Ryszard Buczkowski

ELASTO-PLASTIC INTERFACE MODEL FOR 3D-FRICTIONAL ORTHOTROPIC CONTACT PROBLEMS

The present study deals with the solution of the fully three-dimensional contact/friction problem taking into account microstructural characteristics of the surfaces. An incremental non-associated hardening friction law model analogous to the classical theory of plasticity is used. Two different non-linear friction functions in the orthogonal directions are used to account for the orthotropic properties of the contacting bodies. A frontal solver processing unsymmetric matrices is adopted. Two numerical examples have been selected to show applicability of the method proposed.

A stochastic model of rough surfaces for finite element contact analysis

Abstract This paper is concerned with the development of mathematical models for the normal and tangential stiffness of rough flat surfaces. A detailed statistical analysis of a rough surface is performed in terms of peak distribution and the distribution of curvature at the peaks. A random surface model of elasto-plastically yielding asperities with a Gaussian height distribution combined with mechanical description of a single peak based on Hertz theory coupled with the Mindlin friction theory is investigated. The stochastic model is included in an incremetal finite element procedure to make the two-dimensional contact problem solution possible. The influence of the standard deviation of the height asperities on the values of both the tangential and normal stiffness at the joint interface has been found significant. It is an important factor when determining the overall behaviour of the fixed flat joint; the standard deviation of curvatures has been found to have a secondary effect only.

21-node hexahedral isoparametric element for analysis of contact problems

Because the 20-node solid element of the serendipity family does not fulfil the physical contact requirements properly (the equivalent nodal forces include negative values) a 21-node three-dimensional transient element for the non-linear contact/friction problem is investigated. Construction of the shape functions is described. The proposed transition element is established by adding one node to the top or bottom face of the basic 20-node solid serendipity element for an effective connection between the contact region (21-node elements) and the rest of the structure (20-node elements) with minimum degrees of freedom possible. Comparisons with results calculated for the 3D-contact problem using the combinations of the 8-node element connected to 20-node finite elements prove the high accuracy and overall superiority of the present method. The numerical examples are shown to illustrate the validity and efficiency of the developed technique. The approach may be employed easily in existing computer codes.

Statistical model of strongly anisotropic rough surfaces for finite element contact analysis

The elastic model of anisotropic rough surfaces is considered by approximating the summits by elliptic paraboloids (vertical cross-sections are parabolas and horizontal cross-sections are ellipses). The complete description of anisotropic random surfaces is restricted here to strongly rough surfaces; for such surfaces the summits are represented by highly ecctentric elliptic paraboloids having their semi-major axes oriented in the direction of the grain. The statistical description of random, strongly anisotropic Gaussian surfaces based on the model of Bush et al. [5] is adopted. To calculate the forces and contact area for the single asperity in the elastic range the solution of Hertz is used. For modelling of the discontinuity at the contact surface a quadratic 18-node zero thickness interface element interacting with a transient 21-node hexahedral nite element is used. A beam of rectangular cross-section lying with one of its longitudinal narrow faces against at rigid base is selected to demonstrate applicability of the method proposed. Copyright ? 2000 John Wiley & Sons, Ltd.

Ultrasonic Measurements of Contact Stiffness Between Rough Surfaces

We have used an ultrasonic method to determine the normal and shear stiffness for three different surfaces. The degree of hysteresis for the loading/unloading and stiffness ratio is a function of roughness. Nonlinear contact stiffness characteristics are obtained. The ratio of tangential to normal stiffness KT/KN slowly increases in proportion to normal loading. The novelty of our setup is that at the same time we can measure the reflection coefficient, obtain results for three transducers simultaneously, and measure the approach as a function of load. The presented experimental results of normal contact stiffness measurements have been used for the verification of our theoretical model based on a fractal description of rough surfaces (Buczkowski et al., “Fractal Normal Contact Stiffness of Rough Surfaces,” Arch. Mech. (submitted for publication).