3D Contact Problems Research Articles

An incremental-iterative BEM methodology to solve 3D thermoelastic contact problem including variable thermal resistance in the contact zone

This work presents a new incremental-iterative method based on the boundary element method to solve 3D thermoelastic contact problems including a variable thermal contact resistance. The consideration of a variable thermal contact resistance implies that both thermal and thermoelastic problems are coupled since the variable thermal contact resistance is a function of the contact normal traction. Thus the proposed method determines incrementally the equilibrium configuration of the system by solving the coupled thermal and thermoelastic problems. The correct value of the thermal resistance is obtained iteratively. The robustness and accuracy of the proposed method is shown by solving a numerical problem and comparing the results with other methods presented in the literature.

On the inexact symmetrized globally convergent semi-smooth Newton method for 3D contact problems with Tresca friction: the R-linear convergence rate

ABSTRACTThe semi-smooth Newton method for solving discretized contact problems with Tresca friction in three-dimensional space is analysed. The slanting function is approximated to get symmetric inner linear systems. The primal–dual algorithm is transformed into the dual one so that the conjugate gradient method can be used. The R-linear convergence rate is proved for an inexact globally convergent variant of the method. Numerical experiments conclude the paper.

A damage model for fretting contact between a sphere and a half space using semi-analytical method

This paper presents a fast method of solving 3D contact problems when one of the mating bodies has an elastic-damageable behavior. The damage model is implemented in a semi-analytical model using Eshelby’ s equivalent inclusion method in the contact solver. The proposed technique can be seen as an enrichment technique for which the effect of heterogeneous inclusions is surimposed on the homogeneous solution in the contact algorithm. Contact pressure and subsurface stress field computation time is kept small due to a massive use of 3D and 2D Fast Fourier Transforms. Cuboidal inclusions with the same size as the discretization of the half-space and with the same elastic properties are surimposed. The damage model affects the elastic properties of the cuboidal inclusions. The emphasis is put on the effects of the fretting regimes on the contact pressure and damage evolution.

Winkler Support Model and Nonlinear Boundary Conditions Applied to 3D Elastic Contact Problem Using the Boundary Element Method

This work presents a numerical methodology for modeling the Winkler supports and nonlinear conditions by proposing new boundary conditions. For the boundary conditions of Winkler support model, the surface tractions and the displacements normal to the surface of the solid are unknown, but their relationship is known by means of the ballast coefficient, whereas for nonlinear boundary conditions, the displacements normal to the boundary of the solid are zero in the positive direction but are allowed in the negative direction. In those zones, detachments of nodes might appear, leading to a nonlinearity, because the number of nodes that remain fixed or of the detached ones (under tensile tractions) is unknown. The proposed methodology is applied to the 3D elastic receding contact problem using the boundary element method. The surface tractions and the displacements of the common interface between the two solids in contact under the influence of different supports are calculated as well as the boundary zone of the solid where the new boundary conditions are applied. The problem is solved by a double-iterative method, so in the final solution, there are no tractions or penetrations between the two solids or at the boundary of the solid where the nonlinear boundary conditions are simulated. The effectiveness of the proposed method is verified by examples.

Investigation into static contact behavior in belt rail grinding using a concave contact wheel

In order to establish a theoretical foundation of rail profile reshaping through belt grinding with a concave contact wheel, the static contact behavior between the contact wheel and railhead is preliminarily modeled and investigated. The geometry interference between wheel and rail profile under certain contact conditions is initially analyzed. Based on the integral method, 3D contact problem is then analyzed through transferring it as a series of 2D issues between a thin elastic sheet surrounded by a rigid circle base and a rigid plan, from which the boundary curve function and the stresses distribution of contact zone are developed. Results from both finite element simulations and real contact experiment have validated the availability of qualitative analysis and quantitative prediction of the proposed model. Results from model and validation have agreed that the contact zone shape should be classified into three types due to different contact conditions, namely the ellipse, the triangle, and the saddle-shape.

Coupling a NURBS contact interface with a higher order finite element discretization for contact problems using the mortar method

In this paper, a contact problem between two bodies, discretized by finite elements, is solved by adding an auxiliary NURBS layer between the bodies. The advantages of a smooth contact formulation in a NURBS approach are combined with simple mesh generation procedures for the bodies discretized with finite elements. Mesh tying conditions are used to couple the NURBS layer with the finite element discretization. The NURBS layer is the master side for contact and mesh tying. Mesh tying is enforced either using pointwise or mortar type approaches. Frictionless 2D and 3D contact problems are considered using small deformations. The contact problem is discretized with the mortar method and a penalty approach is used to enforce the contact constraints. A robust element-based quadrature is applied for mortar tying and contact discretizations, thus avoiding computationally expensive segmentation.

A cell-based smoothed finite element method for multi-body contact analysis using linear complementarity formulation

In this paper, the cell-based smoothed finite element using quadrilateral elements (CS-FEM) is used for 2D contact problems which are converted into linear complementarity problems (LCPs), which can be solved efficiently using the Lemke method. The modified Coulomb friction contact model with tangential strength and normal adhesion is considered, which models sticking-slipping, contacting-departing, and bonding-debonding processes, in a unified formulation. Smoothed Galerkin weak-form with contact boundary is deduced, in which the stiffness is implemented using the CS-FEM with 1 smoothing domain (1SD), 2SD, 3SD, 4SD, 8SD, and 16SD for each element. Contact interface equations are discretized through contact point-pairs that are constructed using a master-slave surface algorithm. Intensive numerical examples are given to investigate the effects of contact parameters on contact behaviors and examine the effectiveness of the proposed approach. The numerical results of CS-FEM models are compared with that of FEM-Q4 model, which demonstrates that all CS-FEM models are softer than FEM-Q4 model. The strain energy solutions, obtained using several CS-FEM models, are monotonically decreasing with the number of the SDs for each element increasing. The upper bound solutions in strain energy can be obtained using a CS-FEM-1SD model in our examples, while the lower bound solutions are obtained using CS-FEM-16SD model or FEM-Q4, with FEM-Q4 solution being the lowest.

Large deformation frictional contact analysis with immersed boundary method

This paper proposes a method of solving 3D large deformation frictional contact problems with the Cartesian Grid Finite Element Method. A stabilized augmented Lagrangian contact formulation is developed using a smooth stress field as stabilizing term, calculated by Zienckiewicz and Zhu Superconvergent Patch Recovery. The parametric definition of the CAD surfaces (usually NURBS) is considered in the definition of the contact kinematics in order to obtain an enhanced measure of the contact gap. The numerical examples show the performance of the method.

Numerical Modeling of the Behavior of the Steel-Concrete Interface Contribution by Extended Finite Element Method (X/FEM)

In the reinforced concrete study, the concrete steel connection is a key element» in the behavior of this composite because it will allow the transfer of forces between steel and concrete. The understanding of this phenomenon and its inclusion in the numerical analysis of reinforced concrete structures are the main objects of this research work; the approach suggested for modeling this problem is the extended finite element method (X FEM) that allows the introduction of the interface independently by the mesh. Steel and concrete bond has been studied through a pull-out test as recommended by RILEM. This work provides some ideas about the adhesion’s behavior, thus an experimental campaign was carreid out, measuring the concrete’s andsteel’s constraints and sliding over concrete. The bond stress –slip curve shows a similar behavior between experimental and theoretical results. The obtained results show the improvement of the adhesion constraint according to the increase of concrete compressive strength. Indeed, the transmission of forces between reinforcement and concrete enclosing it gives rise to a relatively complex state of stress. This paper presents a stabilized formulation for 3D contact problems, in the framework of X-FEM. It is shown that the choice of a simple algorithm and the type of mesh (concrete - steel bond) is a good solution for the determination of the adhesion behavior.

Indentation of a Transversely Isotropic Thermoporoelastic Half-Space by a Rigid Circular Cylindrical Punch

Exact solutions to the three-dimensional (3D) contact problem of a rigid flat-ended circular cylindrical indenter punching onto a transversely isotropic thermoporoelastic half-space are presented. The couplings among the elastic, hydrostatic, and thermal fields are considered, and two different sets of boundary conditions are formulated for two different cases. We use a concise general solution to represent all the field variables in terms of potential functions and transform the original problem to the one that is mathematically expressed by integral (or integro-differential) equations. The potential theory method is extended and applied to exactly solve these integral equations. As a consequence, all the physical quantities of the coupling fields are derived analytically. To validate the analytical solutions, we also simulate the contact behavior by using the finite element method (FEM). An excellent agreement between the analytical predictions and the numerical simulations is obtained. Further attention is also paid to the discussion on the obtained results. The present solutions can be used as a theoretical reference when practically applying microscale image formation techniques such as thermal scanning probe microscopy (SPM) and electrochemical strain microscopy (ESM).

Nonsmooth continuation of parameter dependent static contact problems with Coulomb friction

The paper presents a new variant of a nonsmooth continuation algorithm by means of which one can follow branches of solutions to 2D contact problems with Coulomb friction which are parameterized by the coefficient of friction. The algorithm is based on the predictor–corrector technique and uses the active set strategy implementation of the semismooth Newton method.

Contact problem for an orthotropic half-space

Numerical and analytical solutions of the 3D contact problem of elasticity on the penetration of a rigid punch into an orthotropic half-space are obtained disregarding the friction forces.A numericalmethod ofHammerstein-type nonlinear boundary integral equations was used in the case of unknown contact region, which permits determining the contact region and the pressure in this region. The exact solution of the contact problem for a punch shaped as an elliptic paraboloid was used to debug the program of the numerical method. The structure of the exact solution of the problem of indentation of an elliptic punch with polynomial base was determined. The computations were performed for various materials in the case of the penetration of an elliptic or conical punch.

A surface-to-surface scheme for 3D contact problems by boundary face method

The surface-to-surface contact algorithm has been proposed to overcome the drawbacks of node-to-surface algorithm in finite element method implementations. In the surface-to-surface algorithm, contact constraints are imposed between sub-elements rather than between nodes, and an auxiliary plane for each element is introduced to perform overlapping area detection. This work presents a combination of the surface-to-surface algorithm and the boundary face method (BFM) for solving contact problems in three dimensions. The BFM is based on boundary integral equation and is a truly isogeometric method, as it makes direct use of the geometric information of the bounding surface of a body. Apparently, the BFM is more suitable for solving contact problems. In our implementation, the auxiliary plane is no more necessary, but replaced by the boundary faces themselves which already exist in the BFM data structure. Our implementation is natural and can more precisely match the contact conditions between faces, and therefore, higher level of accuracy can be expected. Numerical examples presented have demonstrated the advantages of the combined method.

Object-Oriented Contact Detection Approach for Three-Dimensional Discontinuous Deformation Analysis Based on Entrance Block Theory

AbstractCompared with two-dimensional (2D) contact cases, three-dimensional (3D) contact problems are more complicated in both contact geometry representation and contact detection. The entrance block theory proposed by Shi lays the foundation for solving contact problems in a uniform format. This paper presents a new contact detection approach for 3D polyhedral blocks with the use of entrance block theory. In this approach, contacts between 3D polyhedra were classified into three categories: finite-contact covers (face to face, edge to face, and parallel edge to edge), single-contact covers (vertex to face, crossing edge to edge, vertex to edge, and vertex to vertex), and basic-contact covers (vertex to face and crossing edge to edge). A finite-contact cover consists of several single-contact covers, and all single-contact covers can be identified as basic-contact covers. Thus, the contact detection process can be fulfilled in three phases: a rough search phase to form a potential contacting block list f...

The Influence of Equivalent Contact Area Computation in 3D Extended Node to Surface Contact Elements

This paper extends the frictionless penalty-based node to contact formulation with area regularization to a 3D framework. Based on our previous work [1] focused on axisymmetric modeling, two computational methods are also considered for the determination of the slave node area. The first method, named as the geometrical approach, is based on a force equivalence system, while the second one, named as the consistent approach, is derived from a more sophisticated scheme elaborated upon the virtual work principle. Then, the extended contact elements are derived for the contact formulations with geometrical and consistent area regularization and a consistent linearization is provided accordingly, which guarantees a quadratic rate of convergence of the global Newton Raphson iterative procedure. Finally, two numerical examples assess the performance of both contact formulations with area regularization and demonstrates the robustness and the efficiency of the node to surface contact formulation with consistent area regularization in reproducing a constant contact pressure distribution across the interface between a deformable body and a analytically-defined rigid body, irrespective of the mesh. Our findings will certainly encourage further developments towards the design of a penaltybased node to surface contact algorithm passing the contact patch test, as was already done successfully in 2D contact problems [2].

Boundary face method for 3D contact problems with non-conforming contact discretization

Three-dimensional contact problems without friction have been studied using the boundary face method (BFM). In this paper, a non-conforming contact discretization approach is used to enforce the contact conditions between the two contact surfaces. This method is based on node-to-surface (NTS), and there is no need that the identical discretization is performed along the contact surfaces of both bodies. The contact equations are written explicitly with both tractions and displacements which are retained as unknowns in boundary integral equation (BIE). An iterative procedure is presented to determine the correct contact zone by obtaining a solution compatible with the contact conditions (no interpenetrations between the domains and no tensile on the final contact zone). Several numerical examples have been presented to illustrate the applicability of the method.

A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems

This paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from 3D concentrated frictional shift and rolling contact problems with dry Coulomb friction. The solver combines an active set strategy with a nonlinear conjugate gradient method. One novelty is to consider the tractions of each slip element in a polar coordinate system, using azimuth angles as variables instead of conventional traction variables. The new variables are scaled by the diagonal of the underlying Jacobian. The fast Fourier transform (FFT) technique accelerates all matrix–vector products encountered, exploiting the matrix' Toeplitz structure. Numerical tests demonstrate a significant reduction of the computational time compared to existing solvers for concentrated contact problems.

The R-linear convergence rate of an algorithm arising from the semi-smooth Newton method applied to 2D contact problems with friction

The goal is to analyze the semi-smooth Newton method applied to the solution of contact problems with friction in two space dimensions. The primal-dual algorithm for problems with the Tresca friction law is reformulated by eliminating primal variables. The resulting dual algorithm uses the conjugate gradient method for inexact solving of inner linear systems. The globally convergent algorithm based on computing a monotonously decreasing sequence is proposed and its R-linear convergence rate is proved. Numerical experiments illustrate the performance of different implementations including the Coulomb friction law.

Action of an elliptic punch on a transversally isotropic half-space

The 3D contact problem on the action of a punch elliptic in horizontal projection on a transversally isotropic elastic half-space is considered for the case in which the isotropy planes are perpendicular to the boundary of the half-space. The elliptic contact region is assumed to be given (the punch has sharp edges). The integral equation of the contact problem is obtained. The elastic rigidity of the half-space boundary characterized by the normal displacement under the action of a given lumped force significantly depends on the chosen direction on this boundary. In this connection, the following two cases of location of the ellipse of contact are considered: it can be elongated along the first or the second axis of Cartesian coordinate system on the body boundary. Exact solutions are obtained for a punch with base shaped as an elliptic paraboloid, and these solutions are used to carry out the computations for various versions of the five elastic constants. The structure of the exact solution is found for a punch with polynomial base, and a method for determining the solution is proposed.

A Lookup-Table-Based Approach for Spatial Analysis of Contact Problems

The aim of this work is to present an efficient methodology to deal with general 3D-contact problems. This approach embraces three steps: geometrical definition of 3D surfaces, detection of the candidate contact points, and evaluation of the contact forces. The 3D-contact surfaces are generated and represented by using parametric functions due to their simplicity and ease in handling freeform shapes. This task is carried during preprocessing, which is performed before starting the multibody analysis. The preprocessing procedure can be condensed into four steps: a regular and representative collection of surface points is extracted from the 3D-parametric surface; for each point the tangent vectors to the u and v directions of the parametric surface and the normal vector are computed; the geometrical information on each point is saved in a lookup table, including the parametric point coordinates, the corresponding Cartesian coordinates, and the components of the normal, tangent, and bitangent vectors; the lookup table is rearranged such that the u-v mapping is converted into a 2D matrix being this surface data saved as a direct access file. For the detection of the contact points, the relative distance between the candidate contact points is computed and used to check if the bodies are in contact. The actual contact points are selected as those that correspond to the maximum relative indentation. The contact forces are determined as functions of the indentation or pseudopenetration, impact velocity, and geometric and material properties of the contacting surfaces. In general, lookup tables are used to reduce the computation time in dynamic simulations. However, the application of these schemes involves an increase of memory needs. Within the proposed approach, the amount of memory used is significantly reduced as a result of a partial upload into memory of the lookup table. A slider-crank mechanism with a cup on the top of the slider and a marble ball are used as a demonstrative example. A contact pair is considered between a cup and a marble ball, the contact forces for which are computed using a dissipative contact model.