Key Engineering Materials Vol. 618

Abstract: This article aims at extending the node to surface formulation for contact problems withan area regularization as proposed by [1]. For that purpose, two methods are proposed to computethe equivalent contact area attributed to each slave node. The first method, which is based on a geo-metrical approach through force equivalence, is an original extension of the one proposed in [1] fortwo-dimensional contact problems, i.e. plane stress and plane strain state, to the axisymmetric mod-elling context. The second method relies on an energy consistent way obtained through the virtualwork principle and the same expression for the equivalent contact area as the one originally cited in[2] is then recovered. First, the node to surface strategy with area regularization is introduced and theaforementioned methods for the equivalent contact area are presented in detail and compared. After-wards a consistent linearization technique is applied to achieve a quadratic convergence rate in theNewton Raphson iterative procedure used to solve the non-linear equilibrium equations of the under-lying finite element model. Finally, two axisymmetric numerical examples are provided in order tocompare the aforementioned equivalent contact area evaluations and to demonstrate the performanceand the robustness of the consistent approach especially in the neighbourhood the revolution axis.

Abstract: This paper presents a state-of-the-art in the use of localized Lagrange multipliers (LLMs)for 3D frictional contact problems coupling the Finite Element Method (FEM) and the BoundaryElement Method (BEM). Resolution methods for the contact problem between non-matching mesheshave traditionally been based on a direct coupling of the contacting solids using classical Lagrangemultipliers. These methods tend to generate strongly coupled systems that require a deep knowledgeof the discretization characteristics on each side of the contact zone complicating the process ofmixing different numerical techniques. In this work a displacement contact frame is inserted betweenthe FE and BE interface meshes, discretized and finally connected to the contacting substructuresusing LLMs collocated at the mesh-interface nodes. This methodology will provide a partitionedformulation which preserves software modularity and facilitates the connection of non-matching FEand BE meshes.

Abstract: The paper presents a synthetic review of recent research carried out by the writers [1-6, 7-9] on contact shape optimization coupled with wear and on the steady wear regimes reached in the transient wear process. It was shown that these regimes can also be specified from the optimality conditions. In the analysis several classes of shape optimization problems were considered, namely minimization of wear volume rate, friction dissipation power or wear dissipation power. It was demonstrated that the contact shape evolution tends to steady or quasi-steady states satisfying the minimum principle of the wear dissipation power, resulting in the coaxiality rule requiring the wear rate vector to be collinear with the rigid body wear velocity vector. The application of steady state wear rules in specification of contact states for selected problems is discussed in the paper. The extension of method is presented for the case of multi-zone contact problems for which both transient and steady states have been analyzed.

Abstract: Wear is present in all mechanical interface interaction problems –contact, fretting, orrolling-contact–, and it is one of the main reasons for inoperability in mechanical components. Thepresented work is a review of recent research carried out by the authors [1, 2, 3]. A boundary-element-based methodology to compute anisotropic wear on 3D contact, fretting, or rolling-contact conditionsis presented. Damage on the geometries of the solids and the contact pressures evolution under or-thotropic tribological properties can be predicted using this contact framework, where the formulationuses the Boundary Element Method to compute the elastic inuence coefcients. Contact problem isbased on an Augmented Lagrangian formulation, and restrictions fullment is established by a set ofprojection functions. The boundary element anisotropic wear formulation presented is illustrated withsome examples, in which some studies about the inuence of anisotropic wear on contact variablesevolution are shown.

Abstract: Fretting fatigue denotes the detrimental effect on a material arising from the cyclic sliding of two contacting surfaces with small relative displacements between them. One or both of the components in contact may be subject to bulk stresses caused by cyclic loads. The assessment of the fretting fatigue strength and life of any component is a complicated issue due to the many parameters affecting it, the complexity of the stress fields cyclic variation during fretting and the uncertainties associated to the contact conditions. This paper describes some singular aspects of fretting fatigue related to strength analysis and testing, presents a procedure developed by the authors during the last years to estimate the fretting fatigue strength and life and compares the assessment outcomes with the results of tests carried out by different authors.

Abstract: Boundary element method (BEM) formulations for transient dynamic crack analysis intwo-dimensional (2D) multifield materials are reviwed in this paper. Both homogeneous and lin-ear piezoelectric as well as magnetoelectroelastic material models are considered. Special attentionis paid to properly modeling the non-linear crack-face contact and semi-permeable electric/magneticboundary conditions. Implementation of the corresponding time-domain BEM(TDBEM) is discussedin detail. The proposed TDBEM uses a Galerkin-method for the spatial discretization, whilst thecollocation method is considered for the temporal discretization. Iterative solution algorithms aredeveloped to compute the non-linear crack-face boundary conditions. Crack-tip elements that ac-count for the square-root local behavior of the crack opening displacements (CODs) at the crack-tipsare implemented. In this way, stress intensity factors (SIF), electric displacement intensity factor(EDIF) and magnetic induction intensity factor (MIIF) may be accurately evaluated from the nu-merically computed CODs at the closest nodes to the crack-tips. Numerical examples involving sta-tionary cracks in piezoelectric and magnetoelectroelastic solids under different combined (mechani-cal/electric/magnetic) impact loadings are investigated, in order to illustrate the effectiveness of theproposed approach and characterize the influence of the semi-permeable crack-face boundary condi-tions on the dynamic field intensity factors.

Abstract: The boundary element method (BEM) is a robust and accurate numerical technique to deal contact problems, because the contact among solids occurs along its boundaries. In this regard, this work presents a nonlinear BEM formulation applied to contact problems simulation. The formulation is based on the use of singular or hyper-singular integral equations of BEM, for multi-region contact, and the dual version of BEM to simulate the contact between crack surfaces. The mechanical nonlinear behaviour introduced by the contact is represented by the Coulomb’s friction law. The nonlinear formulation uses the tangent operator technique, in which one uses the derivate set of algebraic equations to construct the corrections field for the nonlinear process. This implicit formulation has shown accurate as the classical approach. However it is faster, in terms of computational time consuming, than the classical nonlinear approach. Examples of simple and multi-region contact problems are presented in order to illustrate the applicability of the proposed nonlinear numerical scheme.

Abstract: Relations between different solutions of an interface crack in a neighborhood of the crack tip given by the open model, frictionless and frictional contact models of interface cracks are analyzed numerically for a penny-shaped interface crack subjected to remote tension. A new analytic expression for the size of the near-tip contact zone in presence of Coulomb friction between crack faces is proposed in the so-called case of the contact zone field embedded in the oscillatory field.

Abstract: In this paper, the frictional contact problem of a homogeneous orthotropic material in contact with a wedge-shaped punch is considered. Materials can behave anisotropically depending on the nature of the processing techniques; hence it is necessary to develop an efficient method to solve the contact problems for orthotropic materials. The aim of this work is to develop a solution method for the contact mechanics problems arising from a rigid wedge-shaped punch sliding over a homogeneous orthotropic half-plane. In the formulation of the plane contact problem, it is assumed that the principal axes of orthotropy are parallel and perpendicular to the contact. Four independent engineering constants , , , are replaced by a stiffness parameter, , a stiffness ratio, a shear parameter, , and an effective Poisson’s ratio, . The corresponding mixed boundary problem is reduced to a singular integral equation using Fourier transform and solved analytically. In the parametric analysis, the effects of the material orthotropy parameters and the coefficient of friction on the contact stress distributions are investigated.