Foundations of Stress Waves Book

Preface     xi
Introduction     1
Elementary Theory of One-Dimensional Stress Waves in Bars     7
Material Coordinate System and Spatial Coordinate System     7
Governing Equations of Longitudinal Waves in Bars in Material Coordinates     10
Characteristic Lines and the Compatibility Relationships along the Characteristic Lines     13
Elastic-Plastic Longitudinal Loading Waves in Semi-Infinite Bars     17
Linear elastic waves     17
Elastic-plastic loading waves     22
Governing Equations of Longitudinal Waves in Bars in Spatial Coordinates     26
Strong Discontinuity and Weak Discontinuity; Shock Waves and Continuous Waves     29
Conservation Conditions across Wave Front, Rankine-Hugoniot Relations     35
Dispersion Effects Induced by the Transverse Inertia     42
Torsion Waves in Cylindrical Bars     51
Interaction of Elastic Longitudinal Waves     57
Coaxial Collision of Two Elastic Bars     57
Interaction of Two Elastic Longitudinal Waves     58
Reflection of Elastic Longitudinal Waves at Fixed End and Free End     60
Coaxial Collision of Two Elastic Bars with Finite Length     62
Reflection and Transmission of Elastic Longitudinal Waves at the Interface of TwoDifferent Bars     66
Reflection and Transmission of Elastic Waves in Bars with Varying Cross Sections     69
Hopkinson Pressure Bar and Flying Piece     74
Split Hopkinson Pressure Bar     76
Dynamic Fracture Induced by Reflective Unloading Waves     87
Interaction of Elastic-Plastic Longitudinal Waves in Bars     95
Interaction of Two Longitudinal Elastic-Plastic Loading Waves in Bars     95
Head-on loading interaction of two strong-discontinuous stress waves     96
Head-on loading interaction of two weak-discontinuous stress waves     99
Reflection of Longitudinal Elastic-Plastic Loading Waves at a Fixed End     102
Governing Equations and Characteristic Lines of Unloading Waves     105
Pursuing Unloading by Strong-Discontinuous Unloading Disturbances     110
Sudden unloading of strong-discontinuous loading wave in a linear hardening bar     110
Sudden unloading of continuous loading waves in a linear hardening bar     116
Sudden unloading of centered plastic loading waves     120
Pursuing Unloading by Weak-Discontinuous Unloading Disturbances     126
Continuously unloading of centered plastic waves     128
Attenuation of shock waves in linearly hardening materials     131
Shock Wave Attenuation Due to Pursuing Unloading     135
Propagating Properties of Elastic-Plastic Boundaries in Semi-Infinite Bars     139
An analysis by the characteristic line method     139
Local linearization method     146
Head-On Unloading     148
High-Speed Impact of a Finite Bar onto a Rigid Target     153
Linear hardening bar     154
Increasingly hardening bar     161
Decreasingly hardening bar     164
General Properties of the Loading-Unloading Boundary Propagation     167
Loading boundary and unloading boundary     167
Elastic-plastic boundary as a singular interface     169
Strong-discontinuous elastic-plastic boundary     170
First order weak-discontinuous boundary     171
Second order weak-discontinuous boundary     176
Discussions on higher-than-second order weak-discontinuous boundaries     180
Higher order isolated points on elastic-plastic boundary     183
Supplementary conditions on loading boundary     190
Rigid Unloading Approximation     197
Rigid Unloading in a Semi-Infinite Bar     197
Rigid unloading in linear hardening plastic bars     197
Rigid unloading in linear elastic-linear hardening plastic bars      200
Rigid unloading in linear elastic-decreasing hardening plastic bars     202
Rigid Unloading in Finite Bars     207
Rigid Unloading Analyses for Shock Wave Propagation     212
Rigid unloading of shock wave propagating in semi-infinite bars     212
Rigid unloading of shock wave propagating in finite bars     215
One-Dimensional Visco-Elastic Waves and Elastic-Visco-Plastic Waves     219
Linear Visco-Elastic Constitutive Relationship     220
Maxwell model     222
Kelvin-Voigt model     224
Standard linear solid model     226
Stress Waves Propagating in Linear Visco-Elastic Bars     227
Longitudinal visco-elastic waves propagating in Kelvin-Voigt bars     227
Longitudinal visco-elastic waves propagating in Maxwell bars     229
Longitudinal visco-elastic waves propagating in standard linear solid bars     230
Solutions of linear visco-elastic longitudinal waves propagating in bars by the characteristics method     233
Split Hopkinson visco-elastic bar     237
Nonlinear Visco-Elastic Constitutive Relationship     246
Stress Waves Propagating in Nonlinear Visco-Elastic Bars     251
Elastic-Visco-Plastic Constitutive Relationship     255
Stress Waves Propagating in Elastic-Visco-Plastic Bars     260
One-Dimensional Strain Plane Waves     265
Governing Equations     265
One-Dimensional Strain Elastic Waves     267
Elastic-Plastic Constitutive Relationship in 1D Strain Condition     270
One Dimensional Strain Elastic-Plastic Waves     276
Influence of Reverse Yield on the Propagation of 1D Strain Elastic-Plastic Wave     279
State Equation of Solids under High Pressures     284
Shock Waves in Solids under High Pressures     292
Shock jump conditions     292
Shock adiabat     297
Interaction of Shock Waves in Solids under High Pressure     308
Plane Waves in Hydro-Elasto-Plastic Media     317
Attenuation of Shock Waves in Hydro-Elasto-Plastic Media     325
One-Dimensional Strain Elasto-Visco-Plastic Waves     333
Spherical Waves and Cylindrical Waves     337
Continuity Equation and Motion Equation     337
Elastic Spherical Waves and Cylindrical Waves     339
Elasto-Plastic Spherical Waves     347
Approximate Analysis for the Fragmentation of Spherical Shells     354
Elasto-Visco-Plastic Spherical Waves and Cylindrical Waves     357
Elastic-Plastic Waves Propagating in Flexible Strings     363
Governing Equations     364
Semi-Infinite Straight String under Abrupt Constant-Velocity Oblique Impact     372
Infinite Straight String under Abrupt Constant-Velocity Oblique Point-Impact     377
Prestretched Strings Subjected to Transverse Impact     388
Experimental investigation of wave velocity in a prestretched string     391
Experimental study on constitutive relationship of string materials     394
Determination of transverse wave velocity from longitudinal wave velocity measurements     396
Elastic-Plastic Waves Propagating in Beams under Transverse Impact (Bending Wave Theory)     399
Basic Assumptions and Governing Equations     399
Elastic Bending Waves     405
Plastic Bending Waves (Elastic-Plastic Beams)     409
Rigid-Plastic Analysis     432
Shear Failure of Beams under Transverse Impact     442
General Theory for Linear Elastic Waves     453
Linear Elastic Waves in Infinite Media     453
Oblique-Incidence, Reflection, and Transmission of Elastic Plane Waves     457
Elastic Surface Waves     467
Numerical Methods for Stress Wave Propagation     475
Characteristics Numerical Method     477
Characteristics numerical method for 1D waves     477
Characteristic surfaces numerical method for 2D waves     482
Finite Difference Method     490
Establishment of finite difference format     491
Convergence of difference formats     494
Stability of difference formats     495
Artificial viscosity     497
Finite Element Method (FEM)     500
Basic procedures of finite element method     500
Examples     503
Appendices     511
References     519
Index     529