Catálogo de publicaciones - libros

Nonlinear boundary problems for in a cylinder is studied within quadratic approximation. When the cylinder coordinates are used, the usual perturbation techniques in separation of variables method inevitably lead to a series of overdetermined systems of linear algebraic equations for the unknown coefficients (in contrast with the Cartesian coordinates). However, if we formally introduce a new function () satisfying the first system of this series, all these overdetermined systems become compatible (remaining overdetermined). Using the new function and the quadratic polynomials of the Bessel functions of radius, we explicitly express the solutions of the nonlinear boundary problem.

Key words: Bessel functions, nonlinear interaction, separation of variables, wave equation.

In the domain of railway dynamics, specific models have been developed based on Hertz and Kalker theory to calculate the normal and tangential stresses in a semi-analytic way, and inserted into multibody codes, in order to ensure fast and reliable simulation of the contact stresses in the presence of dry friction. Recently several advanced contact models have been developed which are able to manage non-Hertzian simulations online. The particular developments proposed by the authors are presented.

Key words: Hertz theory, Kalker theory, Winkler foundation, Coulomb friction, rolling contact, friction, railway, wheel, rail, stress.

For the finite element analysis of rolling contact problems Arbitrary Lagrangian Eulerian (ALE) methods are well established. These techniques enable a time independent formulation for elastic bodies under stationary rolling conditions and for local mesh refinement concentrated to the contact region. A drawback is on the computation of history dependent material properties because the path of material points is not traced inherently. This affects inelastic constitutive behavior as well as frictional contact. In this contribution a mathematically sound approach for the treatment of frictional rolling within the ALE description based on a spatially fixed finite element mesh is suggested. By this novel and fully implicit algorithm the slip velocities are integrated along their path-lines which enables for the treatment of frictional contact as in a material picture. Quadratic convergence behavior and physical reliability will be demonstrated as well as the computability of large scaled finite element tire models.

Key words: Rolling contact, tire, Arbitrary Lagrangian Eulerian (ALE) method, frictional contact.

In this work the non-penetration condition and the interface models for contact taking into account the surface microstructure are investigated in detail. It is done using a homogenization procedure presented by Bandeira et al. [2–5] in order to obtain by numerical simulation the interface behavior for the normal and tangential contact pressures based on statistical surface models. The contact surfaces of both bodies are rough. This paper can be regarded as a complementary study to that presented by Bandeira et al. [5]. Here the plasticity of the asperities is taken into account by assuming a constitutive equation based on an associated von Mises yield function formulated in principal axes, as shown by Pimenta [22]. The plastic zones in the microstructure are shown to study in detail the contact interface. Numerical examples are selected in order to show the ability of the algorithm to represent interface law for rough surfaces considering elastoplastic behavior of the asperities.

Key words: Contact mechanics, contact surface, interface constitutive equation, elastoplasticity.

Penetration problems in geomechanics are extremely difficult to model, because they usually involve large deformation, frictional contact and large variation of material stiffness. This paper proposes a number of strategies to deal with the computational challenges involved in modelling pile installation in geomechanics. In particular, an Arbitrary Lagrangian–Eulerian method is proposed to handle the large deformation and mesh distortion problem. A smooth discretisation of the contact surfaces is proposed to handle the vertex problems of the penetrating body. An automatic time stepping scheme is proposed to solve the nonlinear stiffness equation. The effectiveness of these numerical enhancements will then be demonstrated in the simulation of installation of displacement piles.

Key words: Pile installation, Arbitrary Lagrangian–Eulerian method, frictional contact, Modified Cam Clay.

As it is commonly know, classic Coulomb’s and Amonton’s friction laws, which mainly establish that the friction coefficient is independent of the area of contact, are proven to be not valid in the case of rubber-like materials. In this particular case, and due to their specific mechanical properties, the friction coefficient should be expressed as a function of contact pressure, sliding speed, temperature and lubrication regime, if the latter were the case.

The dependence with the contact pressure is associated to the varying ratio of real (microscopic level) to apparent (macroscopic level) area of contact when the vertical load (contact pressure) is rising. The problem increases in complexity when neither the contact pressure distribution nor the ratio of real to apparent area of contact are uniform along the apparent area of contact, being the cylindrical contact geometry a typical example of this situation. In the present paper, the dependence of the dynamic friction coefficient value with the contact pressure in cylindrical rubber-aluminium contact geometries is analysed in detail.

As commented before, contact pressure distribution is not constant along the whole cylindrical area of contact and, thus, friction coefficient value has to be calculated indirectly from friction force results obtained in tribotesting by means of a mathematical method. In addition, the apparent area of contact in the cylindrical case is also not constant when the vertical load increases. Thus, the robustness of the method has to be improved by comparison of experimental measurements of the apparent area of contact with FEM results of the tribotesting, combining them with the adjustment of the rubber material model. As it will be explained along the paper, the method consists on combining FEM simulations of the tribotesting to obtain contact pressure distributions along the cylindrical area of contact for different vertical loadings, and then on developing a mathematical procedure for obtaining a final analytical expression for the dynamic friction coefficient vs. the contact pressure. Finally, it is checked that this method provides good correlations with already existing friction models which can be found in the literature [2, 3].

Key words: Tribology, polymers, dynamic friction coefficient, contact pressure, finite element method, cylindrical contact geometry.

The physical effect of friction appears in many technical applications. One of the most interesting fields is rubber friction which depends on a variety of parameters, e.g. normal pressure, temperature, relative velocity, surface roughness, lubrication and wear. These properties often lead to operating conditions where the coefficient of friction decreases with respect to the relative velocity. As a consequence unwanted friction induced self-excited vibrations may occur. A model is set up to describe tread block vibrations under consideration of the complex contact properties and their interactions. Therefore, modules are developed describing each single effect. The Hurty/Craig/Bampton transformation is applied to the linear finite element model of the tread block. By considering only some vibration modes the number of degrees of freedom is significantly reduced. The simulation results show the typical tread block vibrations and the attending wear effect which are observed in experiments.

Key words: Rubber friction, tyre tread block, non-linear contact stiffness, wear.

The stick-slip phenomenon constitutes a challenge when referring to tribological design of rubber sealing components in a wide range of pneumatic and hydraulic applications. Several systems such as brake and clutch servo actuators, hydraulic gearshifts and other actuation systems are influenced by this phenomenon which is commonly associated to system control problems (system vibrations & noise) and to the reduction of the service life of rubber sealing components. Under a macroscopic point of view, the stick-slip consists on the sudden and successive change of the state of relative movement between two sliding surfaces in contact from “static” to “sliding”.

In the present paper, two FEM-based approaches are presented with the final objective of developing a numerical predictive tool for the analysis and quantification of this undesired phenomenon. First approach is based on a common existing in literature mass-spring system over a moving surface and implemented into a parametrized FE modelling. The methodology based on the parametrization of the FE simulations allows to study the influence of several system variables such as the frictional force evolution, the mass of the system, the system stiffness and damping and also sliding speed on the frequency and amplitude of the stickslip instability. All the system variables corresponding to the simplified mass-spring model are connected to the real system in the way that an analysis or proposed modification on any of them can be directly translated into effective modifications of the real system to prevent “stick-slip” events.

As an alternative approach to the direct FE simulation, a more affordable technique like the complex eigenvalue analysis of the problem is also applied to this example in order to obtain system instabilities. Even though this technique is more suitable for the analysis of mode-coupling friction instabilities, it is shown that the results in terms of eigenvalues can compared and correlated to the time domain simulation results. Finally, a comparison of both approaches is carried out with the objective of developing a low-time-consuming tool with reasonable accuracy for predicting and quantifying stick-slip phenomena on real rubber sealing components.

Key words: Tribology, polymers, “stick-slip”, friction, finite element method, user subroutine, parametrization, complex eigenvalue analysis.

Results of abrasive wear are identified as irreversible changes in bodies contours and as an increase of a clearance gap between contacting solids. Loose wear particles detached from the bodies transmit loads and displacements at the contact interface. In the contribution, descriptions of displacements and temperatures in the contacting solids are extended by taking into account the effects of the wear process. Illustrative examples demonstrate calculations of the abraded mass and fields of temperatures in pin-on-disc tests.

Key words: Friction, frictional heat, pin-on-disc test, wear, wear debris, wear depth, wear velocity.

Internal stresses occur within a material in the presence of non-uniform deformation. The main types of the internal stresses are the thermal and residual ones and fields of structural defects as well. These stresses have an essential effect on the diffusion processes kinetics. In this case change of the strength material properties takes place. The properties degradation is accompanied by damaging and failing the material. The physical mechanisms underlying changes of properties include, for example, decreasing of surface fracture energy, stress corrosion cracking, and hydrogen embrittlement. The diffusion process is described by a non-stationary equation of a parabolic type under both initial and boundary conditions. The purpose of this paper is simulating the material damage as a result of running the diffusion processes. Triple grain boundaries are considered as structural defects. They serve as stress concentrators under external loadings. This is caused by the orientation dependence of elastic and thermophysical characteristics of the contiguous grain material. The dilatation field of considered defects depends logarithmically on the radial coordinate. Such a dependence enables one to obtain an exact analytical solution for the task on hydrogen segregation kinetics. Analytical relations for the field of atomic hydrogen concentration near the triple grain boundaries are given. If the concentration of hydrogen atoms exceeds the solubility limit at a given temperature, hydride phases are formed in some metals (e.g., Zr). Hydride growth kinetics in the stress field of structural defects under study is considered. The changes of the volume hydride are accompanied by microcrack formation along the grain boundaries.

Key words: Internal stresses, diffusion kinetics, damage simulation.