книги / Устойчивость процессов деформирования вязкопластических тел

Foreword.................................................................................................

6

Author entrance......................................................................................

8

Chapter 1. Criteria and methods of research of deformation processes

stability ..............................................................................

11

§ I. Mathematical definitions and criteria of stability ofproces-

ses ......................................................................................

12

§ 2. Stability with respect to low and finite disturbances of the

main motion parameters, external, initial data, and domain

geometry ...........................................................................

25

§ 3.

Deformation processes stability with respect to disturbances

.

of material functions..........................................................

31

§4. Stability of material with respect to variation of its internal

structure (in connection with composites) and nonmecha­

nical interactions................................................................

36

§5. Instability by numerical simulation of process .................

39

Chapter 2. The general linearized problem on stability of non-linear

flows ...................................................................................

42

§ 6. The general boundary problem on stability with respect to

low disturbances..................................................................

42

6.1. The kinds of constitutive relations of materials (42).

6.2. The

formulation of initial-boundary problem on stability (44). 6.3. The general

scheme of the integral relations method and the basic theorems (48)

§7. Deformation processes stability for solids with linear vector

relations.............................................................................

52

7.1. The formulation of

the problem and its reduction to

eigenva­

lue problem (52). 7.2.

Reduction ot three-dimensional disturbances

to two-dimensional ones

and the generalized Squire theorem (53).

7.3. The generalized Orr—Sommerfeld problem (GOSP) (57). 7.4. The

integral relations method and sufficient integral estimates

of stabi­

lity (59). 7.5. Quadratic functionals minimization and finding estimating

parameter (63)

Chapter 3. Stability of viscoand perfect plastic flows ......................

68

174

C O N T E N T S

§8. The GOSP for processes of deformation of viscoplastic

solids...................................................................................

71

8.1. The estimates of stability of viscoplastic flows as consequences of § 7

results (71). 8.2. The GOSP for one-dimensional viscoplastic shear (74)

§9. The plane viscoplastic Couette flo w .................................

76

9.1. Lower estimates of critical Reynolds numbers (76). 9.2. Estimates of

phase frequency (79)

§ 10. The plane viscoplastic Poiseuille flow ..............................

80

10.1. Lower estimates

of critical Reynolds numbers (80).

10.2. Plane-

§11. Diffusion of vorticity in viscoplastic m edium ...................

84

11.1.

Tangential

velocity discontinuity

at half-plane boundary

(84).

11.2.

Stability of

the exact solution

of the problem on diffusion

of vorticity in viscoplastic half-plane

(87).

11.3. Tangential

stress

discontinuity at half-plane boundary (89) 11.4.

Stability of the

exact

solution of the problem on tangential stress discontinuity at boundary of

viscoplastic half-plane (91)

§ 12. The viscoplastic circular Couette—Taylor flow .................

92

12.4. Axially symmetric disturbances (99). 12.5.

Short wavelength

disturbances and viscous limit (100)

§ 13. The perfect rigid-plastic Couette flo w ..............................

101

§ 14. Hereditary viscoplastic shear flow s....................................

106

14.1. The hereditarx viscoplastic Poiseuille flow

in plane layer (107).

14.2. The hereditary \iscoplasiic Couette flow (108). 14.3. The formulation

of linearized problem on stability (110)

Chapter 4. Some problems on non-steady viscoand perfect plastic

flows in non-canonical domains........................................

113

§15. The perfect rigid-plastic flow inside plane confusor with

curvilinear walls.................................................................

120

15.1.

The formulation of the problem on flow inside plane confusor

with curvilinear walls (121). 15.2. Independence of stress dexiator on ^

and "pseudoradiar flow (123). 15.3. Possible

orthogonal

coordinate

s\stems

(124). 15.4. The analytical soluition of

the problem

for spiral

§ 16. Spherical bubble collapse in viscoplastic and

non-linear

\iscous m ed ia ....................................................................

129