The Mechanical and Thermodynamical Theory of Plasticity

Born out of fifteen years of courses and lectures on continuum mechanics, nonlinear mechanics, continuum thermodynamics, viscoelasticity, plasticity, crystal plasticity and thermodynamic plasticity, The Mechanical and Thermodynamical Theory of Plasticity represents one of the most extensive and in-depth treatises on the mechanical and thermodynamical aspects of plastic and visicoplastic flow. Suitable for student readers and experts alike, it offers a clear and comprehensive presentation of multi-dimensional continuum thermodynamics to both aid in initial understanding and introduce and explore advanced topics.

Covering a wide range of foundational subjects and presenting unique insights into the unification of disparate theories and practices, this book offers an extensive number of problems, figures, and examples to help the reader grasp the subject from many levels. Starting from one-dimensional axial motion in bars, the book builds a clear understanding of mechanics and continuum thermodynamics during plastic flow. This approach makes it accessible and applicable for a varied audience, including students and experts from Engineering Mechanics, Mechanical Engineering, Civil Engineering, and Materials Science.

Plasticity In The 1-D BarIntroduction to Plastic Response The Bar and The Continuum Assumption Motion and Temperature of Points on a Bar Stretch Ratio, Strain, Velocity Gradient, Temperature Gradient Superposition of Deformations Elastic, Plastic, and Thermal Strains Examples of Constitutive Models Mechanical Theory of Rate-Independent PlasticityMechanical Models for Plasticity Temperature-Dependent Plasticity An Infinitesimal Theory of Thermoplasticity Rate-Dependent Models for Plasticity Load Control as Opposed to Strain Control Numerical Integration of Constitutive Equations The Balance Laws Thermodynamic Restrictions on Constitutive Equations Heat Generation and Flow Equilibrium and Quasi-Equilibrium Problems Dynamic Loading Problems: Numerical SolutionDealing with Discontinuities: Jump Conditions Plastic Drawing of Bars Elastic and Plastic (Shock) Waves in a Bar General Comment on Selection of Moduli Notation and Summary Vectors and Tensors Matrix algebra Vectors Tensors Tensor calculus Notation Describing Motion, Deformation and Temperature Position, Velocity, Acceleration And Temperature Configurations of Material Bodies Streamlines and Pathlines Deformation Gradient and Temperature Gradient Stretch and Strain TensorsVelocity Gradient Relative Deformation Triaxial Extension, Simple Shear, Bending and Torsion Small Deformations Notation Elastic, Plastic And Thermal DeformationElastic and Plastic Deformation Gradients Elastic and Plastic Strains Elastic and Plastic Velocity Gradients Infinitesimal Elastic and Plastic Deformations Large Rigid Body Rotations Thermal Deformation and Thermal Strain Notation Traction, Stress and Heat Flux The Traction Vector The Relation between Tractions on Different SurfacesThe Stress Tensor Isotropic Invariants and the Deviatoric Stress Examples of Elementary States of Stress True Stress as Opposed to Engineering Stress The Piola-Kirchhoff, Rotated and Convected Stresses Heat Flux Notation Balance Laws and Jump ConditionsIntroduction Transport Relations Conservation of Mass Balance of Linear Momentum Balance of Angular Momentum Balance of Work snd Energy Entropy and the Entropy Production Inequality Heat Flow and Thermodynamic Processes Infinitesimal Deformations The Generalized Balance Law Jump Conditions Perturbing a Motion Initial and Boundary Conditions Notation Infinitesimal Plasticity A Mechanical Analog for Plasticity Elastic Perfectly-Plastic Response Common Assumptions Von Mises Yield Function with Combined Isotropic and Kinematic Hardening Thermoplasticity Free-Energy of Quadratic Form Scalar Stress and Hardening Functions Multiple Elements in Parallel Multiple Elements in Series Rate-Dependent Plasticity Deformation Plasticity Notation Solutions for Infinitesimal PlasticityHomogeneous Deformations Torsion-Extension of a Thin Circular Cylindrical Tube Compression in Plane Strain Bending Torsion of Circular Members Unloading Torsion of Prismatic Sections Non-Uniform Loading of Bars Cylindrical and Spherical Symmetry Two-Dimensional Problems Heat and Its Generation First-Gradient Thermo-Mechanical Materials First-Gradient Theories Superposition of Pure Translations Superposition of Rigid Body Rotations Material Symmetry First-Gradient State Variable Models Higher Gradient and Non-Local Models Notation Elastic And Thermoelastic Solids The Thermoelastic Solid The Influence of Pure Rigid-Body Translation on the Constitutive Response The Influence of Pure Rigid-Body Rotation on the Constitutive Response Material Symmetry Change of Reference Configuration A Thermodynamically Consistent Model Models Based on Fe And FӨ Specific Free-Energy of Quadratic Form in Strain Heat Generation and Heat Capacity Material Constraints Multiple Material Constraints Superposition of Deformations Notation Finite Deformation Mechanical Theory of Plasticity General Mechanical Theory of Plasticity Rigid Body Motions Material Symmetry Stress Depending Only on Elastic Deformation GradientStress Depending on both Elastic Deformation and Plastic Strain General Comments Deformation Plasticity Notation Thermoplastic Solids A Simple Thermo-Mechanical Analog Thermoplasticity Thermodynamic Constraint Isotropic Examples with J2 Type Yield Functions Superposition of Rigid Body Motions Material Symmetry An Initially Isotropic Material Models Depending on Cp Heat Generation and Heat Flow Specific Free-Energy of Quadratic Form in StrainPlasticity Models Based on Green Strains Heat Flux Vector Material Constraints Models Based on F = Fefөfp Notation Viscoelastic Solids One-Dimensional Linear Viscoelasticity One-Dimensional Nonlinear Viscoelasticity Three-Dimensional Linear Viscoelasticity A One-Element Thermo-Viscoelastic Model Multi-Element Thermodynamic Viscoelastic Model Initially Isotropic Models: Free-Energy and Thermodynamic Stresses Quasi-Linear Viscoelastic Model Material Constraints Models Based on F = Fefөfve Notation Rate-Dependent Plasticity Infinitesimal Mechanical and Thermo-Mechanical Models with Viscoplastic Flow Nonlinear Thermoelastic-Viscoplastic Model Single-Element Viscoelastic-Viscoplastic Full Viscoelastic-Viscoplastic Model Material Constraints Models Based on F = Fefөfvp Notation Crystal plasticity Crystal Structures and Slip Systems Elastic Crystal Distortion Kinematics of Single-Crystal Deformation Resolved Shear Stress and Overstress Yield Function Thermo-Mechanical Models Rate-Dependent Models Notation A Representation of functions Isotropic Transversely Isotropic Orthotropic B Representation for fourth order constants Isotropic Transversely Isotropic Crystal Classes C Basic Equations Basic Equations Curvilinear Coordinates Rectangular Coordinates Cylindrical Coordinates Spherical Coordinates Index