Overview

In this book, well-known scientists discuss modern aspects of generalized continua, in order to better understand modern materials and advanced structures. They possess complicated internal structure, and it requires the development of new approaches to model such structures and new effects caused by it. This book combines fundamental contributions in honor of Victor Eremeyev and his 60th birthday.

Full Product Details

Author:   Holm Altenbach ,  Arkadi Berezovski ,  Francesco dell'Isola ,  Alexey Porubov
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   1st ed. 2023
Volume:   170
Weight:   1.478kg
ISBN:  

9783031261855

ISBN 10:   3031261852
Pages:   745
Publication Date:   14 February 2023
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

1 Effects of 3-D Printing Infill Density Parameter on the Mechanical Properties of PLA Polymer Reza Afshar, Simon Jeanne, and Bilen Emek Abali1.1 Introduction 1.2 Additive Manufacturing 1.3 Materials and Methods 1.3.1 Fused Deposition Modeling (FDM) 1.3.2 Unidirectional Tensile Tests 1.3.3 Digital Image Correlation Method 1.4 Results and Discussions 1.5 Conclusions References 2 Advance Approximate Analytical Solutions of the Contact Problem for an Inhomogeneous Layer Sergei M. Aizikovich, Polina A. Lapina, and Sergei S. Volkov2.1 Introduction 2.2 Statement of the Problem of a Shear of the Surface of an Inhomogeneous Layer 2.3 Integral Equations of Contact Problems 2.4 Numerical Analysis 2.5 Closure References 3 The Direct Approach for Plates Considering Hygrothermal Loading and Residual Kinetics Marcus Aßmus, Zia Javanbakht, and Holm Altenbach3.1 Introduction 3.2 Frame of Reference  3.3 Thermal Effects and Hygroscopic Impact 3.4 Residual Kinetics 3.5 Conclusion References 4 A Technique for Determining True Deformation Diagrams Under Dynamic Tension Using DIC Artem V. Basalin, Anatoly M. Bragov, Aleksandr Yu. Konstantinov,and Andrey R. Filippov4.1 Introduction 4.2 Pneumatic Dynamic Installation for Testing Materials at a Deformation Rate of the Order of 10-100 s−1 4.2.1 Installation Scheme 4.2.2 Methods of Obtaining and Processing Information in the Experiment 4.3 Test Results of Sheet (3 mm) Steel 09G2S in a Wide Range of Strain Rates 4.4 Conclusion References 5 Strain Gradient Elasticity and Dual Internal Variables Arkadi Berezovski5.1 Introduction 5.2 Dual Internal Variables 5.2.1 Evolution Equations 5.2.2 Quadratic Free Energy 5.3 Concluding Remarks References 6 On the Coercivity of Strain Energy Functions in Generalized Models of 6-Parameter Shells Mircea Bîrsan and Patrizio Neff6.1 Introduction 6.2 General 6-Parameter Elastic Shells. Governing Equations 6.3 The Order ℎ3 Model of 6-Parameter Shells made of Cosserat Material 6.3.1 Coercivity Results for the Model of Order ����(ℎ3) 6.3.2 Existence of Minimizers 6.4 The Higher Order Model of Cosserat 6-Parameter Shells References 7 Solving the Equations of Nonlinear Model of Crystalline Media with Complex Lattice and Some Structures of Plane Deformation Anatolii N. Bulygin and Yuri V. Pavlov7.1 Introduction 7.2 Nonlinear Model of Deformation of Crystal Media 7.3 General Solution of Dynamic Equations of Plane Deformation of the Nonlinear Model 7.4 Solving the Micro-Field Equations 7.5 Conclusion References 8 Modal Analysis of a Second-Gradient Annular Plate made of an Orthogonal Network of Logarithmic Spiral Fibers Alessandro Ciallella, Francesco D’Annibale, Francesco dell’Isola,Dionisio Del Vescovo, and Ivan Giorgio8.1 Introduction 8.2 The Model for a Fiber Net Arranged in Logarithmic Spirals 8.3 Modal Analysis 8.4 Conclusions and Future Perspectives References 9 Non-Linear Simplest Reduced Kelvin’s Medium in the Vicinity of the Spherical Stress State: Waves and Instabilities Mikhail A. Drepin and Elena F. Grekova9.1 Introduction and Notation9.2 Basic Equations for the Isotropic Elastic Reduced Kelvin’s Medium in the Vicinity of a Preliminary Stress State 9.2.1 Dynamic Laws of a Nonlinear Reduced Kelvin Medium 9.2.2 Constitutive Relations for a Nonlinear Reduced Kelvin Medium9.2.3 The Simplest Nonlinear Reduced Kelvin Medium. Strain Energy9.2.4 Medium in the Vicinity of a Homogeneous Nonlinear Spherical Deformation State 9.3 Dispersion Relations of the Simplest Elastic Reduced Kelvin Medium in the Vicinity of Preliminary Spherical Strain State for Special Directions of Perturbation Propagation. Waves and Stability9.3.1 Harmonic Waves 9.3.2 Propagation of Harmonic Waves Along the Body Point Axis (ˆ������������ = ±������������0) 9.3.3 Propagation of Harmonic Waves in the Direction Orthogonal to the Body Point Axis (ˆ������������⊥������������0) 9.4 Conclusion References 10 On the Spectrum of Relaxation Times of Coupled Diffusion and Rheological Processes in Media with Microstructure Dmitrii S. Dudin and Ilya E. Keller10.1 Introduction 10.2 Deformations 10.3 Balance Equations 10.4 The Helmholtz Free Energy 10.5 Thermodynamic Inequality 10.6 Constitutive Equations 10.7 Model Problem and its Equations 10.8 Diffusion Coefficients in Coupled System 10.9 Conclusion References 11 Representative Volume Element Size and Length Scale Identification in Generalised Magneto-Elasticity Sinan Eraslan, Inna M. Gitman, Mingxiu Xu, Harm Askes, and René de Borst11.1 Introduction 11.2 Formulation 11.2.1 Homogenisation and Macroscopic Characteristic Length Scale Parameters11.2.2 Determination of RVE Sizes and Identification of Characteristic Length Scale Parameters 11.3 Numerical Results and Discussion11.4 Conclusions References 12 Rayleigh Waves in the Cosserat Half-Space (Reduced Model) and Half-Space of Damaged Material Vladimir Erofeev, Artem Antonov, Anna Leonteva, and Alexey Malkhanov12.1 Introduction 12.2 Rayleigh Waves in the Cosserat Half-space (Reduced Model) 12.3 Rayleigh Waves in the Half-space of Damaged Material 12.4 Conclusion References 13 Validation of a Hemi-Variational Block-Based Approach to the Modelling of Common In-plane Failures in Masonry Structures José Manuel Torres Espino, Jaime Heman Espinoza Sandoval, Chuong Anthony Tran, Roberto Fedele, Emilio Turco, Francesco dell’Isola, LucaPlacidi, Anil Misra, Francisco James León Trujillo, and Emilio Barchiesi13.1 Introduction 13.2 Mathematical Formulation 13.2.1 Vertex Springs and Stiffnesses 13.2.2 Deformation Energy and Impenetrability Potential 13.2.3 Damage Laws 13.2.4 Principle of Minimum Potential Energy 13.2.5 Numerical Model 13.2.6 Stiffness Matrix13.2.7 Algorithm 13.3 Results 13.3.1 Comparative Result 13.3.2 Influence of Mortar Thickness on Masonry Performance 13.3.3 Bending and Shear Sliding 13.3.4 Rocking 13.4 Conclusions and Future Challenges References 14 Size Effects in Cosserat Crystal Plasticity Samuel Forest and Flavien Ghiglione14.1 Introduction 14.2 Problem Setting 14.2.1 Field Equations 14.2.2 Constitutive Equations14.2.3 Studied Boundary Value Problem 14.3 Cosserat Elastoplasticity Based on a Quadratic Potential14.3.1 Simple Glide in Isotropic Elasticity 14.3.2 Crystal Plasticity Based on the Full Stress Tensor 14.3.3 Schmid Law Limited to the Symmetric Part of the Stress Tensor 14.3.4 Comparison with the Curl ���� ���� Model 14.4 Rank One Energy Potential 14.4.1 Elasticity Solution14.4.2 Crystal Plasticity 14.4.3 Comparison with the Curl ���� ���� Model14.5 Combined Potential 14.6 Application to Grain Boundary Behaviour 14.6.1 Cosserat-Phase Field Model of Grain Boundaries 14.6.2 Analytical Solution of a Single Flat Grain Boundary 14.6.3 Grain Boundary Energy References 15. On the Influence of Poisson’s Ratio on Phase Transformations Limiting Surfaces Alexander B. Freidin and Leah L. Sharipova15.1 Introduction15.2 Phase Equilibrium and Phase Transition Zones for Phases with Positive and Negative Poisson’s Ratios15.3 Optimal Laminates and Phase Transformations Limiting Surfaces15.4 Results 15.5 Conclusions References 16. Application of Nonlocal Fick’s Law Within Micropolar Approach Ksenia Frolova, Nikolay Bessonov, and Elena Vilchevskaya16.1 Introduction 16.2 Diffusion in Media Modeled by Micropolar Continuum 16.3 Axially Symmetric Problem 16.4 Results and Discussion 16.5 Conclusions Appendix. Some Remarks on Numerical Approximation References 17 Geometrically Nonlinear Cosserat Elasticity with Chiral Effects Based upon Granular Micromechanics Ivan Giorgio, Anil Misra, and Luca Placidi17.1 Introduction 17.2 Discrete and Continuous Models for Granular Systems 17.2.1 Identification via Piola’s Ansatz 17.2.2 Relative Intergranular Displacement and Related Continuum Deformation Measures 17.2.3 On the Objective (Macro and Micro-macro)Displacement Vectors 17.2.4 On the Objective Tensor 17.2.5 The Objective Scalar Deformation Measures17.3 Elastic Energy Function 17.4 Identification of the Undamaged Isotropic Case 17.4.1 Characterization of the Undamaged Isotropic Case 17.4.2 Macroscopic Isotropic Stiffness Matrices 17.4.3 Identification of the Macroscopic Isotropic Stiffness Matrices 17.5 Conclusion References 18 Study of the Dynamic Properties of Reinforced Concrete Under High-Speed Compression Mikhail E. Gonov, Vladimir V. Balandin, Anatoly M. Bragov,and Aleksandr Yu. Konstantinov18.1 Introduction 18.2 Test Method 18.3 Characteristics of the Tested Materials 18.4 Results of Dynamic Tests for Uniaxial Compression 18.5 Conclusion References19 Multistability of Convective Flows in a Porous Enclosure Vasily Govorukhin, Mezhlum Sumbatyan, and Vyacheslav Tsybulin19.1 Introduction 19.2 Mathematical Formulation of the Problem19.3 Numerical Methods and Extreme Multistability 19.3.1 Spectral Global Galerkin Method 19.3.2 Cosymmetry Preserving Finite-Difference Approximations19.3.3 Continuation on the Hidden Parameter Method 19.4 Multistability References 20 Hydrogen Transport in Framework of Linear Non-Equilibrium Thermodynamics Approach Polina M. Grigoreva and Vladimir A. Polyanskiy20.1 Introduction 20.2 Problem Statement and Governing Equations 20.3 Plane Boundary Value Problem 20.4 ConclusionReferences 21 Classical and Non-Classical Models of Changes in the Young Modulus of Geomaterials Under Alternating Loads Mikhail A. Guzev, Evgenii P. Riabokon, Mikhail S. Turbakov,Vladimir V. Poplygin, Evgenii V. Kozhevnikov, and Evgenii A. Gladkikh21.1 Introduction 21.2 Experimental Studies 21.3 Classical Model of Changes in the Young Modulus Under an Alternating Load 21.4 Non-classical Model of Change in the Young Modulus Under the Alternating Load 21.4.1 Formulation of the Non-classical Model 21.4.2 Building the Solution 21.5 Conclusion References22 Two Approaches to Modeling Viscoelastic Cosserat Continua Elena A. Ivanova22.1 Introduction 22.2 Kinematics and Balance Equations 22.3 Differential Equations Relating the Strain Tensors to the Velocity Vector and the Angular Velocity Vector 22.4 The Reduced Energy Balance Equation and the Heat Conduction Equation: Zhilin’s Method 22.5 Integral Equations Relating the Strain Tensors to the Velocity Vector and the Angular Velocity Vector 22.6 Source Terms in the Strain Balance Equations22.7 The Reduced Energy Balance Equation and the Heat Conduction Equation: A new Method 22.8 A Comparison of two Approaches 22.9 Discussion References 23 Porous Media Models Based on Generalized State Equations with Simple Examples Anna Knyazeva and Nelli Nazarenko23.1 Introduction 23.2 Definitions and General Relationships 23.3 Thermodynamical Relations 23.4 Examples of Particular Problems 23.4.1 Compressible Nonviscous Gas 23.4.2 Compressible Fluid with Bulk Viscosity 23.4.3 Non-ideal Gas Under Non-isothermal Conditions 23.4.4 Binary Non-viscous Imperfect Mixture 23.4.5 Diffusion and Filtration in Media with Double Porosity 23.4.6 Viscous Two-component Fluid in Media with DoublePorosity23.4.7 Nonviscous Two-component Fluid in Porous media with Nano- and Micro-pores 23.5 Conclusion References 24 Ball Indentation of Perforated Circular Hyperelastic Membranes Alexey M. Kolesnikov24.1 Introduction 24.2 Mathematical Model 24.2.1 Axisymmetric Problem of Non-linear Elastic Membranes 24.2.2 Ball Indentation of Perforated Circular Hyperelastic Membranes 24.3 Numerical Results 24.4 Conclusions References25 Integrated Asymptotic Approach to the Structural Mechanics Models Alexander G. Kolpakov and Sergey I. Rakin25.1 Motivation of the Research 25.2 Modern State of Structural Mechanics 25.2.1 Deformation of the “Main” Part of Frame 25.2.2 Deformation of Connecting Units of Frame 25.2.3 “Infinite Rigidity” of Connecting Units 25.2.4 Structural Mechanics Achievements and Limitations 25.3 Integrated Approach to the Computation of Thin-walled Structures 25.3.1 Displacements in the “Main” Part of the Beams 25.3.2 “Rigid” Displacements of the Connecting Unit 25.3.3 Conjugation of the Displacements in the Main Part of a Beam with the “Rigid Body” Displacements of the Connecting Unit 25.3.4 Assembling the Single-beam Domain Functions into the Function in 2-D Frame 25.3.5 Supplement of the Functions (25.5) with the Local Perturbations 25.4 Local Stress-strain State in the Connecting Units 25.5 Representative Fragment of Joint 25.6 Integrated Procedure for Computation of Framework 25.7 Actual Problems 25.8 Conclusions References 26 The Homogenized Delamination Criterion for Fiber-reinforced Plate Alexander G. Kolpakov, Sergey I. Rakin, and Igor V. Andrianov26.1 Introduction 26.2 Boundary Layer 26.3 Numerical Computation Results 26.3.1 Extension Along ��������- or ��������-axis 26.3.2 Shift in ��������2����3-plane 26.4 The Asymptotic Homogenized Strength Criterion of the Interface Zone 26.5 Constructing the Delaminating Strength Criterion26.6 Conclusions References 27 Lightly Loaded Hydrodynamic Thrust Bearing Lubricated by a Non-Newtonian Fluid Ilya I. Kudish, Sergei S. Volkov, and Andrey S. Vasiliev27.1 Introduction 27.2 Formulation of the Lubrication Problem 27.3 Asymptotic Analysis of the Rheological and Motion Equations 27.4 Examples of Some Specific Lubrication Problem Solutions and Discussion 27.5 Closure References 28 The Idea of Using Adhesive Bonds in Shaping of Cold-formed Thin-walled Beam-columnsMarcin Kujawa, Antonio Cazzani, Lukasz Smakosz, ViolettaKonopińska-Zmysłowska, Karol Winkelmann, Faizullah Jan, andCzesław Szymczak28.1 Introduction 28.2 State of the Art28.2.1 Static, Dynamics, and Stability Analysis of Thin-walled Members 28.2.2 Influence of Imperfections 28.2.3 Failure Analysis with Attention to Creep in Adhesive Bonded Metal Members/Structures 28.3 The Rationale for Addressing the Research Problem 28.4 Conclusions References 29 Dissipative Mechano-Electro-Magnetism Simulations in Electronic Components Yiming Liu, Wolfgang H. Müller, and Bilen Emek Abali29.1 Introduction29.2 Governing Equations 29.3 Constitutive Equations 29.4 Generating Weak Forms 29.5 Implementation and Results 29.6 Conclusion References 30 On Possible Reduction of Gradient Theories of Elasticity Sergey A. Lurie, Petr A. Belov, and Yury O. Solyaev30.1 Introduction30.2 Variational Formulation of Gradient Theories 30.3 Structure of Sixth Rank Tensors 30.4 Special Structure of Gradient Part of Potential Energy. Hypothesis on Absence of Divergent Terms30.5 Features of Variational Formulation of Vector-Type Gradient Models 30.6 System of Governing Equilibrium Equations 30.7 On Uniqueness of Reduced Vector-Type Models 30.8 Conclusions References 31 Dynamics of a Rectangular Rigid Body on a Movable Base Vladimir S. Metrikin, Leonid A. Igumnov, and Elena I. Komarova31.1 Introduction 31.2 Mathematical Model31.3 Construction of a Point Mapping of the Poincaré Surface 31.3.1 The Coordinates of the Fixed Point Corresponding to the Symmetrical Periodic Motion. Sustainability 31.3.2 Equations for Determining the Coordinates of a Fixed Point Corresponding to Asymmetric Periodic Motions.Sustainability 31.4 Numerical Results for ¥����(����) = ����sin(��������) 31.5 Numerical Results 31.6 Conclusion References 32 Asymptotically Correct Analytical Model for Flexural Response of a Two-Layer Strip with Contrast Elastic Constants Gennadi Mikhasev and Nguyen Le32.1 Introduction 32.2 Statement of the Problem 32.3 Bernoulli-Euler Type Model for Strip Consisting of Layers with Close Material Constants 32.4 Timoshenko-Reissner Type Model for Strip Consisting of Layers with High-Contrast Elastic Properties 32.4.1 Leading Approximation 32.4.2 First-Order Approximation 32.4.3 One-Dimensional Governing Equation32.5 Free Vibrations 32.6 ConclusionsReferences 33 On Analytical Modeling of Tension-Assisted Winding of Flexible Sheets Aleksandr Morozov, Wilhelm Rickert, and Sergei Shubin33.1 Introduction 33.2 General Assumptions for the Winding Problem 33.3 Winding the First Layer 33.4 Winding the Subsequent Layers 33.5 Conclusions References 34 On Using Rotations as Primary Variables in the Nonlinear Theory of Thin Elastic Shells Wojciech Pietraszkiewicz34.1 Introduction 34.2 Geometry and Deformation of the Reference Surface 34.3 Equilibrium Conditions 34.4 Boundary Value Problem with Independent Rotations 34.5 Constitutive Equations of Rubber-Like Shells References 35 Continuum Description of Extended Mass-in-Mass Metamaterial Models Alexey V. Porubov35.1 Introduction 35.2 Classic Mass-in-Mass Chain 35.3 Chain with Extra Attached Masses35.4 Chain with Extra Internal Attached Masses 35.5 Attached Masses Through one Element of the Main Chain 35.6 Conclusions References 36 Multi-Element Metamaterial’s Design Through the Relaxed Micromorphic Model Leonardo A. Perez Ramirez, Gianluca Rizzi, and Angela Madeo36.1 Introduction 36.2 The Relaxed Micromorphic Model: Constitutive laws,Equilibrium Equations, and Boundary Conditions 36.2.1 Equilibrium Equations 36.2.2 Boundary and Interface Conditions 36.2.3 Numerical Results 36.3 Parametric Study on the Thickness of a Shielding Device: Capability Limit for the Relaxed Micromorphic Model 36.4 Design of a Double Shield Device 36.5 Multiple-Shields Optimization 36.6 Conclusions References37 On Magnetically Induced Motion of Micropolar FerrofluidsWilhelm Rickert, Margarita Dementeva, Gregor Ganzosch, Elena N.Vilchevskaya, and Wolfgang H. Müller37.1 Introduction 37.2 A Flow Problem Coupled to Electromagnetism 37.3 Simplifications and Normalization 37.4 Electromagnetic Force Density 37.5 Initial Values, Boundary Conditions and Implementation 37.6 Results 37.6.1 Slip 37.6.2 No Slip 37.6.3 Homogeneous Magnetic Field 37.7 Summary References 38 Manufacturing Quality Evaluation of Photopolymer Resin 3D-Printed Scaffolds Using Microtomography Evgeniy V. Sadyrin, Andrey L. Nikolaev, Sergei V. Chapek, Dmitry V.Nazarenko, Sergei M. Aizikovich, and Yun-Che Wang38.1 Introduction 38.2 Materials and Methods 38.3 Results and Discussion 38.4 Conclusion References 39 Comparison of Homogenization Techniques in Strain Gradient Elasticity for Determining Material Parameters Bekir Cagri Sarar, M. Erden Yildizdag, and Bilen Emek Abali39.1 Introduction 39.2 Determining Strain Gradient Parameters 39.3 Microscale Structure 39.4 Results and Discussion 39.5 Conclusion References 40 Buckling of Rectangular Micropolar Plate with Prestressed Coatings Denis N. Sheydakov40.1 Introduction 40.2 Micropolar Plate with Prestressed Coatings40.3 Equations of Neutral Equilibrium 40.4 Micropolar Plate with Identical Coatings 40.5 Conclusion References 41 A Cosserat Model for Fiber-Reinforced Elastic Plates David J. Steigmann, Mircea Bîrsan, and Milad Shirani41.1 Introduction 41.2 The Three-Dimensional Cosserat Model for Fiber-Reinforced Elastic Solids 41.2.1 Kinematical Variables and Strain Measures in Cosserat Elasticity 41.2.2 Fiber-Reinforced Materials 41.2.3 Equilibrium and Constitutive Equations 41.3 Plate Theory for Fiber-Reinforced Laminae41.4 Specific Constitutive Assumptions 41.4.1 Coercivity 41.4.2 Minimum Property Appendix References 42 On the Structure of Solutions in the Vicinity of Discontinuity of Boundary Conditions for Gradient ModelsAlexander O. Vatulyan, Sergey A. Nesterov, Victor O. Yurov, and OksanaV. Yavruyan42.1 Introduction 42.2 Constitutive Relations of the Gradient Theory of Elasticity and Electroelasticity 42.3 Problem for a Strip with Delamination 42.4 Problem for an Electroelastic Strip with a Surface Electrode42.5 Conclusion References 43 A Damaged Medium Model for Assessing Life Characteristics of Polycrystalline Structural Alloys with Joint Mechanical Fatigue and Long-Term Strength of Material Ivan A. Volkov, Leonid A. Igumnov, Aleksandr A. Belov, and Andrey I.Volkov43.1 Introduction43.2 Constitutive Relations of the Mathematical Model of Mechanics of Damaged Medium 43.2.1 Constitutive Relations of Thermoviscoplasticity 43.2.2 Evolutionary Equations for Damage Accumulation43.3 Numerical Results 43.4 ConclusionReferences44 Bandgap Properties of a Class of Chiral and Achiral Metamaterials Yun-Che Wang, Tse-Chun Liao, Kai-Wen Tan, and Sergey M. Aizikovich44.1 Introduction 44.2 Theoretical Considerations 44.3 Numerical Considerations 44.4 Results and Discussion 44.5 Conclusions References45 Large Strains of a Spherical Shell with Distributed Dislocations and Disclinations Leonid M. Zubov and Mikhail I. Karyakin45.1 Introduction 45.2 The Model of a Nonlinear Elastic Micropolar Shell 45.3 Continuously Distributed Dislocations in an Elastic MicropolarShell 45.4 Transformation of Incompatibility Equations and EquilibriumEquations 45.5 Equilibrium of a Closed Spherical Shell with DistributedDislocations and Disclinations 45.6 Numerical Results 45.7 Conclusions References 

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