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＜E-Book＞
Variational Methods for Crystalline Microstructure - Analysis and Computation / by Georg Dolzmann
(Lecture Notes in Mathematics. ISSN:16179692 ; 1803)

Edition	1st ed. 2003.
Publisher	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
Year	2003
Language	English
Size	XI, 217 p : online resource
Authors	*Dolzmann, Georg author SpringerLink (Online service)
Subjects	LCSH:Mathematics LCSH:Condensed matter LCSH:Differential equations LCSH:Numerical analysis LCSH:Mathematical physics LCSH:Mechanics FREE:Mathematics FREE:Condensed Matter Physics FREE:Differential Equations FREE:Numerical Analysis FREE:Mathematical Methods in Physics FREE:Classical Mechanics
Notes	Introduction -- Semiconvex Hull of Compact Sets -- Macroscopic Energy for Nematic Elastomers -- Uniqueness and Stability of Microstructure -- Applications to Martensitic Transformations -- Algorithmic Aspects -- Bibliographic Remarks -- A. Convexity Conditions and Rank-one Connections -- B. Elements of Crystallography -- C. Notation -- References -- Index 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 HTTP:URL=https://doi.org/10.1007/b10191

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