Many physical systems require the description of mechanical interaction
across interfaces if they are to be successfully analyzed. Examples in
the engineered world range from the design of prosthetics in biomedical
engi- neering (e. g., hip replacements); to characterization of the
response and durability of head/disk interfaces in computer magnetic
storage devices; to development of pneumatic tires with better handling
characteristics and increased longevity in automotive engineering; to
description of the adhe- sion and/or relative slip between concrete and
reinforcing steel in structural engineering. Such mechanical
interactions, often called contact/impact in- teractions, usually
necessitate at minimum the determination of areas over which compressive
pressures must act to prevent interpenetration of the mechanical
entities involved. Depending on the application, frictional be- havior,
transient interaction of interfaces with their surroundings (e. g., in-
termittent stick/slip), thermo-mechanical coupling, interaction with an
in- tervening lubricant and/or fluid layer, and damage of the interface
(i. e., wear) may also be featured. When taken together (or even
separately!), these features have the effect of making the equations of
mechanical evolu- tion not only highly nonlinear, but highly nonsmooth
as well. While many modern engineering simulation packages possess
impressive capabilities in the general area of nonlinear mechanics, it
can be contended that methodologies typically utilized for contact
interactions are relatively immature in comparison to other components
of a nonlinear finite element package, such as large deformation
kinematics, inelastic material modeling, nonlinear equation solving, or
linear solver technology.
