Modeling of Contact Processes
In this chapter, we present a general description of mathematical modeling of the processes involved in contact between a deformable body and an obstacle or a foundation. Such kind of processes abound in industry and everyday life and, for this reason, a considerable e.ort has been made in their modeling, analysis, and numerical simulations. We present the physical setting, the variables that determine the state of the system, the material behavior that is re.ected in a constitutive law, the input data, the equation of evolution for the state of the system, and the boundary conditions for the system variables. In particular, we provide a description of the frictional contact conditions, including versions of the Coulomb law of dry friction and its regularizations. Most of the notions and results we present here are standard and can be found in many books on mechanics and, therefore, we skip many of the details. In this chapter, all variables are assumed to have su.cient degree of smoothness consistent with developments they are involved in.
KeywordsContact Condition Slip Rate Maxwell Model Frictional Contact Contact Process
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