Cover
......Page 1
ADVANCES IN
CONSTITUTIVE RELATIONS
APPLIED IN COMPUTER CODES......Page 4
ISBN 978-3-211-99708-6......Page 5
PREFACE......Page 6
Table of Contents......Page 9
1.1 Purpose of numerical calculation......Page 10
1.2 General remarks on constitutive relation (s)......Page 11
2.2 General remarks on constitutive relations based on the MES......Page 16
2.3 Adiabatic heating - a specific temperature history during plastic deformation......Page 23
2.4 Most common examples of MES in explicit forms......Page 29
References......Page 54
3.1 Introduction......Page 57
3.2 The concept of the Mechanical Equation of State (MES) in RK constitutive relation......Page 59
3.3 RK constitutive relation with rete and temperature dependent strain hardening......Page 61
3.4 The intergration algorithm for FE calculation, [3.16]......Page 68
3.5 Final discussion......Page 73
References......Page 75
4.1 Rate and temperature sensitivities - general remarks......Page 78
4.2 Instantaneous rate sensitivity and rate sensitivity of strain hardening......Page 79
4.3 Some examples of strain rate history effects, FCC, HCP and BCC metals......Page 84
4.4 Discussion and conclusions......Page 91
References......Page 95
5.1 Strain hardening by differential approximations......Page 97
5.2 Strain rate and temperature effects by differential approximation......Page 100
5.3 Phenomenological models with evolution of strain hardening - BP model......Page 107
5.4 Phenomenological models with evolution of strain hardening - MTS model......Page 113
5.5 Phenomenological models with evolution of strain hardening - modified MTS model, [5.21]......Page 116
References......Page 122
6.2 Dynamic fracture mechanics and dynamic failure mechanics......Page 127
6.3 Fundamentals on time scale in fracture mechanics - loading rate spectrum......Page 129
6.5 Time and temperature dependent local fracture criteria......Page 133
6.6 Cumullative criterion on spall fracture - effects of temperature......Page 141
6.7 Effects of stress triaxiality on failure, fracture and spall......Page 145
6.8 Faillure criterion for impact shearing......Page 150
6.9 Concluding remarks......Page 152
References......Page 153
1 Introduction......Page 156
2.1 Configurations......Page 161
2.2 The deformation gradient......Page 163
2.3 Examples......Page 164
2.4 Polar decomposition theorem......Page 166
2.5 Spectral decomposition......Page 167
2.6 Right and left Cauchy-Green tensors......Page 168
2.7 Green-Lagrange strain tensor......Page 170
2.9 Deformation of area and volume elements......Page 171
2.10 Isochoric and volumetric deformations......Page 172
3.1 Cauchy's stress vector......Page 174
3.2 Cauchy's stress theorem......Page 175
4 Equation of equilibrium......Page 176
5.1 Hyperelastic meterials......Page 177
5.2 Meterials objectivity......Page 178
5.3 Isotropic elastic materials......Page 179
5.5 Constitutive equations in terms of strain invariants......Page 180
5.6 Constitutive equations in terms of principal stretches......Page 182
5.7 Incompressible isotropic hyperelasticity......Page 183
5.8 Compressible hyperelasticity......Page 184
6 Examples of strain energy functions......Page 185
6.1 Incompressible hyperelastic materials......Page 186
6.2 Compressible hyperelastic materials......Page 187
6.3 Other I1 models......Page 188
7.1 Pure azimuthal shear......Page 189
7.2 Illustration......Page 192
7.3 Inflation and extension ofa circular tube......Page 196
7.4 Illustration......Page 200
Bibliography......Page 209
1 Introduction......Page 212
2.1 Motivation......Page 213
2.2 Variational formulation......Page 214
2.3 Discretization and stability analysis......Page 216
2.4 Numerical examples......Page 222
2.5 Remarks......Page 227
3.1 Introduction......Page 228
3.2 DESCRIPTION OF THE METHOD......Page 230
3.3 Assemblage of the cell stiffness matrix......Page 234
3.4 Computational efficiency......Page 236
3.5 Numerical examples......Page 241
3.6 Remarks......Page 245
4.1 Introduction......Page 246
4.2 Theoretical model......Page 247
4.3 Computational method......Page 256
4.4 Numerical examples......Page 260
4.5 Remarks......Page 265
Bibliography......Page 266
1 Introduction......Page 270
2 Academic versus practical problems......Page 272
3.1 Strain localization......Page 273
3.2 The complexity of biomechanical analyses of tooth implants and spine segment......Page 287
3.3 Dental implants......Page 290
3.4 Human spine motion segement......Page 296
3.5 Blast and cumulative fracture criterion......Page 305
4 Concluding remarks......Page 317
Bibliography......Page 319