Elastoplastic Frictional Contact Problems Research Articles

The Influence of the Elastoplastic Behavior and the Load Pattern on the Tribological Properties of Two-Dimensional Frictional Contact Problems

The macromechanical tribological mechanism describes the friction phenomenon by considering the stress and the strain distributions, and the total elastic and plastic deformations. Based on the finite element method (FEM), the elastoplastic frictional contact problem is formulated as an incremental convex programming model (CPM). The Lagrange multiplier approach is adopted for imposing the inequality contact constraints. The Coulomb's friction law and the Prandtl–Reuss flow rule are used for the friction conditions and the elastoplastic behavior, respectively. The frictional contact examples are analyzed using the developed adaptive incremental procedure to elucidate the tribological behavior of the contact bodies and the model applicability.

ADAPTIVE INCREMENTAL FINITE ELEMENT PROCEDURE FOR SOLVING ELASTOPLASTIC FRICTIONAL CONTACT PROBLEMS SUBJECTED TO NORMAL AND TANGENTIAL LOADS

This paper presents a numerical model for analyzing the stresses and displacements of deformable bodies in contact with the presence of friction and material nonlinearity. Based on the finite element method (FEM), the elastoplastic frictional contact problem is formulated as an incremental convex programming model (ICPM) under inequality contact constraints and friction conditions. The classical Coulomb's friction law and the Prandtl–Reuss flow rule with the von Mises yield criterion are used to simulate the interface friction conditions and the elastoplastic behavior of the contacting bodies, respectively. The Lagrange multiplier approach is adopted for imposing the contact constraints. Furthermore, an effective adaptive incremental procedure is developed for solving the elastoplastic frictional contact problems. Examples for the frictional contact having advancing and receding nature are analyzed. The obtained results prove the ability of the developed procedure to investigate the sequence of different events during monotonic application of external loads. In addition, the results elucidate the effect of external side force on the friction behavior in the presence of plastic deformation. Good agreement has been found with published results.

Frictional Contact Problem Study on Compressor by a Parametric Quadratic Programming Method

A locomotive-type turbocharger compressor with 24 blades under combined centrifugal and interference-fit loading was considered in the numerical analysis. The solution of elastoplastic frictional contact problems belongs to the unspecified boundary problems where the interaction between two kinds of nonlinearities should occur. To save the time cost in the numerical computation, multi-substructure technique was adopted in the structural modeling. The effect of fit tolerance, wall thickness of shaft sleeve and rotational speed on the contact stress was discussed in detail in the numerical computation. To decrease the difficulty of the assembling process and make sure the safety of the working state, the amount of interference between the shaft sleeve and shaft by press-fitting should be controlled strictly to avoid the rapid increase of the contact stress. The numerical results show the high accuracy and good convergence of the algorithm presented here. The study play a referenced role in deciding the proper fit tolerance and improving design and manufacturing technology of compressor impellers.

Elastoplastic Frictional Contact Study on Interference Fits of Compressor

The impeller mounted onto the compressor shaft assembly via interference fit is one of the key components of a centrifugal compressor stage. A suitable fit tolerance needs to be considered in the structural design. A locomotive-type turbocharger compressor with 24 blades under combined centrifugal and interference-fit loading was considered in the numerical analysis. The FE parametric quadratic programming (PQP) method which was developed based on the parametric variational principle (PVP) was used for the analysis of stress distribution of 3D elastoplastic frictional contact of impeller-shaft sleeve-shaft. The solution of elastoplastic frictional contact problems belongs to the unspecified boundary problems where the interaction between two kinds of nonlinearities should occur. The effect of fit tolerance, rotational speed and the contact stress distribution on the contact stress was discussed in detail in the numerical computation. The study play a referenced role in deciding the proper fit tolerance and improving design and manufacturing technology of compressor impellers.

Elastoplastic frictional contact problem study on interference fits of compressor

The FE parametric quadratic programming (PQP) method developed from the parametric variational principle (PVP) was used for the analysis of the stress distribution of the 3D elastoplastic frictional contact of an impeller-shaft sleeve-shaft. A locomotive-type turbocharger compressor with 24 blades under combined centrifugal and interference-fit loading was considered in the numerical analysis. The solution of elastoplastic frictional contact problems belongs to unspecified boundary problems where the interaction between two kinds of nonlinearities should occur. To save time in the numerical computation, a multi-substructure technique was adopted in the structural modeling. The effect of fit tolerance, wall thickness of the shaft sleeve, and rotational speed on the contact stress was discussed in detail in the numerical computation. To decrease the difficulty of the assembly process and ensure the safety of the working state, the amount of interference between the shaft sleeve and shaft by press-fitting should be controlled strictly to avoid the rapid increase of contact stress. The numerical results show that the algorithm has high accuracy and good convergence. The study can be referred to in deciding the proper fit tolerance and improving the design and manufacturing technology of compressor impellers.

Non-smooth Nonlinear Equations Methods for Solving 3D Elastoplastic Frictional Contact Problems

Based on the non-smooth nonlinear equations method for modeling three-dimensional elastic frictional contact problems (hereafter called NNEM), the extension to elastoplastic case in which the material nonlinearity is also involved is presented in this paper. Two approaches which combine two methods for solving elastoplastic problem with NNEM are proposed. A Numerical example is given to demonstrate the validation of the approaches.

Some advances and applications in quadratic programming method for numerical modeling of elastoplastic contact problems

This paper reviews briefly some advances and applications in parametric quadratic programming (PQP) method for numerical modeling of elastoplastic contact problems. The parametric variational principle (PVP) and the corresponding finite element model for numerical simulation of 3D elastoplastic frictional contact problems with isotropic/anisotropic (orthotropic) friction law are presented. The finite element software JIFEX is then developed with the application-oriented concept for nonlinear analysis of complex structures in general purposed engineering. Some typical engineering applications such as compressor impeller and the railway wheel/rail contact analysis are shown to illustrate the potential of the software developed.

A new algorithm for numerical solution of 3D elastoplastic contact problems with orthotropic friction law

3D elastoplastic frictional contact problems with orthotropic friction law belong to the unspecified boundary problems with nonlinearities in both material and geometric forms. One of the difficulties in solving the problem lies in the determination of the tangential slip states at the contact points. A great amount of computational efforts is needed so as to obtain high accuracy numerical results. Based on a combination of the well known mathematical programming method and iterative method, a finite element model is put forward in this paper. The problems are finally reduced to linear complementarity problems. A specially designed smoothing algorithm based on NCP-function is then applied for solving the problems. Numerical results are given to demonstrate the validity of the model and the algorithm proposed.

An effective BE algorithm for 3D elastoplastic frictional contact problems

This paper is concerned with an effective boundary element algorithm for the elasto-plastic analysis of three-dimensional frictional contact problems using a quadratic boundary element formulation in the framework of small strains and small displacements. 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 stain 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 frictional punch contact problem.

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.

Automatic load incrementation technique for plane elastoplastic frictional contact problems using boundary element method

The boundary element method in the framework of small strains and small displacements is used to evaluate plane frictional contract problems. Elastoplastic material behaviour is taken into account by means of an initial strain formulation and von Mises yield criterion. The amount of tangential traction at the contact surface is limited by Coulomb's law of friction. The contact conditions are defined for every pair of contact nodes. This is done in a similar way as subregions are coupled in substructuring technique. The set of equations is reduced to non-linear degrees of freedom. Due to the non-linear behaviour of friction and plasticity an incremental loading is necessary. The part of each load increment that just causes a change of contact condition is determined by an automatic load incrementation procedure. In case of elastic material behaviour incremental values are scaled linearly. The method is extended to elastoplastic material behaviour where a fast iterative scheme (Illinois algorithm) is used to determine the desired loading. Results are shown for the Hertz-like problem of two cylindric rollers in contact, a punch problem, and the contact of two teeth of an involute gear. Elastoplastic material is either defined by a bilinear stress-strain relation or by an interpolation of discrete stress-strain values by linear splines.