Overview
- Studies asymptotic theories in prestrained elasticity from a rigorous analytical perspective
- Provides the necessary background information from differential geometry and calculus of variations
- Will be of interest to researchers in both mathematics and engineering
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 101)
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About this book
Prestressed thin films are present in many contexts and applications, such as: growing tissues, plastically strained sheets, engineered swelling or shrinking gels, petals and leaves of flowers, or atomically thin graphene layers. While the related questions about the physical basis for shape formation lie at the intersection of biology, chemistry and physics, fundamentally they are of the analytical and geometrical character, and can be tackled using the techniques of the dimension reduction, laid out in this book.
The text will appeal to mathematicians and graduate students working in the fields of Analysis, Calculus of Variations, Partial Differential Equations, and Applied Math. It will also be of interest to researchers and graduate students in Engineering (especially fields related to Solid Mechanics and Materials Science), who would like to gain the modern mathematical insight and learn the necessary tools.
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Keywords
Table of contents (14 chapters)
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Tools in mathematical analysis
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Dimension reduction in classical elasticity
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Dimension reduction in prestressed elasticity
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Calculus of Variations on Thin Prestressed Films
Book Subtitle: Asymptotic Methods in Elasticity
Authors: Marta Lewicka
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/978-3-031-17495-7
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-17494-0Published: 18 April 2023
Softcover ISBN: 978-3-031-17497-1Published: 18 April 2024
eBook ISBN: 978-3-031-17495-7Published: 17 April 2023
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: IX, 448
Number of Illustrations: 4 b/w illustrations, 16 illustrations in colour
Topics: Optimization, Analysis, Surfaces and Interfaces, Thin Films, Differential Geometry