Plasticity and Creep Theory Examples and Problems

BASIC DEFINITIONS Stress and Strain State Stress tensor Strain tensor Finite Deformations Finite strain tensors in material or spatial coordinates Strain rates tensors Stress tensors in material or spatial descriptions FOUNDATIONS OF PLASTICITY Basic Equations of Perfect Plasticity Uniaxial stress-strain behavior Criteria for yielding in perfect plasticity Stress-strain relations for perfect plasticity Methods of reduction of equations of perfect plasticity Problems Basic Equations of Plastic Hardening Drucker's postulate and the associated flow rule Subsequent yield surfaces for hardening material Theories of plastic hardening Problems Methods of the Theory of Plasticity Analysis of the level of a cross-section Interaction curves on levels of a cross-section or a body Extremum theorems of limit analysis: statically or kinematically admissible solutions Shakedown analysis Integration along characteristics in plane strain problems Problems SOL UTIONS OF ELASTIC-PLASTIC PROBLEMS Elastic-Plastic Torsion and Bending Elastic-plastic torsion of prismatic bars Problems Elastic-plastic bending of prismatic beams and plane frames Problems Elastic-Plastic Analysis of Cylinders, Disks, and Plates Thick-walled tubes, spherical shells and disks Problems Limit analysis of Plates Problems FOUNDATIONS OF CREEP Basic Equations of Uniaxial Creep Models Creep phenomenon Schematizations of creep at constant uniaxial stress Modelling of creep at varying uniaxial stress Linear uniaxial viscoelastic models Modelling of viscoplastic materials Problems Creep Constitutive Equations Under Multiaxial Loading Classical multiaxial creep theories Developed multiaxial creep theories Linear multiaxial viscoelastic equations SOLUTION OF CREEP PROBLEMS Bending, Buckling, and Torsion of Bars Under Creep Conditions Bending and buckling of a prismatic bar made of the linear viscoelastic material Bending of a prismatic be am made of the piece-wise linear elastic/viscoplastic material Bending of a prismatic beam made of the time hardening material Torsion of a circular bar made of the elastic-Bingham material Problems Rotationally Symmetric Creep Problems Creep of a thick-walled tube General formulae for the rotationally-symmetric transient creep problems CREEP RUPTURE Constitutive Equations of Creep Rupture Creep rupture phenomenon Classical creep rupture theories Problems Rotationally Symmetric Creep Rupture Problems Mechanisms of brittle rupture of tubes and disks Design of disks with respect to creep rupture References Author Index Subject Index