Lecture Notes in Mathematics

By: Georg Dolzmann

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Paperback | 26 November 2002

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228 Pages

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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.

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You Can Find This Book In

Non-Fiction Engineering & Technology Technology in General Nanotechnology Medicine Medicine in General Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Science Physics Materials & States of Matter

Chemistry Crystallography Mechanical Engineering & Materials Materials Science Applied Mathematics Classical Mathematics Numerical Analysis

Introduction
Semiconvex Hull of Compact Sets
Macroscopic Energy for Nematic Elastomers
Uniqueness and Stability of Microstructure
Applications to Martensitic Transformations
Algorithmic Aspects
Bibliographic Remarks
Convexity Conditions and Rank-one Connections
Elements of Crystallography
Notation
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

Lecture Notes in Mathematics

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