Calculus of variations on thin prestressed films : asymptotic methods in elasticity / Marta Lewicka.
Lewicka, Marta, author.
2022
QC176.84.E5 L49 2022
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Title Calculus of variations on thin prestressed films : asymptotic methods in elasticity / Marta Lewicka.
Author Lewicka, Marta, author.
ISBN 9783031174957 electronic book
303117495X electronic book
9783031174940
3031174941
DOI https://doi.org/10.1007/978-3-031-17495-7
Published Cham : Birkhäuser, 2022.
Language English
Description 1 online resource (1 volume) : illustrations (black and white, and color).
Item Number 10.1007/978-3-031-17495-7 doi
Call Number QC176.84.E5 L49 2022
Dewey Decimal Classification 530.4275015114
Summary This monograph considers the analytical and geometrical questions emerging from the study of thin elastic films that exhibit residual stress at free equilibria. It provides the comprehensive account, the details and background on the most recent results in the combined research perspective on the classical themes: in Differential Geometry that of isometrically embedding a shape with a given metric in an ambient space of possibly different dimension, and in Calculus of Variations that of minimizing non-convex energy functionals parametrized by a quantity in whose limit the functionals become degenerate. 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Series Progress in nonlinear differential equations and their applications ; v. 101.
Available in Other Form Calculus of variations on thin prestressed films.
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Introduction
Part I: Tools in Mathematical Analysis
-Convergence
Korn's Inequality
Friesecke-James-Mllers Inequality
Part II: Dimension Reduction in Classical Elasticity
Limiting Theories for Elastic Plates and Shells: Nonlinear Bending
Limiting Theories for Elastic Plates and Shells: Sublinear and Linear
Linear Theories for Elastic Plates: Linearized Bending
Infinite Hierarchy of Elastic Shell Models
Limiting Theories on Elastic Elliptic Shells
Limiting Theories on Elastic Developable Shells
Part III: Dimension Reduction in Prestressed Elasticity
Limiting Theories for Prestressed Films: Nonlinear Bending
Limiting Theories for Prestressed Films: Von Krmn-like Theory
Infinite Hierarchy of Limiting Theories for Prestressed Films
Limiting Theories for Weakly Prestressed Films
Terminology and Notation
Index. .

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