Energetic Relaxation to Structured Deformations

A Multiscale Geometrical Basis for Variational Problems in Continuum Mechanics

José Matias, Marco Morandotti, David R. Owen (Autoren)

Buch | Softcover

152 Seiten

2023 | 1st ed. 2023
Springer Verlag, Singapore
978-981-19-8799-1 (ISBN)

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This book is the first organized collection of some results that have been obtained by the authors, their collaborators, and other researchers in the variational approach to structured deformations. It sets the basis and makes more accessible the theoretical apparatus for assigning an energy to a structured deformation, thereby providing motivation to researchers in applied mathematics, continuum mechanics, engineering, and materials science to study the deformation of a solid body without committing at the outset to a specific mechanical theory. Researchers will benefit from an approach in which elastic, plastic, and fracture phenomena can be treated in a unified way.
The book is intended for an audience acquainted with measure theory, the theory of functions of bounded variation, and continuum mechanics. Any students in their last years of undergraduate studies, graduate students, and researchers with a background in applied mathematics, thecalculus of variations, and continuum mechanics will have the prerequisite to read this book.

José Matias is an associate professor at the Department of Mathematics of Instituto Superior Técnico in Lisbon. He was awarded his PhD from Carnegie Mellon University in 1993 and his research interests lie in the field of applied mathematics and calculus of variations. Among other topics, he has studied extensively the mathematical aspects of models for continuum mechanics and differential inclusions. Marco Morandotti is an associate professor at the Department of Mathematical Sciences of Politecnico di Torino. He was awarded his PhD in Applied Mathematics from SISSA, Trieste in 2011 and has been a research scholar at Carnegie Mellon University, Instituto Superior Técnico, and the Technical University of Munich. His research spans some areas of applied mathematics, including models for continuum mechanics, models for defects in solids, the game-theoretic study of multi-agent systems, and the motion of micro-swimmers in viscous fluids. David R. Owen is an emeritus professor at the Department of Mathematical Sciences of Carnegie Mellon University. He was awarded his PhD from Brown University in 1968 in applied mathematics and has been in the faculty at Carnegie Mellon since 1967, apart from visiting position through the years in France, Germany, and Italy. Together with the late Gianpietro Del Piero, he published the first paper on the theory of structured deformations, which he has developed during its evolution from the mechanical to the variational context. His research interests include the mathematical foundations of thermodynamics, mathematical models of the plastic behavior of solids, and multiscale descriptions of geometrical changes in continuous bodies.

1. Introduction.- 2. Mathematical preliminaries.- 3. Energetic relaxation to first-order structured deformations.- 4. Energetic relaxation to second-order structured deformations.- 5. Outlook for future research.

Erscheinungsdatum	22.04.2023
Reihe/Serie	SpringerBriefs on PDEs and Data Science
Zusatzinfo	1 Illustrations, black and white; XII, 152 p. 1 illus.
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Technik ► Maschinenbau
Schlagworte	Bulk and interfacial energy densities • dimension reduction • Energy Minimization • Energy Relaxation • (First-order) structured deformations • Hierarchical structured deformations • Integral representation of functionals • Multiscale geometry • optimal design • periodic homogenization • (Second-order) structured deformations • Upscaling and spatial localization of non-local energies
ISBN-10	981-19-8799-8 / 9811987998
ISBN-13	978-981-19-8799-1 / 9789811987991
Zustand	Neuware