Selected examples, compared with published results, show the validity of the presented finite element approach. Finally, the necking phenomenon of a plate with a hole is studied to explore plastic damage in large strain deformations. This revised version was published online in August 2006 with corrections to the Cover Date.     

Non‐reflecting boundary conditions for atomistic,continuum and coupled atomistic/continuum simulations

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.     

Three‐dimensional numerical solution for wear prediction using a mortar contact algorithm

A finite element formulation to compute the wear between three‐dimensional flexible bodies that are in contact with each other is presented. The contact pressure and the bodies displacements are calculated using an augmented Lagrangian approach in combination with a mortar method, which defines the contact kinematics. The objective of this study is to characterize the wear rate coefficients for bimetallic pairs and to numerically predict the wear depths in new component designs. The proposed method is first validated with the classical pin‐on‐disc problem. Then, experimental results of wear for the metallic pairs used in internal combustion engine valves and inserts are presented and are taken as a reference solution. An example is provided that shows agreement of the numerical and experimental solution. Finally, the proposed algorithm is used to predict the wear in an application example: the wear in an internal combustion engine valve. Copyright © 2013 John Wiley & Sons, Ltd.     

A linearised hp–finite element framework for acousto‐magneto‐mechanical coupling in axisymmetric MRI scanners

We propose a new computational framework for the treatment of acousto‐magneto‐mechanical coupling that arises in low‐frequency electro‐magneto‐mechanical systems such as magnetic resonance imaging scanners. Our transient Newton–Raphson strategy involves the solution of a monolithic system obtained from the linearisation of the coupled system of equations. Moreover, this framework, in the case of excitation from static and harmonic current sources, allows us to propose a simple linearised system and rigorously motivate a single‐step strategy for understanding the response of systems under different frequencies of excitation. Motivated by the need to solve industrial problems rapidly, we restrict ourselves to solving problems consisting of axisymmetric geometries and current sources. Our treatment also discusses in detail the computational requirements for the solution of these coupled problems on unbounded domains and the accurate discretisation of the fields using hp–finite elements. We include a set of academic and industrially relevant examples to benchmark and illustrate our approach. Copyright © 2017 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons, Ltd.     

A novel contact interaction formulation for voxel‐based micro‐finite‐element models of bone

Voxel‐based micro‐finite‐element (μFE) models are used extensively in bone mechanics research. A major disadvantage of voxel‐based μFE models is that voxel surface jaggedness causes distortion of contact‐induced stresses. Past efforts in resolving this problem have only been partially successful, ie, mesh smoothing failed to preserve uniformity of the stiffness matrix, resulting in (excessively) larger solution times, whereas reducing contact to a bonded interface introduced spurious tensile stresses at the contact surface. This paper introduces a novel “smooth” contact formulation that defines gap distances based on an artificial smooth surface representation while using the conventional penalty contact framework. Detailed analyses of a sphere under compression demonstrated that the smooth formulation predicts contact‐induced stresses more accurately than the bonded contact formulation. When applied to a realistic bone contact problem, errors in the smooth contact result were under 2%, whereas errors in the bonded contact result were up to 42.2%. We conclude that the novel smooth contact formulation presents a memory‐efficient method for contact problems in voxel‐based μFE models. It presents the first method that allows modeling finite slip in large‐scale voxel meshes common to high‐resolution image‐based models of bone while keeping the benefits of a fast and efficient voxel‐based solution scheme.     

A non‐local continuum damage approach to model dynamic crack branching

Dynamic crack‐branching instabilities in a brittle material are studied numerically by using a non‐local damage model. PMMA is taken as our model brittle material. The simulated crack patterns, crack velocities, and dissipated energies compare favorably with experimental data gathered from the literature, as long as the critical strain for damage initiation as well as the parameters for a rate‐dependent damage law are carefully selected. Nonetheless, the transition from a straight crack propagation to the emergence of crack branches is very sensitive to the damage initiation threshold. The transition regime is thus a particularly interesting challenge for numerical approaches. We advocate using the present numerical study as a benchmark to test the robustness of alternative non‐local numerical approaches. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of three‐dimensional crack initiation and propagation using the extended finite element method

An Erratum has been published for this article in International Journal for Numerical Methods in Engineering 2005, 63(8): 1228. We present a new formulation and a numerical procedure for the quasi‐static analysis of three‐dimensional crack propagation in brittle and quasi‐brittle solids. The extended finite element method (XFEM) is combined with linear tetrahedral elements. A viscosity‐regularized continuum damage constitutive model is used and coupled with the XFEM formulation resulting in a regularized ‘crack‐band’ version of XFEM. The evolving discontinuity surface is discretized through a C⁰ surface formed by the union of the triangles and quadrilaterals that separate each cracked element in two. The element's properties allow a closed form integration and a particularly efficient implementation allowing large‐scale 3D problems to be studied. Several examples of crack propagation are shown, illustrating the good results that can be achieved. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical computation of the electromagnetic field in the electrodes of a three‐phase arc furnace

In this paper we introduce and numerically solve a mathematical model for numerical simulation of electro‐magnetic field in a three‐phase electric reduction furnace. The model allows us to compute the current distribution on a cross‐section of the three electrodes. A combined boundary element/finite element method is used. Numerical results for real industrial furnaces are shown. As a by‐product we compute the torque on the electrodes due to the Lorentz electromagnetic force. Copyright © 1999 John Wiley & Sons, Ltd.     

Ductile damage analysis of elasto‐plastic shells at large inelastic strains

The objective of this contribution is to model ductile damage phenomena under consideration of large inelastic strains, to couple the corresponding constitutive law with a multi‐layer shell kinematics and to give finally an adequate finite element formulation. An elastic–plastic constitutive law is formulated by using a spatial hyperelasto‐plastic formulation based on the multiplicative decomposition of the deformation gradient. To include isotropic ductile damage the continuum damage model of Rousselier is modified so as to consider large strains and additionally extended by various void nucleation and macro‐crack criteria. In order to achieve numerical efficiency, elastic strains are supposed to be sufficiently small providing a numerical effective integration based on the backward Euler rule. Finite element formulation is enriched by means of the enhanced strain concept. Thus the well‐known deficiencies due to incompressible deformations and the inclusion of transverse strains are avoided. Several examples are given to demonstrate the performance of the algorithms developed concerning large inelastic strains of shells and ductile damage phenomena. Copyright © 2000 John Wiley & Sons, Ltd.     

Efficient numerical strategies for spectral stochastic finite element models

The use of spectral stochastic finite element models results in large systems of equations requiring specialized solution strategies. This paper discusses three different numerical algorithms for solving these large systems of equations. It presents a trade‐off of these algorithms in terms of memory usage and computation time. It also shows that the structure of the spectral stochastic stiffness matrix can be exploited to accelerate the solution process, while keeping the memory usage to a minimum. Copyright © 2005 John Wiley & Sons, Ltd.