Title Computational continuum mechanics of nanoscopic structures : nonlocal elasticity approaches / Esmaeal Ghavanloo, Hashem Rafii-Tabar, Seyed Ahmad Fazelzadeh

Published Cham, Switzerland : Springer, 2019

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Description 1 online resource (xvii, 275 pages) : illustrations (some color) Series Springer tracts in mechanical engineering, 2195-9862 Springer tracts in mechanical engineering, 2195-9862 Contents Intro; Preface; Contents; About the Authors; Abbreviations; 1 Introduction; References; Part I; 2 Fundamental Tenets of Nanomechanics; 2.1 Nanoscopic Structures; 2.1.1 Carbon-Based Nanoscopic Structures; 2.1.2 Nanoparticles; 2.1.3 Nanowires; 2.1.4 Biological Nanoscopic Structures; 2.2 Techniques for Modelling Mechanical Characteristics of Nanoscopic Structures; 2.2.1 Atomistic-Based Modelling Methods; 2.2.2 Continuum Modelling Methods; 2.2.3 Multiscale Simulation Methods; 2.3 Mechanical Behaviour of Nanoscopic Structures: Pertinent Definitions and Concepts 2.3.1 Bending Behaviour of One-Dimensional Nanoscopic Structures2.3.2 Buckling Behaviour; 2.3.3 Vibrational Behaviour; References; 3 Fundamental Notions from Classical Continuum Mechanics; 3.1 Displacement and Strain; 3.1.1 Strain Tensor; 3.1.2 Principal Strains; 3.1.3 Spherical and Deviatoric Strains; 3.1.4 Compatibility Conditions; 3.1.5 Plane Strain Condition; 3.2 Stress Tensor; 3.2.1 Concept of Stress; 3.2.2 Stress on an Arbitrary Surface; 3.2.3 Principal Axes of Stress; 3.2.4 Hydrostatic and Deviatoric Stresses; 3.3 Constitutive Equations; 3.3.1 Generalized Hooke's Law 3.3.2 Material Symmetry3.4 Governing Equations; 3.4.1 Equations of Motion; 3.4.2 Navier Equations of Motion; 3.5 Elastic Energy; References; 4 Essential Concepts from Nonlocal Elasticity Theory; 4.1 Nonlocality and Nonlocal Averaging; 4.2 Spatial Nonlocal Kernels; 4.2.1 Properties of Nonlocal Kernels; 4.2.2 Different Types of Nonlocal Kernels; 4.2.3 Two-Phase Kernels; 4.3 Gradient-Based Nonlocal Elasticity Theory; 4.3.1 Green's Function Kernels; 4.3.2 Alternative Derivation of Gradient-Based Nonlocal Elasticity Theory; 4.4 Laplacian of the Stress Tensor; 4.4.1 Cylindrical Coordinates 4.4.2 Spherical Coordinates4.5 Nonlocal Anisotropic Elasticity; 4.6 Nonlocal Kernels in a Finite Domain; References; 5 Nonlocal Modelling of Nanoscopic Structures; 5.1 Nonlocal Beam Models; 5.1.1 Nonlocal Euler-Bernoulli Beam Theory; 5.1.2 Nonlocal Timoshenko Beam Theory; 5.2 Nonlocal Cylindrical Shell Models; 5.2.1 Governing Equations for Circular Cylindrical Shells; 5.2.2 Nonlocal Classical Shell Model; 5.2.3 Nonlocal First-Order Shear Deformation Theory; 5.3 Nonlocal Plate Models; 5.3.1 The Kirchhoff Plate Theory; 5.3.2 The Reissner-Mindlin Plate Theory; 5.3.3 Circular Nanoplate 5.4 Nonlocal Membrane Theory for Spherical Shell5.5 Nonlocal Models for Nanocrystals; References; 6 Elastic Properties of Carbon-Based Nanoscopic Structures; 6.1 Young's Modulus and Effective Wall Thickness of SWCNTs; 6.2 Anisotropic Elastic Constants of SWCNTs; 6.3 Nonlocal Parameter for Carbon Nanotubes; 6.4 Evaluation of the Nonlocal Parameter for SWCNTs; 6.5 Anisotropic Mechanical Properties of Graphene Sheets; 6.6 Effective Young's Modulus of Fullerene Molecules; References; Part II; 7 Computational Modelling of the Vibrational Characteristics of Zero-Dimensional Nanoscopic Structures Summary This book offers a comprehensive treatment of nonlocal elasticity theory as applied to the prediction of the mechanical characteristics of various types of biological and non-biological nanoscopic structures with different morphologies and functional behaviour. It combines fundamental notions and advanced concepts, covering both the theory of nonlocal elasticity and the mechanics of nanoscopic structures and systems. By reporting on recent findings and discussing future challenges, the book seeks to foster the application of nonlocal elasticity based approaches to the emerging fields of nanoscience and nanotechnology. It is a self-contained guide, and covers all relevant background information, the requisite mathematical and computational techniques, theoretical assumptions, physical methods and possible limitations of the nonlocal approach, including some practical applications. Mainly written for researchers in the fields of physics, biophysics, mechanics, and nanoscience, as well as computational engineers, the book can also be used as a reference guide for senior undergraduate and graduate students, as well as practicing engineers working in a range of areas, such as computational condensed matter physics, computational materials science, computational nanoscience and nanotechnology, and nanomechanics Notes Online resource; title from PDF title page (SpringerLink, viewed February 27, 2019) Subject Continuum mechanics. Elasticity. elasticity. modulus of elasticity. Continuum mechanics Elasticity Form Electronic book Author Rafii-Tabar, H. (Hashem), author. Fazelzadeh, Seyed Ahmad., author ISBN 9783030116507 3030116506 9783030116514 3030116514

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