Constitutive Equations for Contact Interfaces

Abstract

The design of technical systems depends greatly upon the knowledge of the contact behaviour in interfaces which connect different parts of the system. Such systems are very general, examples being cars, printing or copy machines, human joints or implants, unfolding space structures, robots, micro machines or base isolation systems for buildings to protect against earthquakes. Related to the precision which is needed to resolve the mechanical behaviour in the contact interface, different approaches have been established over the centuries to model the mechanical behaviour in the contact area. Two main techniques can be followed to impose contact conditions in the normal direction. These are the formulation of the non-penetration condition as a purely geometrical constraint (the normal contact stresses then follow from the constraint equation), and the development of an elastic or elasto-plastic constitutive laws for the micromechanical approach within the contact area, which yields a response function for the normal contact stresses. Such constitutive equations are often derived from statistical models. For the tangential direction, one has the same situation as for normal contact when stick in the contact interface is considered. Again, either a geometrical constraint equation can be formulated, or a constitutive law for the tangential relative micro displacements between the contacting bodies can be applied. For tangential sliding between bodies, one always has to derive a con-stitutive equation for friction which can be stated in the form of an evolution equation. Usually the frictional evolution depends on different parameters, like normal force, relative tangential velocity, temperature or total slip distance.