Variational Methods for Crystalline Microstructure - Analysis and Computation
Authors: Dolzmann, Georg
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- About this book
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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.
- Table of contents (12 chapters)
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1. Introduction
Pages 1-10
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2. Semiconvex Hulls of Compact Sets
Pages 11-68
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3. Macroscopic Energy for Nematic Elastomers
Pages 69-81
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4. Uniqueness and Stability of Microstructure
Pages 83-126
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5. Applications to Martensic Transformations
Pages 127-152
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Table of contents (12 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Variational Methods for Crystalline Microstructure - Analysis and Computation
- Authors
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- Georg Dolzmann
- Series Title
- Lecture Notes in Mathematics
- Series Volume
- 1803
- Copyright
- 2003
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-540-36125-1
- DOI
- 10.1007/b10191
- Softcover ISBN
- 978-3-540-00114-0
- Series ISSN
- 0075-8434
- Edition Number
- 1
- Number of Pages
- XI, 217
- Topics
