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Mechanics have played an important role in mathematics, from
infinitesimal calculus, calculus of variations, partial
differential equations and numerical methods (finite elements).
Originally, mechanics treated smooth objects. Technological
progress has evoked the necessity to model and solve more
complicated problems, like unilateral contact and friction,
plasticity, delamination and adhesion, advanced materials, etc. The
new tools include convex analysis, differential calculus for convex
functions, and subgradients of convex functions and extensions for
nonconvex problems. Nonsmooth mechanics is a relatively complex
field, and requires a good knowledge of mechanics and a good
background in some parts of modern mathematics. The present volume
of lecture notes follows a very successful advanced school, with
the aim to cover as much as possible all these aspects. Therefore
the contributions cover mechanical aspects as well as the
mathematical and numerical treatment.
The idea for this book was developed in the seminar on problems of
con tinuum mechanics, which has been active for more than twelve
years at the Faculty of Mathematics and Physics, Charles
University, Prague. This seminar has been pursuing recent
directions in the development of mathe matical applications in
physics; especially in continuum mechanics, and in technology. It
has regularly been attended by upper division and graduate
students, faculty, and scientists and researchers from various
institutions from Prague and elsewhere. These seminar participants
decided to publish in a self-contained monograph the results of
their individual and collective efforts in developing applications
for the theory of variational inequalities, which is currently a
rapidly growing branch of modern analysis. The theory of
variational inequalities is a relatively young mathematical
discipline. Apparently, one of the main bases for its development
was the paper by G. Fichera (1964) on the solution of the Signorini
problem in the theory of elasticity. Later, J. L. Lions and G.
Stampacchia (1967) laid the foundations of the theory itself.
Time-dependent inequalities have primarily been treated in works of
J. L. Lions and H. Bnlzis. The diverse applications of the
variational in equalities theory are the topics of the well-known
monograph by G. Du vaut and J. L. Lions, Les iniquations en
micanique et en physique (1972)."
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