Micromechanics with Mathematica - Nomura, Seiichi (Chichester, West Sussex John Wiley & Sons, Inc., 2016)
Coordinate Transformation and Tensors -- Index Notation -- Some Examples of Index Notation in 3-D -- Mathematiea Implementation -- Kronecker Delta -- Permutation Symbols -- Product of Matrices -- Coordinate Transformations (Cartesian Tensors) -- Definition of Tensors -- Tensor of Rank 0 (Scalar) -- Tensor of Rank 1 (Vector) -- Tensor of Rank 2 -- Tensor of Rank 3 -- Tensor of Rank 4 -- Differentiation -- Differentiation of Cartesian Tensors -- Invariance of Tensor Equations -- Quotient Rule -- Exercises -- References -- Field Equations -- Concept of Stress -- Properties of Stress -- (Stress) Boundary Conditions -- Principal Stresses -- Stress Deviator -- Mohr's Circle -- Strain -- Shear Deformation -- Compatibility Condition -- Constitutive Relation, Isotropy, Anisotropy -- Isotropy -- Elastic Modulus -- Orthotropy -- 2-D Orthotropic Materials -- Transverse Isotropy -- Constitutive Relation for Fluids -- Thermal Effect -- Derivation of Field Equations -- Divergence Theorem (Gauss Theorem) -- Material Derivative -- Equation of Continuity -- Equation of Motion -- Equation of Energy -- Isotropic Solids -- Isotropic Fluids -- Thermal Effects -- General Coordinate System -- Introduction to Tensor Analysis -- Definition of Tensors in Curvilinear Systems -- Metric Tensorp10s, gij -- Cavariant Derivatives -- Examples -- Vector Analysis -- Exercises -- References -- Inclusions in Infinite Media -- Eshelby's Solution for an Ellipsoidal Inclusion Problem -- Eigenstrain Problem -- Eshelby Tensors for an Ellipsoidal Inclusion -- Inhomogeneity (Inclusion) Problem -- Multilayered Inclusions -- Background -- Implementation of Index Manipulation in Mathematica -- General Formulation -- Exact Solution for Two-Phase Materials -- Exact Solution for Three-Phase Materials -- Exact Solution for Four-Phase Materials -- Exact Solution for 2-D Multiphase Materials -- Thermal Stress -- Thermal Stress Due to Heat Source -- Thermal Stress Due to Heat Flow -- Airy's Stress Function Approach -- Airy's Stress Function -- Mathematica Programming of Complex Variables -- Multiphase Inclusion Problems Using Airy's Stress Function -- Effective Properties -- Upper and Lower Bounds of Effective Properties -- Self-Consistent Approximation -- Source Code for micromech.m -- Exercises -- References -- Inclusions in Finite Matrix -- General Approaches for Numerically Solving Boundary Value Problems -- Method of Weighted Residuals -- Rayleigh-Ritz Method -- Sturm-Liouville System -- Steady-State Heat Conduction Equations -- Derivation of Permissible Functions -- Finding Temperature Field Using Permissible Functions -- Elastic Fields with Bounded Boundaries -- Numerical Examples -- Homogeneous Medium -- Single Inclusion -- Exercises -- References.
Includes bibliographical references and index.
Keywords: Micromechanics -- Data processing; Mechanics -- Data processing; Mathematica (Computer program language)