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This book offers a comprehensive and timely overview of
the latest developments in the field of biomechanics and
extensive knowledge of tissue structure, function, and
modeling. Gathering chapters written by authoritative
scientists, it reports on a range of continuum and
computational models of solids, and related experimental works, for
biomechanical applications. It discusses cutting-edge advances such
as constitutive modeling and computational simulation
of biological tissues and organs under physiological
and pathological conditions, and their mechanical
characterization. It covers  innovative studies
on arteries, heart, valvular
tissue, and thrombus, brain tumor, muscle, liver,
kidney, and stomach, among others. Written in honor of
Professor Gerhard A. Holzapfel,  the
book provides specialized readers with a thorough and timely
overview of different types of modeling in biomechanics, and
current knowledge about biological structures and function.
As any human activity needs goals, mathematical research needs
problems -David Hilbert Mechanics is the paradise of mathematical
sciences -Leonardo da Vinci Mechanics and mathematics have been
complementary partners since Newton's time and the history of
science shows much evidence of the ben eficial influence of these
disciplines on each other. Driven by increasingly elaborate modern
technological applications the symbiotic relationship between
mathematics and mechanics is continually growing. However, the
increasingly large number of specialist journals has generated a du
ality gap between the two partners, and this gap is growing wider.
Advances in Mechanics and Mathematics (AMMA) is intended to bridge
the gap by providing multi-disciplinary publications which fall
into the two following complementary categories: 1. An annual book
dedicated to the latest developments in mechanics and mathematics;
2. Monographs, advanced textbooks, handbooks, edited vol umes and
selected conference proceedings. The AMMA annual book publishes
invited and contributed compre hensive reviews, research and survey
articles within the broad area of modern mechanics and applied
mathematics. Mechanics is understood here in the most general sense
of the word, and is taken to embrace relevant physical and
biological phenomena involving electromagnetic, thermal and quantum
effects and biomechanics, as well as general dy namical systems.
Especially encouraged are articles on mathematical and
computational models and methods based on mechanics and their
interactions with other fields. All contributions will be reviewed
so as to guarantee the highest possible scientific standards."
Nonsmoothness and nonconvexity arise in numerous applications of
mechan- ics and modeling due to the need for studying more and more
complicated phe- nomena and real life applications. Mathematicians
have started to provide the necessary tools and theoretical results
underpinning these applications. Ap- plied mathematicians and
engineers have begun to realize the benefits of this new area and
are adopting, increasingly, these new tools in their work. New
computational tools facilitate numerical applications and enable
the theory to be tested, and the resulting feedback poses new
theoretical questions. Because of the upsurge in activity in the
area of nonsmooth and noncon- vex mechanics, Professors Gao and
Ogden, together with the late Professor P.D. Panagiotopoulos, had
planned to organize a Minisymposium with the title Nonsmooth and
Nonconvex Mechanics within the ASME 1999 Mechanics & Materials
Conference, June 27-30 1999, Blacksburg, Virginia. After the unex-
pected death of Professor Panagiotopoulos the first two editors
invited the third editor (Professor Stavroulakis) to join them. A
large number of mathematical and engineering colleagues supported
our efforts by presenting lectures at the Minisymposium in which
the available mathematical methods were described and many problems
of nonsmooth and nonconvex mechanics were discussed. The interest
of the many participants encourages us all to continue our research
efforts.
Advances in Mechanics and Mathematics (AMMA) is intended to bridge
the gap by providing multi-disciplinary publications. This volume,
AMMA 2002, includes two parts with three articles by four subject
experts. Part 1 deals with nonsmooth static and dynamic systems. A
systematic mathematical theory for multibody dynamics with
unilateral and frictional constraints and a brief introduction to
hemivariational inequalities together with some new developments in
nonsmooth semi-linear elliptic boundary value problems are
presented. Part 2 provides a comprehensive introduction and the
latest research on dendritic growth in fluid mechanics, one of the
most profound and fundamental subjects in the area of interfacial
pattern formation, a commonly observed phenomenon in crystal growth
and solidification processes.
As any human activity needs goals, mathematical research needs
problems -David Hilbert Mechanics is the paradise of mathematical
sciences -Leonardo da Vinci Mechanics and mathematics have been
complementary partners since Newton's time and the history of
science shows much evidence of the ben eficial influence of these
disciplines on each other. Driven by increasingly elaborate modern
technological applications the symbiotic relationship between
mathematics and mechanics is continually growing. However, the
increasingly large number of specialist journals has generated a du
ality gap between the two partners, and this gap is growing wider.
Advances in Mechanics and Mathematics (AMMA) is intended to bridge
the gap by providing multi-disciplinary publications which fall
into the two following complementary categories: 1. An annual book
dedicated to the latest developments in mechanics and mathematics;
2. Monographs, advanced textbooks, handbooks, edited vol umes and
selected conference proceedings. The AMMA annual book publishes
invited and contributed compre hensive reviews, research and survey
articles within the broad area of modern mechanics and applied
mathematics. Mechanics is understood here in the most general sense
of the word, and is taken to embrace relevant physical and
biological phenomena involving electromagnetic, thermal and quantum
effects and biomechanics, as well as general dy namical systems.
Especially encouraged are articles on mathematical and
computational models and methods based on mechanics and their
interactions with other fields. All contributions will be reviewed
so as to guarantee the highest possible scientific standards."
Mechanics and mathematics have been complementary partners since
Newton's time and the history of science shows much evidence of the
beneficial influence of these disciplines on each other. Driven by
increasingly elaborate modern technological applications the
symbiotic relationship between mathematics and mechanics is
continually growing. However, the increasingly large number of
specialist journals has generated a duality gap between the two
partners, and this gap is growing wider.
Advances in Mechanics and Mathematics (AMMA) is intended to bridge
the gap by providing multi-disciplinary publications. This volume,
AMMA 2002, includes two parts with three articles by four subject
experts. Part 1 deals with nonsmooth static and dynamic systems. A
systematic mathematical theory for multibody dynamics with
unilateral and frictional constraints and a brief introduction to
hemivariational inequalities together with some new developments in
nonsmooth semi-linear elliptic boundary value problems are
presented. Part 2 provides a comprehensive introduction and the
latest research on dendritic growth in fluid mechanics, one of the
most profound and fundamental subjects in the area of interfacial
pattern formation, a commonly observed phenomenon in crystal growth
and solidification processes.
Audience: Scientists and mathematicians, including advanced
students (doctoral and post-doctoral level) at universities and in
industry interested in mechanics and applied mathematics.
Nonsmoothness and nonconvexity arise in numerous applications of
mechan- ics and modeling due to the need for studying more and more
complicated phe- nomena and real life applications. Mathematicians
have started to provide the necessary tools and theoretical results
underpinning these applications. Ap- plied mathematicians and
engineers have begun to realize the benefits of this new area and
are adopting, increasingly, these new tools in their work. New
computational tools facilitate numerical applications and enable
the theory to be tested, and the resulting feedback poses new
theoretical questions. Because of the upsurge in activity in the
area of nonsmooth and noncon- vex mechanics, Professors Gao and
Ogden, together with the late Professor P.D. Panagiotopoulos, had
planned to organize a Minisymposium with the title Nonsmooth and
Nonconvex Mechanics within the ASME 1999 Mechanics & Materials
Conference, June 27-30 1999, Blacksburg, Virginia. After the unex-
pected death of Professor Panagiotopoulos the first two editors
invited the third editor (Professor Stavroulakis) to join them. A
large number of mathematical and engineering colleagues supported
our efforts by presenting lectures at the Minisymposium in which
the available mathematical methods were described and many problems
of nonsmooth and nonconvex mechanics were discussed. The interest
of the many participants encourages us all to continue our research
efforts.
This book offers a comprehensive and timely overview of the latest
developments in the field of biomechanics and extensive knowledge
of tissue structure, function, and modeling. Gathering chapters
written by authoritative scientists, it reports on a range of
continuum and computational models of solids, and related
experimental works, for biomechanical applications. It discusses
cutting-edge advances such as constitutive modeling and
computational simulation of biological tissues and organs under
physiological and pathological conditions, and their mechanical
characterization. It covers innovative studies on arteries, heart,
valvular tissue, and thrombus, brain tumor, muscle, liver, kidney,
and stomach, among others. Written in honor of Professor Gerhard A.
Holzapfel, the book provides specialized readers with a thorough
and timely overview of different types of modeling in biomechanics,
and current knowledge about biological structures and function.
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