mechanics of generalized continua one hundred years after the cosserats 21 advances in mechanics and mathematics

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Mechanics Of Generalized Continua

Author : Gérard A. Maugin
ISBN : 9781441956958
Genre : Mathematics
File Size : 73. 33 MB
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In their 1909 publication Théorie des corps déformables, Eugène and François Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers. The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics and can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.

Advances In Extended And Multifield Theories For Continua

Author : Bernd Markert
ISBN : 9783642227387
Genre : Technology & Engineering
File Size : 25. 29 MB
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Modern computational techniques, such as the Finite Element Method, have, since their development several decades ago, successfully exploited continuum theories for numerous applications in science and technology. Although standard continuum methods based upon the Cauchy-Boltzmann continuum are still of great importance and are widely used, it increasingly appears that material properties stemming from microstructural phenomena have to be considered. This is particularly true for inhomogeneous load and deformation states, where lower-scale size effects begin to affect the macroscopic material response; something standard continuum theories fail to account for. Following this idea, it is evident that standard continuum mechanics has to be augmented to capture lower-scale structural and compositional phenomena, and to make this information accessible to macroscopic numerical simulations.

Multiscale Modeling Of Complex Materials

Author : Tomasz Sadowski
ISBN : 9783709118122
Genre : Technology & Engineering
File Size : 30. 1 MB
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The papers in this volume deal with materials science, theoretical mechanics and experimental and computational techniques at multiple scales, providing a sound base and a framework for many applications which are hitherto treated in a phenomenological sense. The basic principles are formulated of multiscale modeling strategies towards modern complex multiphase materials subjected to various types of mechanical, thermal loadings and environmental effects. The focus is on problems where mechanics is highly coupled with other concurrent physical phenomena. Attention is also focused on the historical origins of multiscale modeling and foundations of continuum mechanics currently adopted to model non-classical continua with substructure, for which internal length scales play a crucial role.

Plasticity Of Pressure Sensitive Materials

Author : Holm Altenbach
ISBN : 9783642409455
Genre : Technology & Engineering
File Size : 85. 34 MB
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Classical plasticity theory of metals is independent of the hydrostatic pressure. However if the metal contains voids or pores or if the structure is composed of cells, this classical assumption is no more valid and the influence of the hydrostatic pressure must be incorporated in the constitutive description. Looking at the microlevel, metal plasticity is connected with the uniform planes of atoms organized with long-range order. Planes may slip past each other along their close-packed directions. The result is a permanent change of shape within the crystal and plastic deformation. The presence of dislocations increases the likelihood of planes slipping. Nowadays, the theory of pressure sensitive plasticity is successfully applied to many other important classes of materials (polymers, concrete, bones etc.) even if the phenomena on the micro-level are different to classical plasticity of metals. The theoretical background of this phenomenological approach based on observations on the macro-level is described in detail in this monograph and applied to a wide range of different important materials in the last part of this book.

Generalized Continua As Models For Classical And Advanced Materials

Author : Holm Altenbach
ISBN : 9783319317212
Genre : Technology & Engineering
File Size : 37. 68 MB
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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

Mechanics Of Generalized Continua

Author : Holm Altenbach
ISBN : 364219219X
Genre : Technology & Engineering
File Size : 76. 34 MB
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This collection on „Mechanics of Generalized Continua - from Micromechanical Basics to Engineering Applications“ brings together leading scientists in this field from France, Russian Federation, and Germany. The attention in this publication is be focussed on the most recent research items, i.e., - new models, - application of well-known models to new problems, - micro-macro aspects, - computational effort, - possibilities to identify the constitutive equations, and - old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.

Trend And Applications Of Mathematics To Mechanics

Author : S. Rionero
ISBN : 9788847003545
Genre : Technology & Engineering
File Size : 80. 73 MB
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Introduction To The Mechanics Of A Continuous Medium

Author : Lawrence E. Malvern
ISBN : OCLC:2309235
Genre : Continuum mechanics
File Size : 60. 99 MB
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Foundations Of Micropolar Mechanics

Author : Victor A. Eremeyev
ISBN : 9783642283536
Genre : Technology & Engineering
File Size : 42. 53 MB
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The book presents foundations of the micropolar continuum mechanics including a short but comprehensive introduction of stress and strain measures, derivation of motion equations and discussion of the difference between Cosserat and classical (Cauchy) continua, and the discussion of more specific problems related to the constitutive modeling, i.e. constitutive inequalities, symmetry groups, acceleration waves, etc.

Generalized Continua As Models For Materials

Author : Holm Altenbach
ISBN : 9783642363948
Genre : Technology & Engineering
File Size : 51. 89 MB
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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

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