(slip lines)

[ ]

, (friction hill)

(upper bound analysis).

,

.

,

.

1)

2)

3)

,

(xy) .

z Levy Misses

.

Tresca

k->

Von misses

*k

Tresca Von

misses

.

Mohr

(Dieter)

+

(1)

(2)

(3)

1,2,3

(4)

(5)

(6)

(7)

(8)

7,8

.

:

(9)

H l

9

(7) (8)

.

7,8

(9)

(10)

9 10

(11)

(12)

11 12

(13)

(14)

1)

2)

( Hencky)

A D

Hencky: ) (15)

B C

(16)

15 16

(17)

, C

(18)

3)

,

Hencky .

. .

Hencky .

4) ,,

=

5) Hencky:

S :

(19)

R :

(20)

. M.Levy

11 12

7 8

(21)

(22)

.

,

,

,

(23)

,

(hosford)

4

.

1

(hosford)

OC: ( )

() K

Hencky

P=2k(

o

.

(Hosford)

.

H/L

.

,

Hencky , .

P

(0,1)

Hencky . (1,1)

(25)

. (n,n)

25.

.

]dy=0=>

.

,

.O Hill

(R.Hill)

.

,

h .

.

r<

.

.

.

x,y

.

(0,1)

(n,n+1) , Hencky

.

, h=

,

.

:

.

R.Hill: The Mathematical Theory of Plasticity

Caddel-Hosford: Metal Forming Mechanics and Metallurgy

L.M Kachanov: Fundamentals of the Theory of Plasticity

Dieter: Mechanical Metallurgy

W.W Sokolovsky :Theory of plasticity