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.     

3D dynamic modeling of powder forming processes via a simple and efficient node-to-surface contact algorithm

In this paper, a simple and efficient contact algorithm is presented for the evaluation of density distribution in three-dimensional dynamic modeling of powder compaction processes. The contact node-to-surface algorithm is employed to impose the contact constraints in large deformation frictional contact, and the contact frictional slip is modified by the Coulomb friction law to simulate the frictional behavior between the rigid punch and the work-piece. The 3D nonlinear contact friction algorithm is employed together with a double-surface cap plasticity model within the framework of large finite element deformation in order to predict the non-uniform relative density distribution during the dynamic simulation of powder die-pressing. The accuracy and robustness of contact algorithm is verified by the impact analysis of two elastic rods, which is compared with the analytical solution. Finally, the performance of computational schemes is illustrated in dynamic modeling of a set of powder components.     

Analysis of a general dynamic history-dependent variational–hemivariational inequality

This paper is devoted to the study of a general dynamic variational–hemivariational inequality with history-dependent operators. These operators appear in a convex potential and in a locally Lipschitz superpotential. The existence and uniqueness of a solution to the inequality problem is explored through a result on a class of nonlinear evolutionary abstract inclusions involving a nonmonotone multivalued term described by the Clarke generalized gradient. The result presented in this paper is new and general. It can be applied to study various dynamic contact problems. As an illustrative example, we apply the theory on a dynamic frictional viscoelastic contact problem in which the contact is modeled by a nonmonotone Clarke subdifferential boundary condition and the friction is described by a version of the Coulomb law of dry friction with the friction bound depending on the total slip.     

Boundary optimal control for nonlinear antiplane problems

We consider a nonlinear antiplane problem which models the deformation of an elastic cylindrical body in frictional contact with a rigid foundation. The contact is modelled with Tresca’s law of dry friction in which the friction bound is slip dependent.The aim of this article is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. The existence of at least one optimal control is proved. Next we introduce a regularized problem, depending on a small parameter ρ, and we study the convergence of the optimal controls when ρ tends to zero. An optimality condition is delivered for the regularized problem.     

Multiscale simulation for description of rubber friction

The interaction between tire and road generates the transferable forces, which are necessary for driving dynamics and safety. These forces are based on friction between rubber material and pavement surface and depend on the roughness of the pavement, the slip velocity, the contact pressure and the temperature. Based on the finite element method, the friction coefficient is calculated by numerical simulation. The roughness of the pavement surface is described by the height difference correlation function (HDCF), which allows partitioning into different length scales. This multiscale approach is suitable to understand and to evaluate friction phenomena. These phenomena are hysteresis friction based on dissipation inside the rubber material and adhesion friction, which describes the direct bonding between two materials. Given, that the material parameters of rubber highly depend on temperature and the frictional dissipation leads to a warming of the rubber, the provision for these effects is necessary for a realistic desciption of friction. The method allows an understanding of friction phenomena on the micro-scale like the real contact area or the microscopic contact pressure. Also, the temperature distribution inside the tire cross-section can be illustrated. The resulting coefficient of friction is validated by experimental data based on linear friction tests and compared to analytical solutions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A model of a reinforced tyre with a rod protector

A tyre design consisting of a steel-cord-reinforced rigid bond with sides connected to the wheel disc and a protector(tread) in contact with the road is examined. The tread is in the form of a set of rods connected by one end to the band, with the other end either free or in contact with the road. The rod end in contact with the road is acted upon by a force applied from the road, represented by a force normal to the road plane and a shear force due to dry friction. If the modulus of the shear force does not exceed the magnitude of the normal force multiplied by the dry friction coefficient, there is no slip at the contact point. In the opposite case, the rod end will be displaced along the road by an amount sufficient to distribute the normal and shear forces. The dynamics of longitudinal and transverse strains of the rods in contact with the road is analysed using the motion separation method in the quasi-static approximation. The behaviour of the tread rods as a function of the vertical displacement of the wheel centre is investigated, the contact area is found and the conditions are determined under which the contact area is divided into parts in which either slip of the rod ends occurs or does not occur, depending on the magnitude of the longitudinal displacement of the wheel centre or its turning relative to the horizontal axis. An analogue of a continuous model of a rod-like tread is considered, and the magnitudes of the forces and moments are found as a function of the wheel disc displacements. The equations of wheel rolling are obtained, and the conditions under which steady motions exist are found.     

A Two-dimensional Contact Problem with Given Region of Adhesion

The two-dimensional indentation of an elastic half-plane bya rigid punch under normal and tangential load is considered.The contact area is divided into an inner region with adhesion,the dimension of which is known beforehand, surrounded by tworegions in which inward slip takes place. The problem is formulatedin terms of a coupled pair of Cauchy type integrals for thenormal and shear stresses at the surface of the half-plane.In the case of friction-free slip these integrals are combinedto an inhomogeneous Fredholm equation which is solved by a methodof successive approximations. In the case when the inward slipis governed by Coulomb friction, the problem is solved by anumerical method.     

The calculation of the energy losses in a sliding elastic contact with friction and wear (the plane problem)

The plane problem of the sliding contact of a punch with an elastic foundation when there is friction and wear is considered. Assuming the existence of a steady solution in a moving system of coordinates, relations are derived between the sliding velocity, the wear, the contact stresses and the displacements for an arbitrary dependence of the wear rate on the contact pressure. Taking into account the presence of a deformation component of the friction force, an equation is written for the balance of the mechanical energy for the punch - elastic base system considered. It is shown that the equality of the work of the external force in displacing the punch to the losses due to friction and the change in the shape of the foundation due to wear is satisfied when the work done by the contact stresses on the increments of the boundary displacements is equal to zero, and the frictional losses must be determined taking into account the non-uniformity of the distributions of the shear contact stresses and the sliding velocity in the contact area. Two special cases of the foundation in the form of a wide and narrow strip are considered, for which the total coefficient of friction is calculated, taking into account the deformation component of the friction force.     

Quasistatic Frictional Problems for Elastic and Viscoelastic Materials

We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution variational inequalities and fixed-point arguments. We also prove that the solution of the viscoelastic problem converges to the solution of the corresponding elastic problem, as the viscosity tensor converges to zero. Finally, we describe a number of concrete contact and friction conditions to which our results apply.     

Evolutional contact with Coulomb's friction on a periodic microstructure

We consider the elasticity problem in a heterogeneous domain with an ε-periodic micro-structure, ε ≪ 1, including a multiple micro-contact in a simply connected matrix domain with inclusions completely surrounded by cracks, which do not connect the boundary, or a textile-like material. The contact is described by the Signorini and Coulomb-friction contact conditions. In the case of the Coulomb friction, the dissipative functional is state dependent, like in [2]. A time discretization scheme from [2] reduces the contact problem to the Tresca one (with prescribed frictional traction or state independent dissipation) on each time-increment. We further look for the spatial homogenization. The limiting energy and the dissipation term in the stability condition were obtained for the contact with Tresca's friction law in [4] for closed cracks and can be extended to textile-like materials. Using these results and the concept of energetic solutions for evolutional quasi-variational problems from [2], for a uniform time-step partition, the existence can be proved for the solution of the continuous problem and a subsequence of incremental solutions weakly converging to the continuous one uniformly in time. Furthermore, the irreversible frictional displacements at micro-level lead to a kind of an evolutional plastic behavior of the homogenized medium. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis and Numerical Approximation of a Contact Problem Involving Nonlinear Hencky-Type Materials with Nonlocal Coulomb’s Friction Law

A static frictional contact problem between an elasto-plastic body and a rigid foundation is considered. The material’s behavior is described by the nonlinear elastic constitutive Hencky’s law. The contact is modeled with the Signorini condition and a version of Coulomb’s law in which the coefficient of friction depends on the slip. The existence of a weak solution is proved by using Schauder’s fixed-point theorem combined with arguments of abstract variational inequalities. Afterward, a successive iteration technique, based on the Ka?anov method, to solve the problem numerically is proposed, and its convergence is established. Then, to improve the conditioning of the iterative problem, an appropriate Augmented Lagrangian formulation is used and that will lead us to Uzawa block relaxation method in every iteration. Finally, numerical experiments of two-dimensional test problems are carried out to illustrate the performance of the proposed algorithm.     

考虑摩擦接触时简谐波透过微缝隙的传播

研究了简谐波透过微缝隙的传播问题．考虑界面摩擦接触,利用Fourier分析技术和半空间解修正法,将边界非线性波动问题简化为一组代数方程并进行了详细的数值计算．给出了分离区、滑移区和粘着区的分布以及界面应力分布和能量分配;讨论了缝隙宽度、摩擦因数、入射角等因素对波动传输的影响．结果表明:由于界面发生局部接触和滑移使得反射波和透射波中含有高频谐波．缝隙宽度与各阶谐波反射、透射系数的关系可为材料及结构的无损检测提供理论依据．     

Resolución numérica de las ecuaciones del movimiento de edificios de varias plantas con no linealidades severas

This paper presents a new algorithm for solving the equations of motion of multi-storey buildings that incorporate frictional energy dissipators as seismic protection. The behavior of the dissipators is represented by Coulomb dry friction models; they introduce severe nonlinearities in the dynamic behavior of the structure every time that the contact conditions (stick or slip) change in the dissipators. These nonlinearities complicate the resolution of the equations of motion as it usually is described by lumped masses models whose degrees of freedom are the displacements of the floors and, as the stick or slip conditions change, the degrees of freedom must be modified: for blocking conditions they are only the displacements of the storeys while under sliding conditions the displacements of the dissipators have to be also considered. In previous articles the accuracy of the proposed algorithm has been verified by comparison with experimental results; as well, the computational efficiency of the algorithm has been confirmed by comparing the required resources (in terms of computation time and of memory allocation) with those of other algorithms. The objectives of this paper are to describe in detail the numerical solution of the equations of motion and present representative examples confirming the ability of the algorithm to reproduce the dynamic behavior of buildings with friction dissipators and reporting preliminarily about the usefulness of such devices to reduce the oscillations of the structure to be protected.     

Modeling of large deformation frictional contact in powder compaction processes

In this paper, the computational aspects of large deformation frictional contact are presented in powder forming processes. The influence of powder–tool friction on the mechanical properties of the final product is investigated in pressing metal powders. A general formulation of continuum model is developed for frictional contact and the computational algorithm is presented for analyzing the phenomena. It is particularly concerned with the numerical modeling of frictional contact between a rigid tool and a deformable material. The finite element approach adopted is characterized by the use of penalty approach in which a plasticity theory of friction is incorporated to simulate sliding resistance at the powder–tool interface. The constitutive relations for friction are derived from a Coulomb friction law. The frictional contact formulation is performed within the framework of large FE deformation in order to predict the non-uniform relative density distribution during large deformation of powder die pressing. A double-surface cap plasticity model is employed together with the nonlinear contact friction behavior in numerical simulation of powder material. Finally, the numerical schemes are examined for efficiency and accuracy in modeling of several powder compaction processes.     

An adaptive NS/ES-FEM approach for 2D contact problems using triangular elements

An adaptive contact analysis approach is presented for 2D solid mechanics problems using only triangular elements and the subdomain parametric variational principle (SPVP). The present approach is implemented for the node-based smoothed FEM (or NS-FEM), the edge-based smoothed FEM (ES-FEM) and the standard FEM models with automatically adaptive refinement scheme. A modified Coulomb frictional contact model and its corresponding discrete equations are introduced. The global discretized system equations are then formulated in an incremental form with the aid of the basic boundary value equations for friction contact and the subdomain parametric variational principle. A simple adaptive refining scheme is presented, and the Voronoi vertices are taken as candidate points to become new nodes because of duality property between the Voronoi diagrams and Delaunay triangulation. The present adaptive approach can properly simulate variable behaviors of a contact interface such as bonding/debonding, contacting/departing, and sticking/slipping. Several examples are presented to numerically validate the proposed approach via the comparison with reference solutions obtained by ABAQUS^®, and to investigate the effects of the various parameters used in the computations on the response of the contact system. The numerical results have demonstrated that the present adaptive contact analysis approach using the ES-FEM has higher accuracy and convergence rate in the strain energy than that using FEM and NS-FEM. However, the latter two methods can provide the lower and upper bound solution for the system strain energy, respectively.     

温差影响下的局部滑移接触行为的研究

针对不同温度装配件间接触界面的局部滑移问题,建立了三维稳态热弹性局部滑移接触的半解析求解模型.基于热弹性理论与热传导方程,构建了半空间受热流载荷和力载荷作用下的频响函数并建立了相应的影响系数矩阵.借助离散卷积-快速Fourier变换等数学工具,实现了针对高温压头与热弹性半空间局部滑移接触问题的高效求解.接触界面间的热量传递满足Fourier热传导定律,并且黏/滑状态由Coulomb定律确定.基于该半解析模型分析了不同荷载及温差对表面法向压力分布、摩擦力分布、刚体位移及接触区黏/滑演化行为的影响.研究结果表明,当法向荷载和切向荷载一定时,温差的上升会导致接触区域的减小,引起接触面法向压力及摩擦力的峰值增大,并且会显著影响黏着区与滑移区的分布情况.     

Modeling of jointed structures using zero thickness interface elements

An important contribution to global damping of mechanical devices is structural damping due tomicroslip effects with friction in joint interfaces. In order to investigate the mechanical behaviour in these contact interfaces numerically, a contact element in the context of Finite Element Method (FEM) is presented. The suggested element is an isoparametric zero thickness element which is well suited for the present problem because the contact area is known and only small relative displacements occur. Arbitrary linear or nonlinear constitutive contact models for normal and tangential contact behaviour can be implemented. Using a proper parametrisation of the contact area, it is possible to apply the element in contact interfaces lying arbitrarily in space and in interfaces discretized with distorted elements. This method is described before a numerical example is compared with experimental results. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The solution of three-dimensional friction contact problems

A variational method is developed for solving friction contact problems, in which the friction obeys Coulomb's of friction law in velocities, and numerical solutions of three-dimensional problems of the contact of a sphere, a cylinder of finite length and a cube with an elastic half-space are constructed. It is established that the maximum frictional forces correspond to a boundary point of the regions of adhesion and slippage. When the number of steps,increase this maximum decreases, and the distribution of the frictional forces becomes smoother. Certain undesirable effects that can arise during numerical implementation of the method – numerical artefacts – are described. These effects can occur in the numerical solution of problems with a different physical content, the mathematical structure of which is similar to the structure of the contact problems investigated, as the artefacts are caused by the presence of unilateral constraints and by the dependence on external effects of the region in which unilateral constraints with an equally sign occur. This problem is solved by an appropriate choice of the load-step zero approximations.     

The sliding of viscoelastic bodies whenthere is adhesion

The plane contact problem of the sliding without friction of a rigid cylinder over a viscoelastic half-space when there is adhesion is solved, neglecting the inertial properties of the half-space. The distribution of the contact pressure, the size and position of the contact area, and the deformation force of resistance to motion of the cylinder are investigated as a function of the adhesion properties of the surfaces, the mechanical characteristics of the half-space and the sliding velocity of the cylinder.     

Development of generalized Iwan model to simulate frictional contacts with variable normal loads

Most friction models are originally proposed to predict restoring forces in mechanical contacts with constant normal load. In practice the contact interface kinematics may involve normal motion in addition to the tangential displacements, leading to variation of the contact normal load. This phenomenon is observed most strongly in contacts with high lateral vibration amplitudes and is known as slap. The current study establishes a general friction model to account for variation in the normal load and enables one to predict the behavior of a contact more precisely. Iwan model (1966) [5] is a suitable candidate for contact interface modeling and is able to represent the stick-micro/macro slip behavior involved in a friction contact. This physical based model is employed in the current work and its physical parameters are generalized to include the normal load variation effects. The model is characterized by a slippage distribution density function and a linear stiffness at stick state. Both these parameters, defined in presence of constant normal load in the original model, are derived considering normal load variation leading to generalization of the contact model. Conventional models with constant normal loads produce symmetric contact interface hysteresis loops, but the developed generalized Iwan model is capable of generating asymmetric hysteresis loops similar to those frequently seen in experiments. The generalized contact model is employed to simulate the measured behavior of a beam with frictional support observed in an experimental test set-up. The contact slippage distribution function is first identified in a constant normal load condition. Next in low levels of contact preloads where variation of the normal load is significant, the identified distribution function in generalized form is employed to predict the experimental observations.