Higher Gradient Materials and Related Generalized Continua

This book discusses recent findings and advanced theories presented at two workshops at TU Berlin in 2017 and 2018. It underlines several advantages of generalized continuum models compared to the classical Cauchy continuum, which although widely used in

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Holm Altenbach Wolfgang H. Müller Bilen Emek Abali Editors

Higher Gradient Materials and Related Generalized Continua

Advanced Structured Materials Volume 120

Series Editors Andreas Öchsner, Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, Esslingen, Germany Lucas F. M. da Silva, Department of Mechanical Engineering, Faculty of Engineering, University of Porto, Porto, Portugal Holm Altenbach, Faculty of Mechanical Engineering, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

Common engineering materials reach in many applications their limits and new developments are required to fulfil increasing demands on engineering materials. The performance of materials can be increased by combining different materials to achieve better properties than a single constituent or by shaping the material or constituents in a specific structure. The interaction between material and structure may arise on different length scales, such as micro-, meso- or macroscale, and offers possible applications in quite diverse fields. This book series addresses the fundamental relationship between materials and their structure on the overall properties (e.g. mechanical, thermal, chemical or magnetic etc) and applications. The topics of Advanced Structured Materials include but are not limited to • classical fibre-reinforced composites (e.g. glass, carbon or Aramid reinforced plastics) • metal matrix composites (MMCs) • micro porous composites • micro channel materials • multilayered materials • cellular materials (e.g., metallic or polymer foams, sponges, hollow sphere structures) • porous materials • truss structures • nanocomposite materials • biomaterials • nanoporous metals • concrete • coated materials • smart materials Advanced Structured Materials is indexed in Google Scholar and Scopus.

More information about this series at http://www.springer.com/series/8611

Holm Altenbach Wolfgang H. Müller Bilen Emek Abali •



Editors

Higher Gradient Materials and Related Generalized Continua

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Editors Holm Altenbach Institut für Mechanik Otto-von-Guericke-Universität Magdeburg Magdeburg, Germany

Wolfgang H. Müller Institut für Mechanik Technische Universität Berlin Berlin, Germany

Bilen Emek Abali Institut für Mechanik Technische Universität Berlin Berlin, Germany

ISSN 1869-8433 ISSN 1869-8441 (electronic) Advanced Structured Materials ISBN 978-3-030-30405-8 ISBN 978-3-030-30406-5 (eBook) https://doi.org/10.1007/978-3-030-30406-5 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, tradem