Variational Methods for Crystalline Microstructure - Analysis and Computation
Edition: 1 edition
Publisher: Springer
Published: January 31, 2003
Language: eng
Format: Paperback
Number of pages: 220
ISBN-13: 9783540001140
Subjects: Mathematics; States of matter; Microstructure; Mechanical Properties Of Materials; Technology; Science; Science/Mathematics; Nanostructures; Differential Equations; General; 74B20, 74G15, 74G65, 74N15, 65M60; Mathematics / Differential Equations; microstructures; nematic elastomers; numerics of microstructures; quasiconvexity; Applied; Material Science; Mathematical Models
Description: 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.