Contact mechanics stress distributions

The classical theory of contact mechanics, due to Hertz, treats the bodies in contact with a hard wall repulsive interaction, i.e. there is no attractive interaction whatsoever, and a steep repulsion comes into play when the surfaces of the bodies are in contact. The Hertzian theory assumes that only normal stresses exist, i.e. the shear stress in the contact region is zero. Under these conditions, the contact radius a), central displacement (3) and the distribution of normal stress (a) are given by the following expressions ... 

The standard model for analyzing QCM data is based on linear mechanics. All forces and stresses are assiuned to be proportional to displacement or speed. Such a linear behavior is a prerequisite for equivalent circuits to apply. Nonlinear behavior, generally speaking, is often found in contact mechanics because of the sharp peaks in the stress distribution. 

It is important to note here that we have only posed a few generic questions we could have asked additional questions had we considered the specifics of the application. For example, when seiecdr materials for implants in bioengineering applications, one must consider many additional ctors, inducfing Is the material toxic to the body Can the material be sterilized When the material comes into contact with body fluid will it corrode or deteriorate Because the human body is a dynamic system, we should also ask How would the material react to mechanical shock and fiitigue Are the mechanical properties of the implant material compatible with those of bone to ensure appropriate stress distributions at contaa surfaces These are examples of additional specific questions that one could ask to find suitable material for a specific application. 

Redox active polymer films are ideally suited to tackling these issues. The properties of many of these electroactive polymers, e.g., their conductivity, charge distribution, shape, etc., can be changed in a controlled and reproducible way in response to environmental stimuli, e.g., a change in the nature of the contacting solution, an applied voltage, light intensity, or mechanical stress. 

But infinite stress is always present in cracking problems and poses no difficulty if an energy-balance theory of crack equilibrium is used (see Fracture Mechanics). Applying this method to the above stress distribution gave the following equation, the so-called JKR equation, for the elastic contact spot diameter d of equal spheres, diameter D and... 

Solutions for simplified cases in which it is assumed that plane sections of the coating remain plane after indentation-induced compression, can be found in the book by Johnson [75]. Johnson s approach was subsequently extended by Jaffar [76]. An early work [24] assumed frictionless contact and used elastic continuum mechanics to estimate the stress distribution in layered materials. In this analysis, force and displacement continuity at the interfaces was satisfied exactly, while the surface displacement condition (profile of the indenter), was only approximated. These authors analyzed indentation stresses created by circular flat-ended and parabolic indenters numerically on both single and multilayer systems, with good results. 

The compliance based treatment of contact mechanics is useful because it relies only on directly measurable quantities, these being the load, displacement and contact radius. It does not rely on information relating to the detailed stress distribution within the material. Often, however, it is useful to have more information about this stress distribution. Analytic theories of non-adhesive contact generally assume that the contact is frictionless, so that the interface is not able to support shear stresses. The Hertzian form of the radial distribution of the normal stress, or contact pressure, for frictionless contact is given by the following expression [1 ] ... 

Adhesive bonding has many advantages, including more uniform stress distributions in comparison to the use of mechanical fasteners such as bolts, rivets, etc. Adhesives provide full contact with mating surfaces, thus forming a barrier to fluids and gasses which may cause degradation in the assembled structure. Adhesives can also function as electrical and/or thermal insulators or conductors in joints. 

Haines D.J., Ollerton E. - Contact Stress Distributions on Elliptical Contact Surfaces Subjected to Radial and Tangential Forces. Proceedings of the Institution of Mechanical Engineers, 1963, Vol. 177, pp. 95-114. 

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