Micromechanics with Mathematica

Detalles Bibliográficos
Autor principal: Nomura, Seiichi
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2016.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title Page
  • Copyright
  • Contents
  • Preface
  • About the Companion Website
  • Chapter 1 Coordinate Transformation and Tensors
  • 1.1 Index Notation
  • 1.1.1 Some Examples of Index Notation in 3-D
  • 1.1.2 Mathematica Implementation
  • 1.1.3 Kronecker Delta
  • 1.1.4 Permutation Symbols
  • 1.1.5 Product of Matrices
  • 1.2 Coordinate Transformations (Cartesian Tensors)
  • 1.3 Definition of Tensors
  • 1.3.1 Tensor of Rank 0 (Scalar)
  • 1.3.2 Tensor of Rank 1 (Vector)
  • 1.3.3 Tensor of Rank 2
  • 1.3.4 Tensor of Rank 3
  • 1.3.5 Tensor of Rank 4
  • 1.3.6 Differentiation
  • 1.3.7 Differentiation of Cartesian Tensors
  • 1.4 Invariance of Tensor Equations
  • 1.5 Quotient Rule
  • 1.6 Exercises
  • References
  • Chapter 2 Field Equations
  • 2.1 Concept of Stress
  • 2.1.1 Properties of Stress
  • 2.1.2 (Stress) Boundary Conditions
  • 2.1.3 Principal Stresses
  • 2.1.4 Stress Deviator
  • 2.1.5 Mohr's Circle
  • 2.2 Strain
  • 2.2.1 Shear Deformation
  • 2.3 Compatibility Condition
  • 2.4 Constitutive Relation, Isotropy, Anisotropy
  • 2.4.1 Isotropy
  • 2.4.2 Elastic Modulus
  • 2.4.3 Orthotropy
  • 2.4.4 2-D Orthotropic Materials
  • 2.4.5 Transverse Isotropy
  • 2.5 Constitutive Relation for Fluids
  • 2.5.1 Thermal Effect
  • 2.6 Derivation of Field Equations
  • 2.6.1 Divergence Theorem (Gauss Theorem)
  • 2.6.2 Material Derivative
  • 2.6.3 Equation of Continuity
  • 2.6.4 Equation of Motion
  • 2.6.5 Equation of Energy
  • 2.6.6 Isotropic Solids
  • 2.6.7 Isotropic Fluids
  • 2.6.8 Thermal Effects
  • 2.7 General Coordinate System
  • 2.7.1 Introduction to Tensor Analysis
  • 2.7.2 Definition of Tensors in Curvilinear Systems
  • 2.7.3 Metric Tensor10, gij
  • 2.7.4 Covariant Derivatives
  • 2.7.5 Examples
  • 2.7.6 Vector Analysis
  • 2.8 Exercises
  • References
  • Chapter 3 Inclusions in Infinite Media
  • 3.1 Eshelby's Solution for an Ellipsoidal Inclusion Problem
  • 3.1.1 Eigenstrain Problem
  • 3.1.2 Eshelby Tensors for an Ellipsoidal Inclusion
  • 3.1.3 Inhomogeneity (Inclusion) Problem
  • 3.2 Multilayered Inclusions
  • 3.2.1 Background
  • 3.2.2 Implementation of Index Manipulation in Mathematica
  • 3.2.3 General Formulation
  • 3.2.4 Exact Solution for Two-Phase Materials
  • 3.2.5 Exact Solution for Three-Phase Materials
  • 3.2.6 Exact Solution for Four-Phase Materials
  • 3.2.7 Exact Solution for 2-D Multiphase Materials
  • 3.3 Thermal Stress
  • 3.3.1 Thermal Stress Due to Heat Source
  • 3.3.2 Thermal Stress Due to Heat Flow
  • 3.4 Airy's Stress Function Approach
  • 3.4.1 Airy's Stress Function
  • 3.4.2 Mathematica Programming of Complex Variables
  • 3.4.3 Multiphase Inclusion Problems Using Airy's Stress Function
  • 3.5 Effective Properties
  • 3.5.1 Upper and Lower Bounds of Effective Properties
  • 3.5.2 Self-Consistent Approximation
  • 3.5.3 Source Code for micromech.m
  • 3.6 Exercises
  • References
  • Chapter 4 Inclusions in Finite Matrix
  • 4.1 General Approaches for Numerically Solving Boundary Value Problems

Ejemplares similares