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  • © 2003

Variational Methods for Crystalline Microstructure - Analysis and Computation

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1803)

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Table of contents (12 chapters)

  1. Front Matter

    Pages I-VIII
  2. 1. Introduction

    • Georg Dolzmann
    Pages 1-10
  3. 2. Semiconvex Hulls of Compact Sets

    • Georg Dolzmann
    Pages 11-68
  4. 4. Uniqueness and Stability of Microstructure

    • Georg Dolzmann
    Pages 83-126
  5. 5. Applications to Martensic Transformations

    • Georg Dolzmann
    Pages 127-152
  6. 6. Algorithmic Aspects

    • Georg Dolzmann
    Pages 153-175
  7. 7. Bibliographic Remarks

    • Georg Dolzmann
    Pages 177-182
  8. B. Elements of Crystallography

    • Georg Dolzmann
    Pages 193-196
  9. C. Notation

    • Georg Dolzmann
    Pages 197-200
  10. References

    • Georg Dolzmann
    Pages 201-209
  11. Index

    • Georg Dolzmann
    Pages 211-212
  12. Back Matter

    Pages 213-217

About this book

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.

Keywords

  • Crystallography
  • REM
  • microstructures
  • nematic elastomers
  • numerics of microstructures
  • quasiconvexity
  • semiconvex hulls
  • partial differential equations

Bibliographic Information

Buying options

eBook USD 54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions