Analysis Of Frictional Contact Problems Research Articles

A Numerical Lagrangian Approach for Analysis of Contact Viscoelastic Problems

The objective of this paper is to develop a finite-element formulation associated with an incremental adaptive procedure established for analysis of frictional contact problems in viscoelastic solids. A generalized Maxwell model has been used to model the viscoelastic constitutive equations in which bulk and shear relaxation functions are represented by the sum of a series of decaying exponential functions of time. A generalized finite-element approach, based on the principle of virtual work, has been developed using an incremental relaxation procedure. The application of the finite element method to contact viscoelastic problems is investigated. The contact treatment between bodies has been studied through an augmented Lagrangian approach. Finally, an example is presented to evaluate the computational solution procedure presented.

Isotropic damage analysis of frictional contact problems using quadratic meshless boundary element method

In this paper, a quadratic meshless boundary element formulation for isotropic damage analysis of contact problems with friction is presented. To evaluate domain-related integrals due to the damage effects, the radial integration method (RIM) based on the use of the approximating the normalized displacements in the domain integrals by a series of prescribed radial basis functions (RBF) is employed. An exponential evolution equation for the damage variable is adopted. The details of coupling the different systems of equations for each body in contact under the several contact conditions are given to obtain the overall system of equations. Numerical examples covering shrink-fit and frictional punch problems are given to demonstrate the efficiency of the present meshless BEM. • A meshless BEM using radial point integration is presented for isotropic damage analysis of frictional contact problems. • An exponential evolution equation for the damage variable is adopted. • It is shown to be a very promising computational tool without resorting to the use of intensive internal nodes.

A Finite Element Solution for Frictional Sliding Contact between Hyper-Elastic and Rigid Bodies

This paper is devoted to the analysis of frictional contact problems with large deformations and displacements between hyper-elastic body and rigid body. The material nonlinearity and contact nonlinearity are separated and, the geometrically nonlinear behavior is described by the total Lagrange formulation. The Coulomb friction law is employed to simulate the friction between rigid vessel and rubber by the use of augmented Lagrange approach with node-to-segment formulation. A formulation of finite element is taken in this paper to describe the frictional contact problem, which is solved by the Newton-Raphson iterative procedure. It is shown that the augmented Lagrange technique significantly avoids locking and over-constraining and provides optimal convergence rate. Finally, the numerical results show that the accuracy and efficiency of augmented Lagrange approach in modeling large deformation frictional contact problem.

Analysis of frictional contact problems for functionally graded materials using BEM

In this paper, a quadratic boundary element formulation for continuously non-homogeneous, isotropic and linear elastic functionally graded material contact problems with friction is presented. To evaluate domain related integrals, the radial integration method (RIM) based on the use of the approximating the normalized displacements in the domain integrals by a series of prescribed radial basis functions (RBF), leading a meshless scheme, is employed. An exponential variation with spatial coordinates is assumed for Young's modulus of the functionally graded materials (FGM), while Poisson's ratio is assumed to be constant. Under the contact conditions, including infinite friction, frictionless and Coulomb friction, different systems of equations for each body in contact are united. Numerical examples including non-confirming contact are given.

Analysis of quasistatic frictional contact problems in nonlinear viscoelasticity with large deformations

A numerical model for the analysis of frictional contact problems in viscoelastic structures, undergoing both material and geometrical nonlinearities is presented. The nonlinear Schapery constitutive viscoelastic model is used for the stress, strain, and time relationships. The constitutive equations are expressed in an incremental form assuming a constant strain rate within each time increment. The hereditary integral is updated at the end of time increment by recursive procedure. The normal contact forces are treated as independent variables. In addition, the regularized Coulomb's friction model is adopted to model the friction throughout the contact interface. The friction resistance is represented by tangential contact stiffness. The Updated Lagrangian approach is adopted to derive the equilibrium equations for the contact systems. The Newton–Raphson iterative scheme is utilized to obtain the converged solution at the end of each time increment. The developed model is verified and compared with the available analytical methods and benchmarks. The applicability of the developed computational incremental iterative scheme is demonstrated by solving two different cases of contact problems with different geometry, loading, and boundary conditions. Numerical results show that material nonlinearity and friction have great effects on viscoelastic contact behavior.

Solving Frictional Contact Problems within the Bipotential Framework

The main objective of this paper is to present a theoretical and numerical analysis of frictional contact problems for large deformation elasto-plastic based on the finite element method (FEM) and the mathematical programming. The study is done on an elasto-plastic material obeying to the von Mises criterion. The Coulomb’s friction contact is used to implement the frictional boundary conditions and is formulated by the bipotential concept leading us to minimize only one variational principle of minimum in displacement. In order to follow up the sequences of large deformations, we have used the sequential analysis procedure; it consists in the updating of material properties and geometrical configuration after each sequence.

Boundary element analysis of 3-D elasto-plastic contact problems with friction

In this paper, a boundary element method for three-dimensional elasto-plastic stress analysis of frictional contact problems in the framework of small strains and small displacements is presented. The contact conditions are used to unite the different system of equations for each body in contact. Several types of contact interface conditions are covered including infinite friction, frictionless and Coulomb friction. In order to include plastic deformation, the initial strain formulation and von Mises yield criterion are employed. The proposed algorithm is applied to the elasto-plastic analysis of the frictionless rigid punch, a large plate with a rigid, circular, cylindrical inclusion under the increasing load and the ceramic femoral head frictional contact problem.

Elasto-plastic static stress analysis of 3D contact problems with friction by using the boundary element method

In this paper, a boundary element method for three-dimensional elasto-plastic stress analysis of frictional contact problems in the framework of small strains and small displacements is presented. The contact conditions are used to unite the different system of equations for each body in contact. Several types of contact interface conditions are covered including infinite friction, frictionless and Coulomb friction. In order to include plastic deformation, the initial strain formulation and von Mises yield criterion are employed. The proposed algorithm is applied to the elasto-plastic analysis of the frictionless rigid punch, a large plate with a rigid, circular, cylindrical inclusion under the increasing load and the ceramic femoral head frictional contact problem.

축대칭 변형체의 마찰 접촉문제에 관한 유한요소 해석

This paper is concerned with the numerical analysis of frictional contact problems in axisymmetric bodies using the rigid-plastic finite element method. A contact finite element method, based on a penalty function, are derived from variational formulations. The contact boundary condition between two deformable bodies is prescribed by the proposed algorithm. The program which can handle frictional contact problem is developed by using pre-existing rigid-plastic finite element code. Some examples used in this paper illustrate the effectiveness of the proposed formulations and algorithms. Efforts focus on the deformation patterns, contact force, and velocity gradient through the various simulations.

Study of variational inequality and equality formulations for elastostatic frictional contact problems

An overview ofvariational inequality andvariational equality formulations for frictionless contact and frictional contact problems is provided. The aim is to discuss the state-of-the-art in these two formulations and clearly point out their advantages and disadvantages in terms of mathematical completeness and practicality. Various terms required to describe the contact configuration are defined.Unilateral contact law and classical Coulomb’s friction law are given.Elastostatic frictional contact boundary value problem is defined. General two-dimensional frictionless and frictional contact formulations for elastostatic problems are investigated. An example problem of a two bar truss-rigid wall frictionless contact system is formulated as an optimization problem based on the variational inequality approach. The problem is solved in a closed form using the Karush-Kuhn-Tucker (KKT) optimality conditions. The example problem is also formulated as a frictional contact system. It is solved in the closed form using a new two-phase analytical procedure. The procedure avoids use of the incremental/iterative techniques and user defined parameters required in a typical implementation based on the variational equality formulation. Numerical solutions for the frictionless and frictional contact problems are compared with the results obtained by using a general-purpose finite element program ANSYS (that uses variational equality formulation). ANSYS results match reasonably well with the solutions of KKT optimality conditions for the frictionless contact problem and the two-phase procedure for the frictional contact problem. The validity of the analytical formulation for frictional contact problems (with one contacting node) is verified. Thevariational equality formulation for frictionless and frictional, contact problems is also studied in detail. The incremental/iterative Newton-Raphson scheme incorporating the penalty approach is utilized. Studies are conducted to provide insights for the numerical solution techniques. Based on the present study it is concluded that alternate formulations and computational procedures need to be developed for analysis of frictional contact problems.

The Boundary Integral Equation Method for Elastoplastic Stres Analysis of Frictional Contact Problems

For two-dimensional elastoplastic stress analysis of frictional contact problems an isoparametric quadratic formulation of the boundary integral equation (BIE) method is presented with emphasis on clarity at the expense of efficiency. The overall system of equation is obtained by using multi-domain approach in which the contact conditions are taken into account to couple the different system of equation for each body in contact, Several types of contact interface conditions are covered including Infinite friction (stick), frictionless and Coulomb friction slip. In order to include plastic deformation in the analysis, the initial strain formulation and von Mises yield criterion are used. In order to evaluate internal stress and strain rates the differentiation of the displacement in elementwise manner is adopted with its compulsory modeling of partial (where plastic deformation is expected) domain. Elastic-perfectly plastic, work-hardening or mixed hardening material behaviour can be assumed. An efficient and robust incremental-iterative process is proposed to find the proper contact conditions. For the numerical implementation, isoparametric three-noded line elements are used to represent the boundary and eight-noded quadrilateral domain cell are used for partially modelling interior domain. The proposed algorithm is applied to the heftz-like indentation problem and the results are, where appropriate, compared with the presented results in the literature to confirm its correctness and robustness.

Finite Element Analysis for Large Deformation Frictional Contact Problems with Finite Sliding.

In the analysis of frictional contact problems with large deformation, the use of a convected coordinate system is a natural approach, by which the frame indifference of friction law can be maintained. However, in the case of the finite element method, a problem arises due to the discontinuity of the local coordinates between elements when sliding extends over the element boundary. In this work, a method is proposed to solve this problem, i.e., although the formulation is essentially based on a convected coordinate system, the sliding term is redefined as a spatial vector and is calculated using the reference configuration. Thus, finite sliding due to large deformation can be treated, regardless of the limitations of element coordinate systems. Also, the corresponding consistent tangent stiffness is derived to obtain quadratic convergence. The effectiveness of the proposed method is verified in this study by two numerical examples, including an elastoplastic frictional contact problem with large deformation.

Finite Element Analysis for Large Deformation Frictional Contact Problems with Finite Sliding.

In the analysis of frictional contact problems with large deformation, use of convected coordinate system is a natural approach, by which the frame indifference of friction law can be maintained. However, in the case of finite element method, a problem arises due to the discontinuity of the local coordinates between elements when the sliding extends over the element boundary. In this work a method is proposed to solve this problem, i.e., although the formulation is essentially based on a convected coordinate system. the sliding term is re-defined as a spatial vector and is calculated using the reference configuration. Thus, the finite sliding due to large deformation can be treated regardless of the limitation of element coordinate systems. Also, the corresponding consistent tangent stiffness is derived to obtain quadratic convergence. The effectiveness of the proposed method is verified by a couple of numerical examples including an elasto-plastic frictional contact problem with large deformation.

A general FE algorithm for 3D incremental analysis of frictional contact problems of elastoplasticity

A theoretical basis of the original incremental description of the frictional contact problem of two thermo-elastic or thermo-elastoplastic (with or without isotropic hardening) bodies moving together is presented. The contact models allows the contact area to change. The friction models account for either Coulomb or elasto-Coulombian slips and assume either constant or varying friction coefficient. The general FE algorithm takes advantage of the proper variational formulation based on the incremental form of the potential energy functional. A general flow diagram for the problem solution is presented. Generation of element stiffnesses and forces, global stiffness matrix and global nodal force vector formation are mentioned in order to provide a background for a thorough presentation of the procedures due to contact aspects such as an algorithm for division of the potential contact area into component parts of gap, adhesion, and slip (or gap, elastic slip, and elasto-Coulombian slip), an algorithm for imposing unilateral normal contact and adhesion constraints, an algorithm for calculation of frictional terms (friction force increments and surface stiffnesses), and special iterative scheme within an incremental step. The algorithm is coded in program PLAST described in a companion paper.

A general FE computer program for 3D incremental analysis of frictional contact problems of elastoplasticity

The paper presents an original computer program PLAST for incremental analysis of 3D geometrically (unknown geometry of contact) and physically (frictional) non-linear contact problems of elasticity (thermoelasticity) or elastoplasticity (thermoelastoplasticity ) with or without strain hardening. Linearized contact problems of elastoplasticity and elasticity can also be analyzed. The program is based on the general algorithm combining different procedures for Coulomb and elasto-Coulombian friction models with or without hardening. All the friction terms for both the models are consistently defined as global (on the level of structure nodes). The program is assigned for large moving or stationary technological structures consisting of two bodies in contact with or without manufacturing or assemblage deviations. The capabilities of the program include strain and stress, stress concentration and contact analyses. The program can cooperate with commercial pre- and postprocessors. Verification of the program is based on calculations of test examples that can be easily checked analytically. Usefulness of the program for technological problems is supported with real turbomachinery blade attachment calculations.

An effective two‐dimensional frictional contact model for arbitrary curved geometry

AbstractA finite element model is developed on the basis of a variational formulation of the perturbed Lagrange type and the classical Coulomb law of friction, for the analysis of frictional contact problems in two dimensions. The model accounts for all geometric/kinematic non‐linearities associated with large sliding motions as well as arbitrary contact‐surface curvatures. Explicit forms for the contact force and tangent stiffness operators and a penalty‐type format is utilized in the implementation. An extensive number of numerical simulations are used to demonstrate the effectiveness and practical usefulness of the model.

Boundary element analysis of two‐dimensional elastoplastic contact problems

AbstractIn this paper a boundary element method for two‐dimensional elastoplastic stress analysis of frictional contact problems is presented. The bodies in contact are treated as separate regions. The contact conditions are used to join the different system of equations for different regions of contacted bodies and, hence, an overall system of equation is obtained. An incremental and iterative procedure can be used to find the contact load, or the contact extent and the proper contact conditions. To include the plastic deformation in the analysis, the initial strain algorithm is employed. Elastic‐perfectly plastic or work‐hardening material behaviour can be assumed. For the numerical analysis, an isoparametric three‐noded line elements are used to represent the boundary and eight‐noded quadrilateral or six‐noded triangular elements are used for the interior of the domain. The displacement rates and traction rates are assumed to vary quadratically and the shape functions for the interior strain rates are also of quadratic type. As an example, the behaviour of an elastic and elastoplastic body with a smooth, circular inclusion under the increasing load is presented.

Boundary element analysis of elasto-plastic contact problems

In this paper a boundary element method for two-dimensional elasto-plastic stress analysis of frictional contact problems is presented. The bodies in contact are treated as separate regions. The contact conditions are used to join the different system of equations for different regions of contacted bodies and hence an overall system of equations would be obtained. An incremental and iterative procedure can be used to find the contact load, or the contact extent and the proper contact conditions. To include the plastic deformation in the analysis the initial strain algorithms is employed. Elastic-perfectly plastic or work-hardening material behavior can be assumed. For the numerical analysis, isoparametric three-noded line elements are used to represent the boundary and eight-noded quadrilateral and six-noded triangular elements are used for the interior of the domain. The displacement rates and traction rates are assumed to vary quadratically and the shape functions for the interior strain rates are also of quadratic type. As an example the behavior of an elastic and elasto-plastic body with a smooth, circular inclusion under the increasing load is presented.

Analysis of frictional contact problems in high field superconducting magnets for a hadron collider

In order to achieve the extremely high magnetic fields (8 to 10 Tesla) required for CERN's LHC (large hadron collider) project superconducting coils are used in the deflecting magnets. One possible technology is the use of the brittle material Nb,Sn, which must be kept at low temperatures (4.2 K). The cooling down process and the variation of the strong electromagnetic forces during operation require special care. These situations are simulated by a finite element model taking into account the frictional contact between the individual components of the magnet assembly. In addition to the stress and strain distribution in the magnet the knowledge of local relative motions generating frictional heat is important for the consideration of the stability of the superconducting material.

Finite element analysis of Hertz contact problem with friction

A new finite element method of solution for the design and analysis of frictional contact problems is presented. The nonlinear problem is solved by imposing geometric constraints on the pseudo equilibrium configuration, defined as a configuration at which the compatibility conditions are violated. The compatibility conditions are satisfied through a load step applied to the pseudo equilibrium configuration. The contact conditions of sticking, slipping, rolling or tension release is determined from the relative magnitudes of the normal and tangential global nodal forces. The classical Hertz contact problem is analyzed with and without friction between the contacting bodies and good agreement is found between the analytical and the numerical solutions.