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Homogenization is a fairly new, yet deep field of mathematics which
is used as a powerful tool for analysis of applied problems which
involve multiple scales. Generally, homogenization is utilized as a
modeling procedure to describe processes in complex structures.
Applications of Homogenization Theory to the Study of Mineralized
Tissue functions as an introduction to the theory of
homogenization. At the same time, the book explains how to apply
the theory to various application problems in biology, physics and
engineering. The authors are experts in the field and collaborated
to create this book which is a useful research monograph for
applied mathematicians, engineers and geophysicists. As for
students and instructors, this book is a well-rounded and
comprehensive text on the topic of homogenization for graduate
level courses or special mathematics classes. Features: Covers
applications in both geophysics and biology. Includes recent
results not found in classical books on the topic Focuses on
evolutionary kinds of problems; there is little overlap with books
dealing with variational methods and T-convergence Includes new
results where the G-limits have different structures from the
initial operators
This book addresses the need for a fundamental understanding of the
physical origin, the mathematical behavior and the numerical
treatment of models which include microstructure. Leading
scientists present their efforts involving mathematical analysis,
numerical analysis, computational mechanics, material modelling and
experiment. The mathematical analyses are based on methods from the
calculus of variations, while in the numerical implementation
global optimization algorithms play a central role. The modeling
covers all length scales, from the atomic structure up to
macroscopic samples. The development of the models ware guided by
experiments on single and polycrystals and results will be checked
against experimental data.
Homogenization is a fairly new, yet deep field of mathematics which
is used as a powerful tool for analysis of applied problems which
involve multiple scales. Generally, homogenization is utilized as a
modeling procedure to describe processes in complex structures.
Applications of Homogenization Theory to the Study of Mineralized
Tissue functions as an introduction to the theory of
homogenization. At the same time, the book explains how to apply
the theory to various application problems in biology, physics and
engineering. The authors are experts in the field and collaborated
to create this book which is a useful research monograph for
applied mathematicians, engineers and geophysicists. As for
students and instructors, this book is a well-rounded and
comprehensive text on the topic of homogenization for graduate
level courses or special mathematics classes. Features: Covers
applications in both geophysics and biology. Includes recent
results not found in classical books on the topic Focuses on
evolutionary kinds of problems; there is little overlap with books
dealing with variational methods and T-convergence Includes new
results where the G-limits have different structures from the
initial operators
The book presents the latest findings in experimental plasticity,
crystal plasticity, phase transitions, advanced mathematical
modeling of finite plasticity and multi-scale modeling. The
associated algorithmic treatment is mainly based on finite element
formulations for standard (local approach) as well as for
non-standard (non-local approach) continua and for pure macroscopic
as well as for directly coupled two-scale boundary value problems.
Applications in the area of material design/processing are covered,
ranging from grain boundary effects in polycrystals and phase
transitions to deep-drawing of multiphase steels by directly taking
into account random microstructures.
This book addresses the need for a fundamental understanding of the
physical origin, the mathematical behavior and the numerical
treatment of models which include microstructure. Leading
scientists present their efforts involving mathematical analysis,
numerical analysis, computational mechanics, material modelling and
experiment. The mathematical analyses are based on methods from the
calculus of variations, while in the numerical implementation
global optimization algorithms play a central role. The modeling
covers all length scales, from the atomic structure up to
macroscopic samples. The development of the models ware guided by
experiments on single and polycrystals and results will be checked
against experimental data.
Variational calculus has been the basis of a variety of powerful
methods in the ?eld of mechanics of materials for a long time.
Examples range from numerical schemes like the ?nite element method
to the determination of effective material properties via
homogenization and multiscale approaches. In recent years, however,
a broad range of novel applications of variational concepts has
been developed. This c- prises the modeling of the evolution of
internal variables in inelastic materials as well as the initiation
and development of material patterns and microstructures. The IUTAM
Symposium on "Variational Concepts with Applications to the -
chanics of Materials" took place at the Ruhr-University of Bochum,
Germany, on September 22-26, 2008. The symposium was attended by 55
delegates from 10 countries. Altogether 31 lectures were presented.
The objective of the symposium was to give an overview of the new
dev- opments sketched above, to bring together leading experts in
these ?elds, and to provide a forum for discussing recent advances
and identifying open problems to work on in the future. The
symposium focused on the developmentof new material models as well
as the advancement of the corresponding computational techniques.
Speci?c emphasis is put on the treatment of materials possessing an
inherent - crostructure and thus exhibiting a behavior which
fundamentally involves multiple scales. Among the topics addressed
at the symposium were: 1. Energy-based modeling of material
microstructures via envelopes of n- quasiconvex potentials and
applications to plastic behavior and pha- transformations.
An intensive development of the theory of generalized analytic
functions started when methods of Complex Analysis were combined
with methods of Functional Analysis, especially with the concept of
distributional solutions to partial differential equations. The
power of these interactions is far from being exhausted. In order
to promote the further development of the theory of generalized
analytic functions and applications of partial differential
equations to Mechanics, the Technical University of Graz organized
a conference whose Proceedings are contained in the present volume.
The contributions on generalized analytic functions (Part One) deal
not only with problems in the complex plane (boundary value and
initial value problems), but also related problems in higher
dimensions are investigated where both several complex variables
and the technique of Clifford Analysis are used. Part Two of the
Proceedings is devoted to applications to Mechanics. It contains
contributions to a variety of general methods such as L p-methods,
boundary elements and asymptotic methods, and hemivariational
inequalities. A substantial number of the papers of Part Two,
however, deals with problems in Ocean Acoustics. The papers of both
parts of the Proceedings can be recommended to mathematicians,
physicists, and engineers working in the fields mentioned above, as
well as for further reading within graduate studies.
Variational calculus has been the basis of a variety of powerful
methods in the ?eld of mechanics of materials for a long time.
Examples range from numerical schemes like the ?nite element method
to the determination of effective material properties via
homogenization and multiscale approaches. In recent years, however,
a broad range of novel applications of variational concepts has
been developed. This c- prises the modeling of the evolution of
internal variables in inelastic materials as well as the initiation
and development of material patterns and microstructures. The IUTAM
Symposium on "Variational Concepts with Applications to the -
chanics of Materials" took place at the Ruhr-University of Bochum,
Germany, on September 22-26, 2008. The symposium was attended by 55
delegates from 10 countries. Altogether 31 lectures were presented.
The objective of the symposium was to give an overview of the new
dev- opments sketched above, to bring together leading experts in
these ?elds, and to provide a forum for discussing recent advances
and identifying open problems to work on in the future. The
symposium focused on the developmentof new material models as well
as the advancement of the corresponding computational techniques.
Speci?c emphasis is put on the treatment of materials possessing an
inherent - crostructure and thus exhibiting a behavior which
fundamentally involves multiple scales. Among the topics addressed
at the symposium were: 1. Energy-based modeling of material
microstructures via envelopes of n- quasiconvex potentials and
applications to plastic behavior and pha- transformations.
An intensive development of the theory of generalized analytic
functions started when methods of Complex Analysis were combined
with methods of Functional Analysis, especially with the concept of
distributional solutions to partial differential equations. The
power of these interactions is far from being exhausted. In order
to promote the further development of the theory of generalized
analytic functions and applications of partial differential
equations to Mechanics, the Technical University of Graz organized
a conference whose Proceedings are contained in the present volume.
The contributions on generalized analytic functions (Part One) deal
not only with problems in the complex plane (boundary value and
initial value problems), but also related problems in higher
dimensions are investigated where both several complex variables
and the technique of Clifford Analysis are used. Part Two of the
Proceedings is devoted to applications to Mechanics. It contains
contributions to a variety of general methods such as L p-methods,
boundary elements and asymptotic methods, and hemivariational
inequalities. A substantial number of the papers of Part Two,
however, deals with problems in Ocean Acoustics. The papers of both
parts of the Proceedings can be recommended to mathematicians,
physicists, and engineers working in the fields mentioned above, as
well as for further reading within graduate studies.
The book presents the latest findings in experimental plasticity,
crystal plasticity, phase transitions, advanced mathematical
modeling of finite plasticity and multi-scale modeling. The
associated algorithmic treatment is mainly based on finite element
formulations for standard (local approach) as well as for
non-standard (non-local approach) continua and for pure macroscopic
as well as for directly coupled two-scale boundary value problems.
Applications in the area of material design/processing are covered,
ranging from grain boundary effects in polycrystals and phase
transitions to deep-drawing of multiphase steels by directly taking
into account random microstructures.
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