This book is a useful source of knowledge for engineers and scientists in the field of mechanics of deformation and destruction of composite materials.

In Chapter 1 three-dimensional equations of elasticity theory composed for the case of finite displacements and deformations of solids have been analyzed. It is found that the generally accepted simplifications known in the literature and carried out for the case of small deformations result in equations that are considered to be absolutely correct and consistent in all scientific and educational literature on mechanics of deformable solid bodies. However, this conclusion is not sufficiently well-founded as confirmed by formulation and solution of problems on the basis of generally accepted equations for determining both the stress-strain state (SSS) and the critical loads and buckling modes. In Chapter 2 the theoretical and experimental methods for determining the mechanical characteristics of fiber-reinforced plastics (FRPs) based on tensile and compression tests of flat specimens with [0] s , [±90] s, and [±45] 2s lay-ups are analyzed. For FRPs with [±45] 2s lay-ups, relations are derived for determining the components of lamina strains and stresses in the orthotropy axes of FRP monolayer in terms of axial strains and Poisson ratios of specimens measured in experiments. In Chapter 3 the structure of a unidirectional fibre composite of two types ELUR-P carbon fibre based on KhT-118 cold-curing binder and HSE 180 REM prepreg based on hot-curing binder has been studied. The diameters of fibres and fibre bundles (filaments) of both types of composites have been measured. Based on the results of the analysis of the composite material structure, a refined formulation of the linearised problems of a refined statement of linearized problems on flat internal multiscale buckling modes of a rigid lamina with either fibers or a fiber bundle is presented taking into account their interaction with an epoxy matrix. In Chapter 4 for shells of a layered structure based on the Timoshenko's model, taking into account the transverse compression used for each layer, two versions of two-dimensional equations are constructed that describe geometrically nonlinear deformation with arbitrary displacements and small deformations. The formulation of a linear problem on the initial (subcritical) stress-strain state of a test specimen from a unidirectional fibrous composite with the [90 0 ] s structure during tension-compression tests with shear is given. A numerical method for solving the formulated problem is developed, which is based on the reduction of the original problem to a system of integro-algebraic equations and the search for their numerical solution by the finite sum method. In Chapter 5 conclusions were done and directions for further research have been identified.

Important contribution to the mechanics of deformation and destruction of composite material Nonlinear equations of elasticity theory for finite displacements and small deformations Written by certified experts

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Vitaly Paimushin EDUCATION 1981 Doctor in Physics and Mathematics. WORK POSITIONS 1980 - 2013 Head of Strength of Materials Department, Kazan National Research Technical University named after A.N. Tupolev, Kazan, Russia. Have been prepared lecture notes on courses "Strength of materials" and "Mechanics of structures and materials". Have been teaching several courses such as strength of materials, mechanics of structures and materials, solid mechanics from 1980 to the present time. 1981-Now Supervisor of Ph.D. students since 1975 and doctorate candidates since 1980 (supervised totally 37 Ph.D. and 9 D.Sc. up to now) 1985-2013 Professor at Department of Strength of Materials, Kazan National Research Technical University named after A.N. Tupolev, Kazan, Russia. 2013 - Now Professor at Department of Structural Strength, Kazan National Research Technical University named after A.N. Tupolev, Kazan, Russia Academic distinctions 1. Honored scientist of Tatarstan Republic (1992 year) 2. Honored scientist of Russian Federation (2001 year) 3. State Prize of the Republic of Tatarstan in the field of science and technology (2004 year) 4. Tatarstan academy of science award named after H. Mushtari (1995 year) 5. Member of the National Committee on Theoretical and Applied Mechanics 6. Member of the editorial board of the journal "Russian Aeronautics' 7. Member of the editorial board of the journal "Proceedings of the higher educational institutions, Mathematics.", 8. Member of the editorial board of the journal "Mechanics of Composite Materials" 9. Academician of the Academy of Sciences of the Republic of Tatarstan, 10. Academician of Russian Aviation and aeronautics. Andris Chate EDUCATION 1992 Doctor of Engineering Science (Dr.sc.ing.) in Mechanics of Deformable Solids, Riga Technical University (RTU), Latvia 1981 PhD in Materials Science and Engineering, Institute of Polymer Mechanics, Latvian Academy of Science, Latvia WORK POSITIONS 2009 - Now Leading Researcher, Riga Technical University, Institute of Materials and Structures, Faculty of Civil Engineering (FCI), RTU, Latvia 2009 - Now Head of Institute of Materials and Structures, FCI, RTU, Latvia 2003 - Now Professor at Department of Composite Materials and Structures, FCI, RTU, Latvia 2003 - 2019 Head of Department of Composite Materials and Structures, FCI, RTU, Latvia 1984 - Now More than 30 fellowships (visiting researcher, mobility grants; each fellowship with duration 1 - 3 - 6 months): - University of Kassel, Germany; University of Wales, Swansea, UK; Royal Institute of Technology, Sweden. Sergey Kholmogorov EDUCATION 2008 - Engineering Diploma in Aircraft and Helicopter field, Kazan National Research Technical University named after A.N. Tupolev, Kazan, Russia 2015 PhD in Physics and Mathematics, Kazan Federal University, Kazan, Russia. 2015-2018 Assistant of Department of Structural Strength, Kazan National Research Technical University named after A.N. Tupolev 2018-Now Associate professor of Department of Structural Strength, Kazan National Research Technical University named after A.N. Tupolev Makarov Maksim EDUCATION 2014 Master Degree in Mathematics, Institute of Computer Mathematics and Information Technologies, Kazan Federal University, Kazan, Russia. 2018 Internship, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany 2019 PhD in Physics and Mathematics , Kazan Federal University, Kazan, Russia. WORK POSITIONS 2023-Now Senior researcher, Kazan Federal (Volga Region) University, Kazan, Russia 2023-Now Associate Professor, Kazan Federal (Volga Region) University, Kazan, Russia Rusla

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