Contact stresses: a short survey of models and methods of computations

Abstract

Contact stresses are identified as normal and tangential forces between contacting solids. The normal stresses are modeled using unilateral and complementary conditions, elastic response and normal compliance. Friction laws describe the tangential traction. Friction of materials depends on pressure, sliding velocity, surface temperature, time of contact, surface roughness and presence of wear debris. Phenomenological, micromechanical and atomic-scale models as well as non-classical models of anisotropic and heterogeneous friction are important steps in the development of friction modeling. Sophisticated friction models are desirable in vibrating systems, materials processing, rolling contacts, rubber and polymers, geomechanics, bioengineering and living systems. Main numerical methods in contact mechanics are: finite element method, boundary element method and discrete element method. To include specific contact constraints, the following computing techniques are applied: Lagrange multipliers, penalty function, perturbated and augmented Lagrangian methods, mathematical programming methods. The advances of adhesion and impact modeling are outlined in this paper.

Fast FE–BEM algorithms for orthotropic frictional contact

“…Some works in the literature have studied and developed different friction models. Curnier [1] presents a general theory of friction, Michalowski and Mróz [2] and Mróz and Stupkiewicz [3] consider an orthotropic model with a non-associated sliding rule, and Zmitrowicz [4][5][6][7] takes into account more sophisticated friction models.…”

If holm had used a Scanning Tunneling Microscope: What the nanoscientists are teaching us about electrical contacts

“…Some models assume frictionless contact and others add continuum models of adhesion to the elements. A survey of numerical modeling techniques and methods used to determine contact stresses is found in [26]. Megalingam et al reviews all existing models and provides a comprehensive elastic-plastic single-asperity contact model [23].…”

Motion of a thin elliptic plate under symmetric and asymmetric orthotropic friction forces

“…It can be shown that integrals in the third equation of system (25) is equal to zero for elliptical and circular contact areas. So, finally we have:…”