Models and Phenomena in Fracture Mechanics

1 Fundamentals and Basic Relations.- 1.1 Energy Release and Energy Criterion.- 1.2 Some Methods for Determination of Energy Release.- 1.3 Other Examples of the Energy Release Phenomenon.- 1.4 Stress Intensity Criterion.- 1.5 Some Fracture-Associated Phenomena.- 2 Fourier Transform and Related Topics.- 2.1 Continuous Fourier Transform.- 2.2 Wiener-Hopf Technique.- 2.3 Laplace and Fourier Transform.- 2.4 Discrete Fourier Transform.- 3 Waves.- 3.1 Waves of Sinusoidal and Exponential Types.- 3.2 Waves in Periodic Structures.- 3.3 Forced Waves.- 3.4 Waves in Homogeneous Space and Half-Space.- 3.5 Nonlinear Waves in a String.- 4 One-dimensional Models.- 4.1 String Model.- 4.2 Bending Beam Model.- 5 Static Cracks in a Linearly Elastic Body.- 5.1 Field Representations.- 5.2 Kolosov-Muskhelishvili Representation.- 5.3 Papkovich Representation.- 5.4 Crack in an Unbounded Plane.- 5.5 Asymptotes.- 5.6 Homogeneous Solutions.- 5.7 Integral Equations for a General Crack System.- 5.8 Crack Interaction.- 5.9 Energy Release Under Crack Kink.- 5.10 Cohesive Zone Model.- 5.11 Penny-Shaped Crack.- 5.12 Betti#x2019;s Theorem and the Weight Functions.- 6 Nonlinear Elastic Body.- 6.1 Some Data from Nonlinear Elasticity.- 6.2 Lagrangian and Eulerian Interpretation of Linear Elasticity.- 6.3 Strains in the Neighborhood of a Singular Point.- 6.4 Exact Relationships for the Energy Release and Some Consequences.- 7 Viscoelastic Fracture.- 7.1 Some Data from Viscoelasticity.- 7.2 Stationary Crack and Collinear Crack System.- 7.3 Growing Crack.- 7.4 Cohesive Zone for Viscoelastic Material.- 8 Elastic-Plastic Fracture.- 8.1 Elastic-Plastic Fields.- 8.2 Fixed Cracks.- 8.3 Growing Cracks.- 8.4 Elastic-Plastic Dynamic Fracture.- 9 Dynamic Fracture in a Homogeneous Elastic Medium.- 9.1 Some BasicRelations.- 9.2 Crack Tip Asymptotes and the Energy Release.- 9.3 Factorization of the Fundamental Solutions.- 9.4 Uniform Crack Propagation.- 9.5 Nonuniform Crack Speed Problem.- 9.6 Self-Similar Dynamic Problems.- 9.7 Dynamic Crack in a Plate Under Bending.- 9.8 Principle of Maximum Energy Dissipation Rate.- 10 Cracks in a Bending Plate.- 10.1 Asymptotic Solution for a Single Crack.- 10.2 Radial Cracking with Closure.- 10.3 Self-Similar Dynamic Problem.- 11 The Square-Cell Lattice.- 11.1 Preliminaries.- 11.2 Some Introductory Remarks.- 11.3 Elastic Lattice: Formulation and the Governing Equation.- 11.4 Factorization.- 11.5 Solutions.- 11.6 Viscoelastic Lattice.- 12 Triangular-Cell Elastic Lattice.- 12.1 Introductory Remarks.- 12.2 General Properties of Fundamental Solutions.- 12.3 Equations and General Solutions.- 12.4 Macrolevel-Associated Solution.- 12.5 Microlevel Solutions.- 12.6 Concluding Remarks.- 13 Phase Transition Waves.- 13.1 Introductory Remarks.- 13.2 Macrolevel Solution.- 13.3 Discrete Chain.- 13.4 Higher-Order-Derivative Model.- 13.5 Concluding Remarks.- 14 Dynamic Amplification Factor in Fracture and Phase Transition.- 14.1 Introductory Remarks.- 14.2 Line of Viscoelastic Oscillators.- 14.3 DOR and SAR Domains for Viscoelastic Oscillator.- 14.4 Viscoelastic Square-Cell Lattice.- 14.5 Slow Phase Transition Wave in a Chain.- 14.6 Triangular-Cell Lattice Irregularities in Fracture.- References.