Calculus of Variations on Thin Prestressed Films: Asymptotic Methods in Elasticity

This book discusses the analytical and geometrical questions arising from the study of thin elastic films with residual stress at free equilibria,using techniques from differential geometry and calculus of variations. It applies to various applications in biology,chemistry,and physics,such as growing tissues,plastically strained sheets,engineered swelling or shrinking gels,petals and leaves of flowers,and atomically thin graphene layers.

Format: Hardback
Length: 448 pages
Publication date: 18 April 2023
Publisher: Birkhauser Verlag AG

This monograph delves into the analytical and geometrical challenges arising from the study of thin elastic films that exhibit residual stress at free equilibria. It presents a comprehensive account, providing detailed insights and background on the latest developments in the combined research perspective on classical themes in Differential Geometry and Calculus of Variations. These themes involve isometrically embedding shapes with given metrics in ambient spaces of potentially different dimensions, as well as minimizing non-convex energy functionals parametrized by quantities that approach degenerate limits. Prestressed thin films find applications in various contexts and fields, including growing tissues, plastically strained sheets, engineered swelling or shrinking gels, flower petals, and atomically thin graphene layers. While the underlying questions about shape formation intersect biology, chemistry, and physics, their analytical and geometrical nature allows for tackling them using the dimension reduction techniques outlined in this book. The text is intended for mathematicians and graduate students engaged in Analysis, Calculus of Variations, Partial Differential Equations, and Applied Math. It also holds relevance for researchers and graduate students in Engineering, particularly those interested in Solid Mechanics and Materials Science, who seek to gain modern mathematical insights and acquire the necessary tools for their research.

Weight: 852g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031174940
Edition number: 1st ed. 2023