Authors:
- Reviews displacement-based and stress-based theories of linear piezoelectric and piezomagnetic materials
- Gives an account of the corresponding variational principles
- Presents a random field formulation of piezoelectricity and piezomagnetism
Part of the book series: SpringerBriefs in Applied Sciences and Technology (BRIEFSAPPLSCIENCES)
Part of the book sub series: SpringerBriefs in Mathematical Methods (BRIEFSMATHMETH)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
About this book
Random fields are a necessity when formulating stochastic continuum theories. In this book, a theory of random piezoelectric and piezomagnetic materials is developed. First, elements of the continuum mechanics of electromagnetic solids are presented. Then the relevant linear governing equations are introduced, written in terms of either a displacement approach or a stress approach, along with linear variational principles. On this basis, a statistical description of second-order (statistically) homogeneous and isotropic rank-3 tensor-valued random fields is given. With a group-theoretic foundation, correlation functions and their spectral counterparts are obtained in terms of stochastic integrals with respect to certain random measures for the fields that belong to orthotropic, tetragonal, and cubic crystal systems. The target audience will primarily comprise researchers and graduate students in theoretical mechanics, statistical physics, and probability.
Authors and Affiliations
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Division of Mathematics and Physics, Mälardalen University, Västerås, Sweden
Anatoliy Malyarenko
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Department of Mechanical Science and Engineering, Institute for Condensed Matter Theory Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, USA
Martin Ostoja-Starzewski
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Department of Mechanical Sciences and Engineering, University of Illinois at Urbana-Champaign, Urbana, USA
Amirhossein Amiri-Hezaveh
Bibliographic Information
Book Title: Random Fields of Piezoelectricity and Piezomagnetism
Book Subtitle: Correlation Structures
Authors: Anatoliy Malyarenko, Martin Ostoja-Starzewski, Amirhossein Amiri-Hezaveh
Series Title: SpringerBriefs in Applied Sciences and Technology
DOI: https://doi.org/10.1007/978-3-030-60064-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-60063-1Published: 06 November 2020
eBook ISBN: 978-3-030-60064-8Published: 05 November 2020
Series ISSN: 2191-530X
Series E-ISSN: 2191-5318
Edition Number: 1
Number of Pages: XI, 97
Number of Illustrations: 1 b/w illustrations, 1 illustrations in colour
Topics: Probability Theory and Stochastic Processes, Classical and Continuum Physics, Magnetism, Magnetic Materials, Condensed Matter Physics