| Preface | 5 |
|---|
| I Basic equations of continuum mechanics | 19 |
|---|
| 1 Basic equations of continuous media | 21 |
| 1.1 Methods of describing motion of continuous media | 21 |
| 1.1.1 Coordinate systems and methods of describing motion of continuous media | 21 |
| 1.1.2 Eulerian description | 22 |
| 1.1.3 Lagrangian description | 23 |
| 1.1.4 Differentiation of bases | 23 |
| 1.1.5 Description of deformations and rates of deformation of a continuous medium | 25 |
| 1.2 Conservation laws. Integral and differential forms | 27 |
| 1.2.1 Integral form of conservation laws | 27 |
| 1.2.2 Differential form of conservation laws | 29 |
| 1.2.3 Conservation laws at solution discontinuities | 31 |
| 1.2.4 Conclusions | 32 |
| 1.3 Thermodynamics | 33 |
| 1.3.1 First law of thermodynamics | 33 |
| 1.3.2 Second law of thermodynamics | 34 |
| 1.3.3 Conclusions | 36 |
| 1.4 Constitutive equations | 36 |
| 1.4.1 General form of constitutive equations. Internal variables | 36 |
| 1.4.2 Equations of viscous compressible heat-conducting gases | 39 |
| 1.4.3 Thermoelastic isotropic media | 39 |
| 1.4.4 Combined media | 40 |
| 1.4.5 Rigid-plastic media with translationally isotropic hardening | 42 |
| 1.4.6 Elastoplastic model | 43 |
| 1.5 Theory of plastic flow. Theory of internal variables | 44 |
| 1.5.1 Statement of the problem. Equations of an elastoplastic medium | 44 |
| 1.5.2 Equations of an elastoviscoplastic medium | 48 |
| 1.6 Experimental determination of constitutive relations under dynamic loading | 50 |
| 1.6.1 Experimental results and experimentally obtained constitutive equations | 50 |
| 1.6.2 Substantiation of elastoviscoplastic equations on the basis of dislocation theory | 54 |
| 1.7 Principle of virtual displacements. Weak solutions to equations of motion | 58 |
| 1.7.1 Principles of virtual displacements and velocities | 58 |
| 1.7.2 Weak formulation of the problem of continuum mechanics | 60 |
| 1.8 Variational principles of continuum mechanics | 61 |
| 1.8.1 Lagrange’s variational principle | 61 |
| 1.8.2 Hamilton’s variational principle | 62 |
