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Dolzmann D. — Variational Methods for Crystalline Microstructure - Analysis and Computation
Dolzmann D. — Variational Methods for Crystalline Microstructure - Analysis and Computation

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Название: Variational Methods for Crystalline Microstructure - Analysis and Computation

Автор: Dolzmann D.

Аннотация:

Phase transformations in solids typically lead to surprising mechanical behaviour with far reaching technological applications. The mathematical modeling of these transformations in the late 80s initiated a new field of research in applied mathematics, often referred to as mathematical materials science, with deep connections to the calculus of variations and the theory of partial differential equations. This volume gives a brief introduction to the essential physical background, in particular for shape memory alloys and a special class of polymers (nematic elastomers). Then the underlying mathematical concepts are presented with a strong emphasis on the importance of quasiconvex hulls of sets for experiments, analytical approaches, and numerical simulations.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 228

Добавлена в каталог: 22.05.2008

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Предметный указатель
Algorithm for the computation of envelopes      156
Algorithm for the computation of laminates      166
Austenite      194
Austenite-martensite transformation      3
Body centered unit cell      194
Bravais lattice      193
Cofactor      197
Compatible wells      189
Compound twin      196
Computation of laminates      163
Computation of rank-one convex envelopes      154
Condition $\mathcal{H}_N$      186
Conditions for uniqueness of microstructure, condition $(C_b)$      89
Conditions for uniqueness of microstructure, condition $(C_{tf})$      111
Conditions for uniqueness of microstructure, condition $(\tilde{C}_b)$      103
Constrained point      11
Convexity conditions      183
Crystallographic point groups      193
Cubic      193
D-convexity      185
Dirac mass      187
Eight point set      13
Energy well      2
Excess rotation      85 96
Face centered unit cell      194
Four-well problem      42
Gradient Young measure      187
Hexagonal      193
Homogeneous Young measure      187
Incompatible wells      27 189
Infinite laminate      171
Laminate      187
Laminate of finite order      188
Lamination convex hull      185
Lamination method      7 11
Macroscopic phase diagram      72
Martensite      194
Minor relation      8
Monoclinic      193
Multi-well set      2
Nematic director      70
Nematic elastomers      69
One-well problem      26
Orthogonal group      198
Orthorhombic      193
Point group      194
Polar decomposition      198
Polyaffine functions      8
Polyconvex hull      7 185
Polyconvex measure      187
Polyconvexity      183
Quadratic forms      184
Quasiconvex hull      5 185
Quasiconvexity      183
Radon measures      186
Rank-one connection      4
Rank-one connection, existence      190
Rank-one convex hull      7 185
Rank-one convexity      183
Relaxed energy      69
Second order laminate      188
Semiconvex hull      7
Separation method      7 11
Sets defined by singular values in three dimensions      59
Sets defined by singular values in two dimensions      58
Signed singular values      198
Simple laminate      8 188
Singular value      198
Splitting method      11
Stability      87
Stability of microstructure      83
Taylor bound      51
Tetragonal      193
Three-well problem      39
Triclinic      193
Twin, compound      196
Twin, type-I      196
Twin, type-II      196
Twinning system      195
Two-well problem in three dimensions      55
Two-well problem in two dimensions      27
Unconstrained point      11
Uniqueness in cubic to orthorhombic transformations      135
Uniqueness in cubic to tetragonal transformations      128
Uniqueness in cubic to trigonal transformations      134
Uniqueness in tetragonal to monoclinic transformations      143
Uniqueness of microstructure      83
Unit cell      194
Young measure      7
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