The scientific goal of the action is to develop new and non-standard mathematical and numerical tools
directly motivated by the needs of the analysis of various classes of contact problems in mechanics
which are of fundamental importance in technology, industry and real engineering applications. The overall
objective of the project is to conduct the ground-breaking research in the field of the Mathematical Theory
of Contact Mechanics in physical sciences and engineering. The project crosses the borderlines among
mathematics, mechanics, computer science, and material science. It addresses new and emerging areas of
research: theory of contact in quasicrystals, variational inequalities on nonconvex sets, hemivariational
inequalities, shape optimization and optimal shape design, theory of contact in fluid mechanics, and contact
problems in hyperelasticity.
The scientific results and the knowhow of the project are important for society in many aspects.
They are of interest to areas of research and industry. Potential applications include economic profits
due to more accurate prediction of the material stress, displacement, friction and damage under
various contact regimes. Although the project is mainly oriented at mathematics,
and mathematics contributes a lot to a general mass culture, the action has potential applications
in such areas as, for example, automobile industry, building sciences, civil engineering, metal
engineering, or mechanical models in medicine. The interdisciplinary aspects are exemplified
by the fact that the publications written by the project members are cited both in mathematical papers
as well as in engineering ones.
The role of basic science is very important since it has fundamental influence on science, technology
and other disciplines. We agree with the common belief that our culture is only just approaching the
state in which mathematics will be able to begin a wide penetration of social consciousness. The project
also contributes to the promotion of such a statement. European industry will benefit greatly from many
improvements and tools that will come out from the action. There are many European academic and
industrial sites that currently understand and use rigorous methods of Contact Mechanics because
of the economic profits.
On the European level, significant benefits come from promoting science and scientific career as well as
from raising the standards of research. The project contributes to the major objectives of Research Executive
Agency since it will strengthen the process of development of research activities and increase international
and interdisciplinary mobility of researchers in Europe. The main dissemination media of the results
of the project are peer-reviewed publications, lectures, conferences, events promoting the research
aimed at various audiences, and teaching activities of seconded researchers.
