| foreword . preface common notations 1. constitutive equations for viscoelastic bodies 1.1 introduction 1.2 stress relaxation 1.3 creep 1.4 response functions, stress relaxation modulus, creep compliance 1.5 model theory, basic elements 1.6 two-element models 1.7 other rheological models 1.8 boltzmann superposition principle and integral type constitutive equations 1.9 constitutive equations for linear viscoelastic bodies 1.10 the relationships between differential type and integral type constitutive equations 1.11 thermorheologically simple materials, time-temperature shift principle 1.12 nonlinear viscoelastic bodies problems 2. linear viscoelastic problems and methods of solution 2.1 laplace transforms 2.2 discussions on differential type constitutive equations 2.3 governing equations for the theory of isothermal homogeneous quasi-static viscoelasticity .2.4 viscoelastic-elastic correspondence principle 2.5 application range and generalization of the classical correspondence principle 2.6 plane stress or plane strain creep compliance 2.7 plane stress or plane strain relaxation modulus 2.8 time factors 2.9 relations between creep compliance and relaxation modulus 2.10 simplification of inversion, quasi-elastic approximation problems 3. linear viscoelastic fracture mechanics 3.1 introduction 3.2 crack-boarder stress and displacement fields of viscoelastic bodies 3.3 plane strain creep compliances for usual rheological models 3.4 stress and displacement fields for a variety of viscoelastic cracked bodies under biaxial load 3.5 condition for the critical equilibrium of a cracked body 3.6 condition for crack instability 3.7 delayed crack instability 3.8 comparison between theory and experiments 3.9 mixed mode crack problems 3.10 double-beam and double-plate model viscoelastic crack problems 3.11 application example, crack problem of a concrete buttressed dam 3.12 conclusions of this chapter problems 4. volterra integral equations 4.1 volterra integral equations of the second kind 4.2 resolvent operators 4.3 fractional exponential function and its asymptotic properties 4.4 application of rabotnov fractional exponential kernel in viscoelasticity 4.5 bounded operators, limiting theorems problems 5. viscoelastic fracture mechanics 5.1 introduction 5.2 fracture model and basic assumptions 5.3 boltzmann's principle, integral operator forms of constitutive equations for viscoelastic bodies 5.4 volterra's principle and its application in solving viscoelastic cracked problems 5.5 incubation period of crack growth 5.6 first stage of quasi-static slow subcritical crack growth period transition stage 5.7 second stage of quasi-static slow subcritical crack growth period main stage of slow growth 5.8 propagation of an opening mode crack having a small failure zone in viscoelastic bodies .. 5.9 lifetime of a viscoelastic plate with a macroscopic crack 5.10 determination of the lifetime of a cracked polymer plate, comparison with experiments 5.11 lifetime of a cracked viscoelastic body in cases of non-uniformly distributed failure stress 5.12 application to a crack problem of a concrete buttressed dam 5.13 crack propagation in anisotropic viscoelastic bodies 5.14 conclusions of this chapter problems 6. theory of thermoviscoelasticity and crack problems 6.1 energy balance law and entropy production inequality 6.2 thermodynamic formulation of constitutive equations based on helmholtz free energy 6.3 thermodynamic formulation of constitutive equations based on gibbs free energy 6.4 thermodynamic restrictions 6.5 boundary value problems of thermoviscoelasticity 6.6 solution techniques for boundary problems of thermoviscoelasticity 6.7 thermoviscoelastic three-dimensional crack problems 6.8 nonlinear theory of thermoviscoelasticity problems 7. nonlinear viscoelastic fracture mechanics 7.1 introduction 7.2 mathematical description of crack extension 7.3 general balance law 7.4 global and local balance laws 7.5 balance equations in reference configuration 7.6 thermodynamic inconsistency of the classical fracture theory 7.7 conditions for crack extension 7.8 axioms of constitution, constitutive equation with internal variables 7.9 constitutive equations for materials with fading memory 7.10 constitutive equations of integral type materials 7.11 governing equations for nonlinear thermoviscoelastic fracture mechanics 7.12 nonlocal theory of basic balance laws of fracture mechanics 7.13 conclusions of this chapter problems reverences appendix a. time factors a.1 time factors for standard linear bodies a.2 time factors for a variety of viscoelastic bodies (k= constant) a.3 time factors for a variety of viscoelastic bodies (general cases) appendix b. concise table of usual laplace transforms appendix c. an outline of relevant knowledge of mathematics c.1 sets, mappings, groups c.2 topological spaces c.3 normed linear spaces, hilbert spaces c.4 curvilinear coordinates, base vectors, metric tensor c.5 coordinate transformations, tensors c.6 tensor algebra c.7 second-order tensors and linear transformations c.8 eigenvalues of second-order tensor, eigenvectors and invariants c.9 covariant differentiation, christoffel symbols c.10 absolute differentials and absolute derivatives of tensor fields c.11 riemann-christoffel curvature tensor, riemannian spaces c.12 manifolds c.13 torsion tensors, non-riemannian spaces c.14 curvilinear orthogonal coordinates and physical components of tensors c.15 cylindrical coordinates and spherical coordinates c.16 integral theorems c.17 some usual formulae c.18 two-point tensors appendix d. an outline of relevant knowledge of rational continuum mechanics d.1 bodies d.2 configurations d.3 motions d.4 coordinate systems, base vectors, metric tensors and line elements d.5 strain tensors d.6 material time derivatives and spatial gradients d.7 deformation gradients d.8 velocity gradient, deformation rate tensor and spin tensor d.9 piola-kirchhoff stress tensor d.10 polar decomposition theorem author index subject index ... |
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