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Energetic Relaxation to Structured Deformations

A Multiscale Geometrical Basis for Variational Problems in Continuum Mechanics

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  • © 2023

Overview

Authors:
  1. José Matias

    1. Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal

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  2. Marco Morandotti

    1. Department of Mathematical Sciences, Politecnico di Torino, Turin, Italy

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  3. David R. Owen

    1. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, USA

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  • Provides state-of-the-art results and techniques in compact presentation style
  • Offers a broad introduction to newcomers
  • Presents in-depth techniques for readers acquainted with the field

Part of the book series: SpringerBriefs on PDEs and Data Science (SBPDEDS)

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Introduction

    • José Matias, Marco Morandotti, David R. Owen
    Pages 1-13

  3. Mathematical Preliminaries

    • José Matias, Marco Morandotti, David R. Owen
    Pages 15-26

  4. Energetic Relaxation to First-Order Structured Deformations

    • José Matias, Marco Morandotti, David R. Owen
    Pages 27-105

  5. Energetic Relaxation to Second-Order Structured Deformations

    • José Matias, Marco Morandotti, David R. Owen
    Pages 107-128

  6. Outlook for Future Research

    • José Matias, Marco Morandotti, David R. Owen
    Pages 129-152
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Keywords

About this book

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.

Authors and Affiliations

  • Instituto Superior Técnico, University of Lisbon, Lisbon, Portugal

    José Matias

  • Department of Mathematical Sciences, Politecnico di Torino, Turin, Italy

    Marco Morandotti

  • Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, USA

    David R. Owen

About the authors

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.

Bibliographic Information

  • Book Title: Energetic Relaxation to Structured Deformations

  • Book Subtitle: A Multiscale Geometrical Basis for Variational Problems in Continuum Mechanics

  • Authors: José Matias, Marco Morandotti, David R. Owen

  • Series Title: SpringerBriefs on PDEs and Data Science

  • DOI: https://doi.org/10.1007/978-981-19-8800-4

  • Publisher: Springer Singapore

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023

  • Softcover ISBN: 978-981-19-8799-1Published: 19 April 2023

  • eBook ISBN: 978-981-19-8800-4Published: 18 April 2023

  • Series ISSN: 2731-7595

  • Series E-ISSN: 2731-7609

  • Edition Number: 1

  • Number of Pages: XII, 152

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Solid Mechanics, Optimization

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