UMAT_Damage

S U B R O U T I N E

U M A T(S T R E S S,S T A T E V,D D S D D E,S S E,S P D,S C D,

1R P L,D D S D D T,D R P L D E,D R P L D T,S T R A N,D S T R A N,

2T I M E,D T I M E,T E M P,D T E M P,P R E D E F,D P R E D,M A T E R L,N D I,N S H R,N T E N S,

3N S T A T V,P R O P S,N P R O P S,C O O R D S,D R O T,P N E W D T,C E L E N T,

4D F G R D0,D F G R D1,N O E L,N P T,K S L A Y,K S P T,K S T E P,K I N C)

C

I N C L U D E

'A B A_P A R A M.I N C'

C

C H A R A C T E R

*80M A T E R L

D I M

E N S I O N

S T R E S S(N T E N S),S T A T E V(N S T A T V),

1D D S D D E(N T E N S,N T E N S),D D S D D T(N T E N S),D R P L D E(N T E N S),

2S T R A N(N T E N S),D S T R A N(N T E N S),T I M E(2),P R E D E F(1),D P R E D(1),

3P R O P S(N P R O P S),C O O R D S(3),D R O T(3,3),

4D F G R D0(3,3),D F G R D1(3,3)

C

D I M

E N S I O N

E E L A S(6),E P L A S(6),

F L O W(6)

P A R A M E T E R

(O N E=1.0D0,T W O=2.0D0,T H R E E=3.0D0,S I X=6.0D0)

D A T A

N E W T O N,T O L E R/10,1.D-6/

C

C-----------------------------------------------------------

C U M A T F O R I S O T R O P I C E L A S T I C I T Y A N

D I S O T R O P I C P L A S T I C I T Y

C J2F L O W T H E O R Y

C C A N N O T B E U S E

D F O R P L A N

E S T R E S S

C-----------------------------------------------------------

C P R O P S(1)-E

C P R O P S(2)-N U

C P R O P S(3)-S Y I E L D

C C A L L S A H A R

D F O R C U R V

E O

F S Y I E L D V S.P E E Q

C-----------------------------------------------------------

C

I F T H E N

(N D I.N E.3)

(6,1)

W R I T E

F O R M A T

1(//,30X,'***E R R O R-T H I S U M A T M A Y O N L Y B E U S E D F O R', 1'E L E M E N T S W I T H T H R E E D I R E C T S T R E S S C O M P O N E N T S')

E N D I F

C

C E L A S T I C P R O P E R T I E S

C

E M O D=P R O P S(1)

E N U=P R O P S(2)

I F

(E N U.G T.0.4999.A N D.E N U.L T.0.5001)E N U=0.499

E B U L K3=E M O D/(O N E-T W O*E N U)

E G2=E M O D/(O N E+E N U)

E G=E G2/T W O

E G3=T H R E E*E G

E L A M=(E B U L K3-E G2)/T H R E E

C

C E L A S T I C S T I F F N E S S

C

D O

20K1=1,N T E N S

10K2=1,N T E N S

D O

D D S D D E(K2,K1)=0.0

10C O N T I N U E

20C O N T I N U E

C

D O

40K1=1,N D I

D O

30K2=1,N D I

D D S D D E(K2,K1)=

E L A M

30C O N T I N U E

D D S D D E(K1,K1)=

E G2+E L A M

40C O N T I N U E

D O

50K1=N D I+1,N T E N S

D D S D D E(K1,K1)=

E G

50C O N T I N U E

C

C C A L C U L A T E S T R E S S F R O M E L A S T I C S T R A I N S

C

70K1=1,N T E N S

D O

D O

60K2=1,N T E N S

S T R E S S(K2)=S T R E S S(K2)+D D S D D E(K2,K1)*D S T R A N(K1)

60C O N T I N U E

70C O N T I N U E

C

C R E C O V E R E L A S T I C A N

D P L A S T I C S T R A I N S

C

80K1=1,N T E N S

D O

E E L A S(K1)=S T A T E V(K1)+D S T R A N(K1)

E P L A S(K1)=S T A T E V(K1+N T E N S)

80C O N T I N U E

E Q P L A S=S T A T E V(1+2*N T E N S)

C

C I F N O Y I E L

D S T R

E S S I S G I V E N,M A T E R I A L I S T A K E N T O B E E L A S T I C

C

I F T H E N

(N P R O P S.G T.2.A N D.P R O P S(3).G T.0.0)

C

C M I S E S S T R E S S

C

S M I S E S=(S T R E S S(1)-S T R E S S(2))*(S T R E S S(1)-S T R E S S(2))+ 1(S T R E S S(2)-S T R E S S(3))*(S T R E S S(2)-S T R E S S(3))+

1(S T R E S S(3)-S T R E S S(1))*(S T R E S S(3)-S T R E S S(1))

D O

90K1=N D I+1,N T E N S

S M I S E S=S M I S E S+S I X*S T R E S S(K1)*S T R E S S(K1)

90C O N T I N U E

S M I S E S=S Q R T(S M I S E S/T W O)

C

C H A R

D

E N I N G C U R V E,G E T Y I E L D S T R E S S

C

N V A L U E=N P R O P S/2-1

C A L L

A H A R D(S Y I E L0,H A R D,E Q P L A S,P R O P S(3),N V A L U E)

C

C D E T E R M I N E I F A C T I V E L Y Y I E L D I N G

C

I F T H E N

(S M I S E S.G T.(1.0+T O L E R)*S Y I E L0)

C

C F L O W

D I R

E C T I O N

C

S H Y D R O=(S T R E S S(1)+S T R E S S(2)+S T R E S S(3))/T H R E E

O N E S Y=O N E/S M I S E S

D O

110K1=1,N D I

F L O W(K1)=O N E S Y*(S T R E S S(K1)-S H Y D R O)

110C O N T I N U E

D O

120K1=N D I+1,N T E N S

F L O W(K1)=S T R E S S(K1)*O N E S Y

120C O N T I N U E

C

C S O L V E F O R E Q U I V S T R E S S,N E W T O N I T E R A T I O N

C

S Y I E L D=S Y I E L0

D E Q P L=0.0

D O

130K E W T O N=1,N E W T O N

R H S=S M I S E S-E G3*D E Q P L-S Y I E L D

D E Q P L=D E Q P L+R H S/(E G3+H A R D)

C A L L

A H A R D(S Y I E L D,H A R D,E Q P L A S+D E Q P L,P R O P S(3),N V A L U E)

I F G O T O

(A B S(R H S).L T.T O L E R*S Y I E L0)140

130C O N T I N U E

W R I T E

(6,2)N E W T O N

F O R M A T

2(//,30X,'***W A R N I N G-P L A S T I C I T Y A L G O R I T H M D I D N O T', 1'C O N V E R G E A F T E R',I3,'I T E R A T I O N S')

140C O N T I N U E

E F F H R D=E G3*H A R D/(E G3+H A R D)

C

C C A L C S T R E S S A N

D U P D A T

E S T R A I N S

C

D O

150K1=1,N D I

S T R E S S(K1)=F L O W(K1)*S Y I E L D+S H Y D R O

E P L A S(K1)=E P L A S(K1)+T H R E E*

F L O W(K1)*D E Q P L/T W O

E E L A S(K1)=E E L A S(K1)-T H R E E*

F L O W(K1)*D E Q P L/T W O

150C O N T I N U E

D O

160K1=N D I+1,N T E N S

S T R E S S(K1)=F L O W(K1)*S Y I E L D

E P L A S(K1)=E P L A S(K1)+T H R E E*

F L O W(K1)*D E Q P L

E E L A S(K1)=E E L A S(K1)-T H R E E*

F L O W(K1)*D E Q P L

160C O N T I N U E

E Q P L A S=E Q P L A S+D E Q P L

S P D=D E Q P L*(S Y I E L0+S Y I E L D)/T W O

C

C J A C O B I A N

C

E F F G=E G*S Y I E L D/S M I S E S

E F F G2=T W O*E F F G

E F F G3=T H R E E*E F F G2/T W O

E F F L A M=(E B U L K3-E F F G2)/T H R E E

D O

220K1=1,N D I

D O

210K2=1,N D I

D D S D D E(K2,K1)=

E

F F L A M

210C O N T I N U E

D D S D D E(K1,K1)=

E

F F G2+E F F L A M

220C O N T I N U E

D O

230K1=N D I+1,N T E N S

D D S D D E(K1,K1)=

E

F F G

230C O N T I N U E

D O

250K1=1,N T E N S

D O

240K2=1,N T E N S

D D S D D E(K2,K1)=D D S D D E(K2,K1)+F L O W(K2)*F L O W(K1)

1*(E F F H R D-E F F G3)

240C O N T I N U E

250C O N T I N U E

E N D I F

E N D I F

C

C S T O R E S T R A I N S I N S T A T E V A R I A B L E A R R A Y

C

D O

310K1=1,N T E N S

S T A T E V(K1)=E E L A S(K1)

S T A T E V(K1+N T E N S)=E P L A S(K1)

310C O N T I N U E

S T A T E V(1+2*N T E N S)=E Q P L A S

S I G M A K K=S T R E S S(1)+S T R E S S(2)+S T R E S S(3)

E f f e c t i v e_s t r e s s=S Q R T(0.5*((S T R E S S(1)-S T R E S S(2))**2

1+(S T R E S S(2)-S T R E S S(3))**2+(S T R E S S(3)-S T R E S S(1))**2)

2+6.*(S T R E S S(4)**2+S T R E S S(5)**2+(S T R E S S(6)**2)))

S T A T E V(2+2*N T E N S)=S T A T E V(2+2*N T E N S)+E f f e c t i v e_s t r e s s*D E Q P L R s i g m a=S I G M A K K/E f f e c t i v e_s t r e s s/3.

S T A T E V(3+2*N T E N S)=S T A T E V(3+2*N T E N S)

1+D S I N H(1.5*R s i g m a)*S I G M A K K*D E Q P L

S T A T E V(4+2*N T E N S)=S T A T E V(2+2*N T E N S)+S T A T E V(3+2*N T E N S)

S T A T E V(5+2*N T E N S)=S T A T E V(5+2*N T E N S)+D E X P(1.5*R s i g m a)*D E Q P L S T A T E V(6+2*N T E N S)=R s i g m a

C

R E T U R N

E N D

C

C

S U B R O U T I N E

A H A R D(S Y I E L D,H A R D,E Q P L A S,T A

B L E,N V A L U E)

C

I N C L U D E

'A B A_P A R A M.I N C'

D I M

E N S I O N

T A B L E(2,N V A L U E)

C

C S E T Y I E L

D S T R

E S S T O L A S T V A L U E O

F T A B L E,H A R D E N I N

G T O Z E R O

S Y I E L D=T A B L E(1,N V A L U E)

H A R D=0.0

C

C I F M O R E T H A N O N E E N T R Y,S E A R C H T A B L E

C

I F T H E N

(N V A L U E.G T.1)

D O

10K1=1,N V A L U E-1

E Q P L1=T A B L E(2,K1+1)

I F T H E N

(E Q P L A S.L T.E Q P L1)

E Q P L0=T A B L E(2,K1)

I F T H E N

(E Q P L1.L E.E Q P L0)

(6,1)

W R I T E

F O R M A T

1(//,30X,'***E R R O R-P L A S T I C S T R A I N M U S T B E',

1'E N T E R E D I N A S C E N D I N G O R D E R')

C A L L

X I T

E N D I F

C

C C U R R E N T Y I E L

D S T R

E S S A N D H A R D E N I N G

C

D E Q P L=E Q P L1-E Q P L0

S Y I E L0=T A B L E(1,K1)

S Y I E L1=T A B L E(1,K1+1)

D S Y I

E L=S Y I E L1-S Y I E L0

H A R D=D S Y I E L/D E Q P L

S Y I E L D=S Y I E L0+(E Q P L A S-E Q P L0)*H A R D

G O T O

20

E N D I F

10C O N T I N U E

20C O N T I N U E

E N D I F

R E T U R N

E N D

C

S U B R O U T I N E

U V A R M(U V A R,D I R E C T,T,T I M E,D T I M E,C M N A M E,O R N A M E, 1N U V A R M,N O E L,N P T,N L A Y E R,N S P T,K S T E P,K I N C,

2N D I,N S H R,C O O R D,J M A C,J M A T Y P,M A T L A Y O,L A C C F L G) C

I N C L U D E

'A B A_P A R A M.I N C'

C

C H A R A C T E R

*80C M N A M E,O R N A M E

D I M

E N S I O N

U V A R(*),T I M E(2),D I R E C T(3,3),T(3,3),C O O R D(*), $J M A C(*),J M A T Y P(*)

C U S E R

D

E

F I N E D D I M E N S I O N S T A T E M E N T S

C H A R A C T E R

*3F L G R A Y(15)

D I M

E N S I O N

A R R A Y(6),J A R R A Y(15)

C

C T h e d i m e n s i o n s o f t h e v a r i a b l e s A R R A Y a n d J A R R A Y

C m u s t b e s e t e q u a l t o o r g r e a t e r t h a n15

C

G E T V R M('E P',A R R A Y,J A R R A Y,F L G R A Y,J R C D,

C A L L

$J M A C,J M A T Y P,M A T L A Y O,L A C C F L G)

U V A R(1)=-(2*A R R A Y(2)-A R R A Y(3)-A R R A Y(1))/(A R R A Y(3)-A R R A Y(1))

C

C A L L

G E T V R M('S P',A R R A Y,J A R R A Y,F L G R A Y,J R C D,

$J M A C,J M A T Y P,M A T L A Y O,L A C C F L G)

U V A R(2)=-(2*A R R A Y(2)-A R R A Y(3)-A R R A Y(1))/(A R R A Y(3)-A R R A Y(1))

R E T U R N

E N D