Table of Contents

1 contains a short literature survey and a description of aims of the book and used approaches.- 2 presents a short tutorial, where the employed physical theories, the popular methods of theory of composites and certain mathematical approaches are described.- 3 Devoted to the transport properties of fiber and particle-reinforced composites. Besides of detection of their effective properties, local fields on the micro-level and an influence of the non-ideal contact between the matrix and inclusions are investigated.- 4 Edge effects are also studied.- 5. Besides of detection of the effective properties, the edge effects in fiber composite materials are investigated.- 6 presents the problems aimed at the transition of the load from the fiber to the matrix for elastic and viscoelastic composites, various types of fiber composite fracture, and the buckling phenomena of fibers in fiber-reinforced composites.- 7 is devoted to problems of perforated membranes, plates and shells.- 8 Nonlinear elastic problems are analyzed.

About the Author

Igor V. Andrianov was born in the Ukraine (former Soviet Union (fSU)) in 1948. He obtained his Master of Applied Mechanics degree from Dnepropetrovsk State University (DSU, Ukraine) in 1971, his PhD in Structural Mechanics from the DSU in 1975, and his DSc in Mechanics of Solids from the Moscow State Institute of Electronics and Mathematics in 1990. From 1974 to 1977, he was a Research Scientist at the DSU, from 1977 to 1990, an Associate Professor, and from 1990 to 1997, a Full Professor of Mathematics at Dnepropetrovsk Civil Engineering Institute. From 2006 to 2013 he was a Research Scientist at RWTH Aachen University (Germany). Andrianov is the author or co-author of 14 books and more than 300 papers in peer-reviewed journals. He has presented papers at more than 150 international congresses, conferences, and seminars, and also supervised 21 PhD students. Selected as a Soros Professor (1996). His research interests include Mechanics of Solids, Mechanics of Composite Materials, Nonlinear Dynamics, and Asymptotic Methods.Jan Awrejcewicz, Head of the Department of Automation, Biomechanics and Mechatronics, Head of Ph.D. School on 'Mechanics' (since 1996) and of graduate/postgraduate programs on Mechatronics (since 2006). Recipient of multi-doctor honoris causa and the Humboldt Award. Author/co-author of over 730 journal papers and refereed international conference papers and 48 monographs. Editor of 22 books and 26 journal special issues. Principal investigator in 39 research grants by Polish Ministry of Education and Science (21), Committee for Scientific Research (17), National Science Centre (2). Member of Editorial Boards of 74 Journals (15 with IF). Organizer and Head of the series of 14 International Conferences Dynamical Systems-Theory and Application (Lodz, 1992-2017) and of 3 International Conferences “Mechatronics: Ideas for Industrial Applications” (Warsaw 2012; Lodz, 2014; Gdansk, 2015), Chair of the "International Conference of the Polish Society of Biomechanics" (Lodz, 2014). Research interest:  His papers and research cover various disciplines of mathematics, mechanics, biomechanics, automatics, physics and computer oriented sciences, with main focus on nonlinear processes.
Vladyslav V. Danishevskyy obtained his Masters (1996), Ph.D. (1999), and Doctor of Sciences (2008) degrees in Structural Mechanics from Prydniprovska State Academy of Civil Engineering and Architecture, Ukraine. He is a Full Professor at this Academy. He has authored 3 monographs and over 50 journal papers refereed by SCOPUS. Among his awards are Soros Post-Graduate Student’s Award (1997), Prize of the National Academy of Sciences of Ukraine for the best academic achievement among young scientists (2000), Alexander von Humboldt Foundation Research Fellowship (2001), NATO Research Fellowship (2003), NATO Reintegration Grant (2005), institutional academic co-operation grant of the Alexander von Humboldt Foundation (2007), research grant of the German Research Foundation (2014), Marie-Curie Research Fellowship by the European Union’s Horizon 2020 research and innovation programme (2015). He has conducted long-term research abroad in RWTH Aachen University, Germany (2001–2002), in the University of Rouen, France (2003–2004), and in Keele University, UK (2015– 2017). His research interests cover mechanics of heterogeneous media and structures, asymptotic methods, nonlinear dynamics.