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Over the past 50 years, strain gradient material theories have been
developed for the continuum modeling of size effects in materials
and structures in terms of their elasticity, plasticity and
fracturing. This book puts forward a unifying perspective to
combine existing theories involving the higher order gradient of
the strain tensor, or of plastic strain. It begins by reviewing
experimental findings on the existence (or non-existence) of size
effects on the mechanics of materials. In turn, the book devises
first, second and higher order strain gradient theories from
general principles, and presents constitutive frameworks that
satisfy thermodynamic requirements. The special case of strain
gradient plasticity is then developed and illustrated via
computational analyses of size effects on the plasticity of metals
at small scales. In closing, the book explains the origin of
gradient effects in the case of lattice structures by drawing on
homogenization theory.
Over the past 50 years, strain gradient material theories have been
developed for the continuum modeling of size effects in materials
and structures in terms of their elasticity, plasticity and
fracturing. This book puts forward a unifying perspective to
combine existing theories involving the higher order gradient of
the strain tensor, or of plastic strain. It begins by reviewing
experimental findings on the existence (or non-existence) of size
effects on the mechanics of materials. In turn, the book devises
first, second and higher order strain gradient theories from
general principles, and presents constitutive frameworks that
satisfy thermodynamic requirements. The special case of strain
gradient plasticity is then developed and illustrated via
computational analyses of size effects on the plasticity of metals
at small scales. In closing, the book explains the origin of
gradient effects in the case of lattice structures by drawing on
homogenization theory.
The book helps to answer the following questions: How far have the
understanding and mesoscale modeling advanced in recent decades,
what are the key open questions that require further research and
what are the mathematical and physical requirements for a mesoscale
model intended to provide either insight or a predictive
engineering tool? It is addressed to young researchers including
doctoral students, postdocs and early career faculty,
This volume is devoted to an actual topic which is the focus
world-wide of various research groups. It contains contributions
describing the material behavior on different scales, new existence
and uniqueness theorems, the formulation of constitutive equations
for advanced materials. The main emphasis of the contributions is
directed on the following items - Modelling and simulation of
natural and artificial materials with significant microstructure, -
Generalized continua as a result of multi-scale models, -
Multi-field actions on materials resulting in generalized material
models, - Theories including higher gradients, and - Comparison
with discrete modelling approaches
Gabrio Piola works had an enormous impact on the development of
applied mathematics and continuum mechanics. An excellent
scientific committee who took it upon themselves to translate his
complete works. In a second step, they commented Piola's work and
compared it to modern theories in mechanics in order to stress
Piola's impact on modern science and proofs that he has set
milestones in applied mathematics. This book presents Piola's
original Italian text together with ist translations and their
comments. It shows impressively that Gabrio Piola's work must still
be regarded as a modern theory.
This volume is devoted to an actual topic which is the focus
world-wide of various research groups. It contains contributions
describing the material behavior on different scales, new existence
and uniqueness theorems, the formulation of constitutive equations
for advanced materials. The main emphasis of the contributions is
directed on the following items - Modelling and simulation of
natural and artificial materials with significant microstructure, -
Generalized continua as a result of multi-scale models, -
Multi-field actions on materials resulting in generalized material
models, - Theories including higher gradients, and - Comparison
with discrete modelling approaches
This volume presents contributions describing the micro- and
macro-behaviours, new existence and uniqueness theorems, the
formulation of multi-scale problems, etc. and now it is time to
ponder again the state of matter and to discuss new trends and
applications. The main focus is directed on the following items -
Modelling and simulation of materials with significant
microstructure, - Generalized continua as a result of multi-scale
models, - Multi-field actions on materials resulting in generalized
material models, and - Comparison with discrete modelling
approaches
Gabrio Piola works had an enormous impact on the development of
applied mathematics and continuum mechanics. An excellent
scientific committee who took it upon themselves to translate his
complete works. In a second step, they commentedPiola s work and
compared it to modern theories in mechanics in order to stress
Piola s impact on modern science and proofs that he has set
milestones in applied mathematics.
This book presents Piola's original Italian text together with ist
translations and their comments. It shows impressively that Gabrio
Piola s work must still be regarded as a modern theory."
In mechanical engineering and structural analysis there is a
significant gap between the material models currently used by
engineers for industry applications and those already available in
research laboratories. This is especially apparent with the huge
progress of computational possibilities and the corresponding
dissemination of numerical tools in engineering practice, which
essentially deliver linear solutions. Future improvements of design
and life assessment methods necessarily involve non-linear
solutions for inelastic responses, in plasticity or
viscoplasticity, as well as damage and fracture analyses.
The dissemination of knowledge can be improved by software
developments, data base completion and generalization, but also by
information and training. With such a perspective Non-Linear
Mechanics of Materials proposes a knowledge actualization, in order
to better understand and use recent material constitutive and
damage modeling methods in the context of structural analysis or
multiscale material microstructure computations.
This volume presents contributions describing the micro- and
macro-behaviours, new existence and uniqueness theorems, the
formulation of multi-scale problems, etc. and now it is time to
ponder again the state of matter and to discuss new trends and
applications. The main focus is directed on the following items -
Modelling and simulation of materials with significant
microstructure, - Generalized continua as a result of multi-scale
models, - Multi-field actions on materials resulting in generalized
material models, and - Comparison with discrete modelling
approaches
In mechanical engineering and structural analysis there is a
significant gap between the material models currently used by
engineers for industry applications and those already available in
research laboratories. This is especially apparent with the huge
progress of computational possibilities and the corresponding
dissemination of numerical tools in engineering practice, which
essentially deliver linear solutions. Future improvements of design
and life assessment methods necessarily involve non-linear
solutions for inelastic responses, in plasticity or
viscoplasticity, as well as damage and fracture analyses.
The dissemination of knowledge can be improved by software
developments, data base completion and generalization, but also by
information and training. With such a perspective Non-Linear
Mechanics of Materials proposes a knowledge actualization, in order
to better understand and use recent material constitutive and
damage modeling methods in the context of structural analysis or
multiscale material microstructure computations.
This scarce antiquarian book is a selection from Kessinger
PublishingA AcentsAcentsa A-Acentsa Acentss Legacy Reprint Series.
Due to its age, it may contain imperfections such as marks,
notations, marginalia and flawed pages. Because we believe this
work is culturally important, we have made it available as part of
our commitment to protecting, preserving, and promoting the world's
literature. Kessinger Publishing is the place to find hundreds of
thousands of rare and hard-to-find books with something of intere
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