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Foreword; Contents; Contributors; Mathematical Models and Finite Element Approaches for Nanosized Piezoelectric Bodies with Uncoulped and Coupled Surface Effects; 1 Introduction; 2 Model of Piezoelectric Materials with Damping and Surface Effects; 3 Week Formulations of Dynamic Problem; 4 Finite Element Approaches; 4.1 Nonstationary Problems; 4.2 Static Problems; 4.3 Steady-State Oscillation Problems; 4.4 Modal Problems; 4.5 Mode Superposition Method for Steady-State Oscillation Problems; 4.6 Mode Superposition Method for Nonstationary Problems
4.7 The Newmark Scheme for Solving Non-stationary Problems5 Concluding Remarks; References; On the Theory of Acoustic Metamaterials with a Triple-Periodic System of Interior Obstacles; 1 Introduction; 2 Mathematical Formulation of the Problem; 3 The Properties of the Basic Integral Equation; 4 Calculation of the Wave Characteristics; 5 Conclusions; References; 3 Analytical and Computer Methods to Evaluate Mechanical Properties of the Metamaterials Based on Various Models of Polymeric Chains; Abstract; 1 Introduction; 2 Simulation of the Adsorption Process; 3 Model "Polymer-Substrate"
4 Simulation of the Simplest Types of Mechanical Deformation5 Simulation of Ferroelectric Properties of Thin Films; 6 Application to Surface Elasticity; 7 Conclusion; Acknowledgements; References; Identification of Arrays of Cracks in the Elastic Medium by the Ultrasonic Scanning ; 1 Introduction; 2 Basic Equations of the Elasticity Theory for Anti-plane Mode of Deformation; 3 Mutual Influence of the Elementary Cracks; 4 Identification Problem and Some Details of the Numerical Algorithm; 5 Conclusions; References
5 Short-Wave Diffraction of Elastic Waves by Voids in an Elastic Medium with Double Reflections and TransformationsAbstract; 1 Introduction; 2 Problem Statement; 3 Method of Solution; 4 Single Reflection of the Longitudinal Wave by the Cavity Surface; 5 Single Reflection of the Transverse Wave by the Cavity Surface; 6 The Double Re-Reflection of Elastic Waves in View of All Possible Transformations; 7 Conclusion; Acknowledgements; References; Finite Element Modeling and Computer Design of Anisotropic Elastic Porous Composites with Surface Stresses; 1 Introduction
2 Homogenization of Two-Phase Elastic Nanocomposite by Effective Moduli Method3 Finite Element Approximations; 4 Modeling of Representative Volumes; 5 Numerical Results and Discussion; References; Acceleration Waves in Media with Microstructure; 1 Introduction; 2 Basic Equations of a Hyperelastic Media with Internal Variables; 3 Acceleration Waves; 4 Example: Micropolar Media; 5 Conclusions; References; Models of Active Bulk Composites and New Opportunities of the ACELAN Finite Element Package; 1 Introduction; 2 Effective Moduli Method for Thermopiezomagnetoelectric Composites
4.7 The Newmark Scheme for Solving Non-stationary Problems5 Concluding Remarks; References; On the Theory of Acoustic Metamaterials with a Triple-Periodic System of Interior Obstacles; 1 Introduction; 2 Mathematical Formulation of the Problem; 3 The Properties of the Basic Integral Equation; 4 Calculation of the Wave Characteristics; 5 Conclusions; References; 3 Analytical and Computer Methods to Evaluate Mechanical Properties of the Metamaterials Based on Various Models of Polymeric Chains; Abstract; 1 Introduction; 2 Simulation of the Adsorption Process; 3 Model "Polymer-Substrate"
4 Simulation of the Simplest Types of Mechanical Deformation5 Simulation of Ferroelectric Properties of Thin Films; 6 Application to Surface Elasticity; 7 Conclusion; Acknowledgements; References; Identification of Arrays of Cracks in the Elastic Medium by the Ultrasonic Scanning ; 1 Introduction; 2 Basic Equations of the Elasticity Theory for Anti-plane Mode of Deformation; 3 Mutual Influence of the Elementary Cracks; 4 Identification Problem and Some Details of the Numerical Algorithm; 5 Conclusions; References
5 Short-Wave Diffraction of Elastic Waves by Voids in an Elastic Medium with Double Reflections and TransformationsAbstract; 1 Introduction; 2 Problem Statement; 3 Method of Solution; 4 Single Reflection of the Longitudinal Wave by the Cavity Surface; 5 Single Reflection of the Transverse Wave by the Cavity Surface; 6 The Double Re-Reflection of Elastic Waves in View of All Possible Transformations; 7 Conclusion; Acknowledgements; References; Finite Element Modeling and Computer Design of Anisotropic Elastic Porous Composites with Surface Stresses; 1 Introduction
2 Homogenization of Two-Phase Elastic Nanocomposite by Effective Moduli Method3 Finite Element Approximations; 4 Modeling of Representative Volumes; 5 Numerical Results and Discussion; References; Acceleration Waves in Media with Microstructure; 1 Introduction; 2 Basic Equations of a Hyperelastic Media with Internal Variables; 3 Acceleration Waves; 4 Example: Micropolar Media; 5 Conclusions; References; Models of Active Bulk Composites and New Opportunities of the ACELAN Finite Element Package; 1 Introduction; 2 Effective Moduli Method for Thermopiezomagnetoelectric Composites