Sergiu Spinu

Modelling of Rough Contact between Linear Viscoelastic Materials

The important gradients of stress arising in rough mechanical contacts due to interaction at the asperity level are responsible for damage mechanisms like rolling contact fatigue, wear, or crack propagation. The deterministic approach to this process requires computationally effective numerical solutions, capable of handling very fine meshes that capture the particular features of the investigated contacting surface. The spatial discretization needs to be supported by temporal sampling of the simulation window when time-dependent viscoelastic constitutive laws are considered in the description of the material response. Moreover, when real surface microtopography is considered, steep slopes inevitably lead to localized plastic deformation at the tip of the asperities that are first brought into contact. A computer model for the rough contact of linear viscoelastic materials, capable of handling deterministic contact geometry, complex viscoelastic models, and arbitrary loading histories, is advanced in this paper. Plasticity is considered in a simplified manner that preserves the information regarding the contact area and the pressure distribution without computing the residual strains and stresses. The model is expected to predict the contact behavior of deterministic rough surfaces as resulting from practical engineering applications, thus assisting the design of durable machine elements using elastomers or rubbers.

Numerical Simulation of Elastic-Plastic Non-Conforming Contact

A fast algorithm for elastic-plastic non-conforming contact simulation is presented in this work. While the elastic response of a material subjected to load application is reversible, plasticity theory describes the irreversible behavior of the material in reaction to loading beyond the limit of elastic domain. Therefore, elastic-plastic response of contacting bodies to loading beyond yield strength is needed to assess the load-carrying capacity of the mechanical contact. The modern approach in simulating elastic-plastic contact is based on the algorithm originally proposed by Mayeur, (Mayeur, 1996), employing Betti’s reciprocal theorem. Although Mayeur developed a model for the three-dimensional problem, numerical implementation was restricted to two-dimensional case, due to lack of formulas for the influence coefficients. Problem generalization is due to Jacq, (Jacq, 2001), and to Jacq et al. (Jacq et al., 2002), who advanced a complete semi-analytical formulation for the three-dimensional elastic-plastic contact. The algorithm was later refined by these authors, (Wang & Keer, 2005), who improved the convergence of residual and elastic loops. The main idea of their Fast Convergence Method (FCM) is to use the convergence values for the current loop as initial guess values for the next loop. This approach reduces the number of iterations if the loading increments are small. Nelias, Boucly, and Brunet, (Nelias et al., 2006), further improved the convergence of the residual loop. They assessed plastic strain increment with the aid of a universal algorithm for integration of elastoplasticity constitutive equations, originally proposed by Fotiu and Nemat-Nasser, (Fotiu & Nemat-Nasser, 1996), as opposed to existing formulation, based on Prandtl-Reuss equations, (Jacq, 2001). As stated in (Nelias et al., 2006), this results in a decrease of one order of magnitude in the CPU time. Influence of a tangential loading in elastic-plastic contact was investigated by Antaluca, (Antaluca, 2005). Kinematic hardening was added by Chen, Wang, Wang, Keer, and Cao, (Chen et al.,2008), who advanced a three-dimensional numerical model for simulating the repeated rolling or sliding contact of a rigid sphere over an elastic-plastic half-space. The efficiency of existing elastic-plastic contact solvers, (Jacq et al., 2002; Wang & Keer, 2005) is impaired by two shortcomings. Firstly, the algorithms are based on several levels of iteration, with the innermost level having a slow convergence. Secondly, the effect of a three-dimensional distribution in a three-dimensional domain, namely residual stresses related to plastic strains, is computed using two-dimensional spectral algorithms.

A Numerical Study of the Partial Slip Elliptical Contact under Fretting Conditions

The technologically important elliptical contact undergoing fretting is simulated using previously advanced state-of-the-art numerical tools. The influence of contact ellipse eccentricity on various contact parameters is assessed. An analogy with the circular contact is found when tractions equations are written in dimensionless coordinates in case of similarly elastic materials. However, when an elastic mismatch is introduced, the stick area no longer follows proportionally the established contact area.

Contact Stress State in Elastic Layers

This paper presents the discrete counterpart of an existing continuous formulation for an elastic layer loaded symmetrically. The influence coefficients based numerical approach allows for computing contact stresses induced in the elastic layer by arbitrary shaped indenters. The newly developed code is validated against existing pressure distributions in layer contact for quadratic form punches.Copyright

Viscoelastic Contact Simulation under Harmonic Cyclic Load

Characterization of viscoelastic materials from a mechanical point of view is often performed via dynamic mechanical analysis (DMA), consisting in the arousal of a steady-state undulated response in a uniaxial bar specimen, allowing for the experimental measurement of the so-called complex modulus, assessing both the elastic energy storage and the internal energy dissipation in the viscoelastic material. The existing theoretical investigations of the complex modulus’ influence on the contact behavior feature severe limitations due to the employed contact solution inferring a nondecreasing contact radius during the loading program. In case of a harmonic cyclic load, this assumption is verified only if the oscillation indentation depth is negligible compared to that due to the step load. This limitation is released in the present numerical model, which is capable of contact simulation under arbitrary loading profiles, irregular contact geometry, and complicated rheological models of linear viscoelastic materials, featuring more than one relaxation time. The classical method of deriving viscoelastic solutions for the problems of stress analysis, based on the elastic-viscoelastic correspondence principle, is applied here to derive the displacement response of the viscoelastic material under an arbitrary distribution of surface tractions. The latter solution is further used to construct a sequence of contact problems with boundary conditions that match the ones of the original viscoelastic contact problem at specific time intervals, assuring accurate reproduction of the contact process history. The developed computer code is validated against classical contact solutions for universal rheological models and then employed in the simulation of a harmonic cyclic indentation of a polymethyl methacrylate half-space by a rigid sphere. The contact process stabilization after the first cycles is demonstrated and the energy loss per cycle is calculated under an extended spectrum of harmonic load frequencies, highlighting the frequency for which the internal energy dissipation reaches its maximum.

Numerical Analysis of Load Carrying Capacity in the Contact between High-Order Surfaces

The strength of the contact between high-order polynomial surfaces, optimized as to induce a close to uniform pressure distribution on the contact area, is investigated by computer simulation. Three type of contact conditions are examined, i.e. frictionless, gross slip and partial slip, and the depth and magnitude of the maximum of von Mises equivalent stress field is assessed using the Greens functions for the elastic half-space and a multi-summation technique based on the fast Fourier transform and on the convolution theorem. The set of simulations allows formulating recommendations concerning the use of punches bounded by high-order polynomial surfaces to increase the load-carrying capacity of the non-conforming mechanical contact.

Some Aspects Regarding the Analysis of Straight Rods with Polygonal Cross Section Subjected to Torsion

The present paper aims to model straight rods having regular polygonal cross sections, analyzing in particular triangular cross sections (isosceles and equilateral triangles) as well as rectangular cross sections subjected to torsion. Stress and strain states for such cross sections under torsion were determined and plotted as 3D and contour plots using Mathcad. Keywords: torsion, polygonal cross section, modeling.

Numerical Simulation of Slip-Stick Elastic Contact

Fretting defines a condition in which mechanical contacts are subjected to alternating tangential displacements, small compared to dimensions of contact area, due to oscillating loading conditions. Fretting wear and fretting fatigue are between the most important factors responsible for contact failure, especially when high loads are transmitted through non-conforming contacts, leading to highly localized stress concentrators in the vicinity of the contact region. Prediction of life span of machine elements working in such conditions requires assessment of stress and strain in the contacting bodies, which is the main subject of Contact Mechanics. Although fretting is intrinsically a multidisciplinary process, involving adhesion, oxidation, abrasion and pitting, modern approach suggests that contact stresses play a chief role.

Improved Pressure Distribution in Elliptic Elastic Contacts between High-Order Surfaces

The improvement of mechanical contacts or microcontacts seeks a nearly uniform current density over most of contact area. When microtopography is homogeneous, this aim is achieved if nominal shape of contacting surfaces yields a nearly uniform central pressure which decreases monotonously to zero in contour points. These authors derived recently this shape for circular contacts by employing high-order surfaces. This paper extends this result to elliptical contacts. Some results are used to this end, derived for elliptical elastic contacts between high-order surfaces. As homogeneous high order surfaces lead to a highly nonuniform pressure distribution, central pressure is flattened by making the first derivatives of pressure vanish in contact center. Then, the contacts between fourth, sixth, and eighth, order surfaces are analyzed and recurrence relations for pressure distribution and contact parameters are proposed.

A NUMERICAL SOLUTION TO THE CATTANEO-MINDLIN PROBLEM PART I: ALGORITHM DESCRIPTION

The Cattaneo-Mindlin problem addresses the elastic spherical contact undergoing normal and tangential loading, when the tangential force is less than a limiting value inducing a gross-slip regime. The principles of problem digitization and the state of the art in solving the normal contact problem are overviewed. A numerical model for the Cattaneo-Mindlin problem is advanced and solved via conjugate gradient method. Shear tractions are derived as the solution of the linear system arising from discretization of integral equation of deformation. Complementarity conditions, assessing the stick or slip status of cells in the contact area, and static force equilibrium, are enforced during conjugate gradient iterations, thus eliminating the need for additional iterative levels.