Alber H.D., Dold A. (Ed) — Materials with Memory: Initial-Boundary Value Problems for Constitutive Equations with Internal Variables :: Электронная библиотека попечительского совета мехмата МГУ

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Alber H.D., Dold A. (Ed) — Materials with Memory: Initial-Boundary Value Problems for Constitutive Equations with Internal Variables

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Название: Materials with Memory: Initial-Boundary Value Problems for Constitutive Equations with Internal Variables

Авторы: Alber H.D., Dold A. (Ed)

Аннотация:

This book contributes to the mathematical theory of systems of differential equations consisting of the partial differential equations resulting from conservation of mass and momentum, and of constitutive equations with internal variables. The investigations are guided by the objective of proving existence and uniqueness, and are based on the idea of transforming the internal variables and the constitutive equations. A larger number of constitutive equations from the engineering sciences are presented. The book is therefore suitable not only for specialists, but also for mathematicians seeking for an introduction in the field, and for engineers with a sound mathematical background.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2008

Количество страниц: 180

Добавлена в каталог: 04.07.2008

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Предметный указатель

$\Gamma$ -star-shaped      92 93 95
Accretive operator      140
Associated free energy      26
Bingham, body      14
Bingham, law      14
Cauchy — Kowalevski, Theorem of      4
Causal mapping      139
Characteristic function      32
Classes of constitutive e $\mathcal{I}$ quations of $\mathcal{TM}^{*}$ , $\mathcal{TG}$ , $\mathcal{TM}$ , $\mathcal{T(MG)}$       59
Classes of constitutive equations, definition of $\mathcal{M}^{*}$ , $\mathcal{G}$ , $\mathcal{M}$ , $\mathcal{MG}$       26
Clausius — Duhem inequality      145 146 147
Collapse theorem      29
Compatibility conditions      4 75 93 97 104
Complementary subspace, definition      77
Conservation law of energy      144
Conservation law of linear momentum      8 144
Conservation law of mass      144
Conservation law of moment of momentum      145
Crystallographic model      21 38
Deformation gradient      144
Dilatant      14
Dynamic problem      31
Elasticity tensor      8
entropy      145
Flow rule      11
Glide plain      21
Hardening      97 106ff 118
Hardening, isotropic      16ff
Hardening, kinematic      15ff
History functional, realization of      139
Hysteresis loop      142
Internal dissipation, inequality of      150
Korn's first and second inequalities      48 54
Lax — Milgram, Theorem of      54
Legendre transform      150 151 152
Material function      118

Material objectivity, principle of      144
Monotone, maximal monotone, definition      26 27ff 31 45ff 59 100
Monotone, monotone operator, definition      24
Monotone, monotone vector field, definition      24
Norton's law      14
Proper function, definition      25
Pseudo-plastic      14
Quasi-static problem, definition      29
Set-valued map, domain of      10
Set-valued map, inverse of      50
Set-valued map, range of      50
Shakedown theorem      29
Simple material      144
Slip system      21
Sobolev spaces $H_{m} (\Omega)$ , $\overset{\circ}{H}_{m} (\Omega)$       46
Star-shaped      92
Strain, strain rate      18 20
Strain, strain tensor, Green      144 152
Strain, strain tensor, inelastic      111
Strain, strain tensor, linear      8
Strain, strain tensor, macroscopic      21
Strain, strain tensor, plastic      8 11 13 20 21 107 117
Strain, strain tensor, viscous      13
Stress, backstress      15
Stress, deviator      12
Stress, overstress      20
Stress, stress tensor, Cauchy      7
Stress, stress tensor, Piola — Kirchhoff      144 145
Subdifferential, definition      25
Thermodynamically admissible      9
Transformation $\mathcal{T}_{H}$ of pairs, definition      58
Weak divergence      46 53
Weak formulation of initial-boundary value problems      47 56
Weak Neumann boundary condition      47 53 55
Yield criterion, Tresca's      12
Yield criterion, von Mises      11
Yield surface      99 100

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