Power Law UMAT
December ��� ����
� Mechanics
No summmation in the following expressions��
�
ij
� S
ij
� p�
ij
���
p � k tr � ���
For shear components introduce engineering strain�
�
ij
� ��
ij
���
S
ii
�
�
�
�
�
�
�
�
m��
�
�
�
ii
�
�
and S
ij
�
�
�
�
�
�
�
�
m��
�
�
�
ij
�
�
� �
� �
�
�
�
�
ij
�
ij
�
�
�
�
�
�
�
�
X
�
�
ii
� �
X
�
�
ij
�
�
�
�
�
�
�
�
�
�
�
X
�
�
ii
�
�
�
X
�
�
ij
��
�
�
��
ii
��
jj
� �
ij
and
��
ij
��
kl
� �
ik
�
jl
���
I
ijkl
�
�
�
��
ik
�
jl
� �
il
�
jk
� ���
J �
�
�
ij
�t�
t�
�
�
kl
�t�
t�
�
��
ij
�t�
t�
��
kl
�t�
t�
���
�
� tr �
��
kl
� �
kl
���
��
��
kk
�
�
��
��
�
��
kk
�
�
��
�
�
� �
P
�
�
ii
�
��
kk
�
�
��
�
kk
����
��
��
kl
�
�
��
��
�
��
kl
�
�
��
�
�
�
�
�
�
P
�
�
ij
�
��
kl
�
�
��
�
kl
����
Now we can compute
�S
��
�
�S
ii
��
kk
�
�
�
�
�
�
�
�
m��
�
�
�
�
�
m� �
�
��
��
kk
�
ii
�
��
ii
��
kk
�
����
�
�
�
�
�
�
�
�
m��
�
�
�
�
�
��m � ��
��
�
�
kk
�
ii
� �
ik
�
�S
ij
��
kk
�
�
�
�
�
�
�
�
m��
�
�
�
�
�
m� �
�
��
��
kk
�
ij
�
��
ij
��
kk
�
����
�
�
�
�
�
�
�
�
m��
�
�
�
�
��m� ��
��
�
�
kk
�
ij
�S
ii
��
kl
�
�
�
�
�
�
�
�
m��
�
�
�
�
�
m� �
�
��
��
kl
�
ii
�
��
ii
��
kl
�
�� �
�
�
�
�
�
�
�
�
m��
�
�
�
�
�m� ��
��
�
�
kl
�
ii
�S
ij
��
kl
�
�
�
�
�
�
�
�
m��
�
�
�
�
�
m� �
�
��
��
kl
�
ij
�
��
ij
��
kl
�
��
�
�
�
�
�
�
�
�
�
m��
�
�
�
�
�
�m� ��
��
�
�
kl
�
ij
� �
ik
�
jl
�
�p
��
kk
�
ij
� k
� tr �
��
kk
�
ij
� k�
ij
and
�p
��
kl
�
ij
� k
� tr �
��
kl
�
ij
� � ����
�
Now we can compute Jacobian�
J
iikk
�
��
ii
��
kk
�
�S
ii
��
kk
�
�p
��
kk
����
�
�
�
�
�
�
�
�
m��
�
�
�
�
�
��m� ��
��
�
�
kk
�
ii
� �
ik
�
� k
J
ijkk
�
��
ij
��
kk
�
�S
ij
��
kk
����
�
�
�
�
�
�
�
�
m��
�
�
�
�
��m� ��
��
�
�
kk
�
ij
J
iikl
�
��
ii
��
kl
�
�S
ii
��
kl
�
�p
��
kl
����
�
�
�
�
�
�
�
�
m��
�
�
�
�
�m� ��
��
�
�
kl
�
ii
J
ijkl
�
��
ij
��
kl
�
�S
ij
��
kl
����
�
�
�
�
�
�
�
�
m��
�
�
�
�
�
�m� ��
��
�
�
kl
�
ij
� �
ik
�
jl
�
and Stress�
�
ii
� S
ii
� p �
�
�
�
�
�
�
�
m��
�
�
�
�
�
ii
� k tr � ����
�
ij
� S
ij
�
�
�
�
�
�
�
�
m��
�
�
�
�
�
ij
����
�
� Coding
PNLT � k ����
TERM� �
�
�
�
�
�
�
�
m��
�
�
�
�
�� �
TERM� �
��m� ��
��
�
��
�
TERM� �
�
�
TERM� TERM� ����
For Jacobian�
J
iikk
� TERM� �TERM� �
kk
�
ii
� �
ik
� � PNLT ����
J
iikl
� J
klii
� TERM� �
ii
�
kl
����
J
ijkl
�
�
�
TERM� �
�
�
TERM� �
ij
�
kl
� �
ik
�
jl
� ����
For Stress�
�
ii
� TERM� �
ii
� PNLT tr � ����
�
ij
�
�
�
TERM� �
ij
����
� ABAQUS input �le� Uniaxial Tension
�HEADING
UMAT � POWER LAW INCOMPRESSIBLE MATERIAL� C�D� ��� UMATPLT�
�WAVEFRONT MINIMIZATION�SUPPRESS
�NODE�NSET�ALLN
��� �� ��
�� �� ��
��� �� ��
��� �� ��
��� �� ��
�� �� ��
��� �� ��
��� �� ��
�ELEMENT�TYPE�C�D��ELSET�ALLE
����
�������
����
�SOLID SECTION�ELSET�ALLE�MATERIAL�ALLE
�MATERIAL�NAME�ALLE
�USER MATERIAL�CONSTANTS��
�� E v POWER sig� eps� StTol Pnlt
�� E�� �� ��� �� �� E�
�� E
�USER SUBROUTINE
SUBROUTINE UMAT�STRESS�STATEV�DDSDDE�SSE�SPD�SCD�
� RPL�DDSDDT�DRPLDE�DRPLDT�STRAN�DSTRAN�
TIME�DTIME�TEMP�DTEMP�PREDEF�DPRED�MATERL�NDI�NSHR�NTENS�
� NSTATV�PROPS�NPROPS�COORDS�DROT�PNEWDT�CELENT�
� DFGRD��DFGRD��NOEL�NPT�KSLAY�KSPT�KSTEP�KINC�
C
INCLUDE �ABA�PARAM INC�
C
CHARACTER�� CMNAME
DIMENSION STRESS�NTENS��STATEV�NSTATV��
� DDSDDE�NTENS�NTENS��DDSDDT�NTENS��DRPLDE�NTENS��
STRAN�NTENS��DSTRAN�NTENS��TIME�
��PREDEF����DPRED����
� PROPS�NPROPS��COORDS����DROT������
� DFGRD�������DFGRD������
C
DIMENSION STRANT�
��DELTA�����
C
PARAMETER �ONE�� �D��TWO�
�D��THREE�� �D��SIX�
�D��
� HALF� �D�� ZERO � � �D��
DATA NEWTON�TOLER����� D�
�
C
C KRONECKER�S DELTA
C
DATA DELTA �� �D��� �D��� �D��
� � �D��� �D��� �D��
� �D��� �D��� �D��
C
C �����������������������������������������������������������
C UMAT FOR ISOTROPIC ELASTICITY AND ISOTROPIC PLASTICITY
C J
FLOW THEORY
C �����������������������������������������������������������
C PROPS��� � E
C PROPS�
� � NU
C PROPS��� � POWER � POWER LAW EXPONENT
C PROPS��� � SIG�
C PROPS��� � EPS�
C PROPS�
� � STTOL � �ELASTIC� STRAIN��YIELD� STRAIN
C PROPS��� � PNLT � PENALTY FOR INCOMPRESSIBILTY
C �����������������������������������������������������������
C
C
C COMPUTE TOTAL STRAIN
C
DO K����NTENS
STRANT�K�� � STRAN�K���DSTRAN�K��
ENDDO
C
C COMPUTE MEAN STRAIN
C
STNMN � ZERO
DO K� � ��NDI
STNMN � STNMN � STRANT�K���STRANT�K��
ENDDO
DO K� � ��NDI�NTENS
STNMN � STNMN � HALF�STRANT�K���STRANT�K��
ENDDO
�
STNMN � �TWO�THREE�STNMN���HALF
C
C ELASTIC PROPERTIES
C
EMOD�PROPS���
ENU�PROPS�
�
IF�ENU GT � ���� AND ENU LT � ����� ENU�� ���
EBULK��EMOD��ONE�TWO�ENU�
EG
�EMOD��ONE�ENU�
EG�EG
�TWO
EG��THREE�EG
ELAM��EBULK��EG
��THREE
C
C MATERIAL PROPERTIES AND PENALTIES
C
POWER � PROPS���
SIG� � PROPS���
EPS� � PROPS���
STTOL � PROPS�
��EPS�
PNLT � PROPS����EMOD
C
C SWITCH FOR LINEAR�POWER LAW BEHAVIOR
C
IF �STNMN LE STTOL� THEN
C
C ELASTIC STIFFNESS
C
DO
� K����NTENS
DO �� K
���NTENS
DDSDDE�K
�K���ZERO
�� CONTINUE
� CONTINUE
C
DO �� K����NDI
DO �� K
���NDI
DDSDDE�K
�K���ELAM
�� CONTINUE
DDSDDE�K��K���EG
�ELAM
�
�� CONTINUE
DO �� K��NDI���NTENS
DDSDDE�K��K���EG
�� CONTINUE
C
C CALCULATE STRESS FROM ELASTIC STRAINS
C
DO �� K����NTENS
DO
� K
���NTENS
STRESS�K
��STRESS�K
��DDSDDE�K
�K���DSTRAN�K��
� CONTINUE
�� CONTINUE
C
ELSE
C
C NON�LINEAR BEHAVIOR
C
C PRESSURE
C
VOLDEF � � �
DO K� � ��NDI
VOLDEF � VOLDEF � STRANT�K��
ENDDO
PRESS � PNLT�VOLDEF
C
C PRECOMPUTED TERMS
C
TERM� � TWO�THREE��STNMN�EPS�����POWER�ONE��SIG��EPS�
TERM
� �POWER�ONE��TWO�THREE��STNMN�STNMN�
TERM� � HALF�TERM��TERM
C
C STRESS
C
DO K� � ��NDI
STRESS�K�� � TERM��STRANT�K�� � PRESS
ENDDO
DO K� � NDI��� NTENS
STRESS�K�� � HALF�TERM��STRANT�K��
ENDDO
�
C
C JACOBIAN
C
C
C JACOBIAN � TENSION�TENSION COMPONENTS
C
DO K� � ��NDI
DO K
� ��NDI
DDSDDE�K��K
� � TERM���TERM
�
� STRANT�K���STRANT�K
��DELTA�K��K
�� � PNLT
ENDDO
ENDDO
C
C JACOBIAN � TENSION�SHEAR COMPONENTS
C
DO K� � ��NDI
DO K
� NDI���NTENS
DDSDDE�K��K
� � TERM��STRANT�K���STRANT�K
�
DDSDDE�K
�K�� � DDSDDE�K��K
�
ENDDO
ENDDO
C
C JACOBIAN � SHEAR�SHEAR COMPONENTS
C
DO K� � NDI���NTENS
DO K
� NDI���NTENS
DDSDDE�K��K
� � HALF�TERM��� HALF�TERM
�
� STRANT�K���STRANT�K
��DELTA�K��NDI�K
�NDI� �
ENDDO
ENDDO
ENDIF
C
RETURN
END
�BOUNDARY
��PINNED
�
��
�
�
���
���
���
��
���
���
�STEP�INC����
�STATIC
� �
�
�BOUNDARY
������
������
�����
������
�EL PRINT
S
SINV
E
EE
�NODE PRINT
U�RF
�EL FILE�FREQ���
S�E
�RESTART�WRITE
�END STEP
��
� ABAQUS BC� Shear Test
�BOUNDARY
�����
�����
�����
�����
����
�����
����
�����
����
�����
����
�����
�STEP�INC����
�STATIC
� �
�
�BOUNDARY
�
���
��
���
�
���
��
���
�EL PRINT
��
� Results for Uniaxial Tension Test
ELEMENT PT FOOT� MISES TRESC PRESS INV�
NOTE
� � � ���� � ���� � ���� � ����
�
� ���� � ���� � ���� � ����
� � � ���� � ���� � ���� � ����
� � � ���� � ���� � ���� � ����
� � � ���� � ���� � ���� � ����
�
� ���� � ���� � ���� � ����
� � � ���� � ���� � ���� � ����
� � � ���� � ���� � ���� � ����
MAXIMUM � ���� � ���� � ���� � ����
ELEMENT � � � �
� Results for Shear Test
ELEMENT PT FOOT� MISES TRESC PRESS INV�
NOTE
� � ���� ���� �
����E��� � ����E���
�
���� ���� �� �
��E��� � ����E���
� � ���� ���� �
����E��� � ����E���
� � ���� ���� �� �
��E��� � ����E���
� � ���� ���� �� ���
E��
� ����E���
�
���� ����
����E��� � ����E���
� � ���� ���� � ����E��
� ����E���
� � ���� ���� �
�
�E��
� ����E���
MAXIMUM ���� ���� �
�
�E��
� ����E���
��
ABAQUS
1
23 DISPLACEMENT MAGNIFICATION FACTOR = 1.00 ORIGINAL MESH DISPLACED MESH
TIME COMPLETED IN THIS STEP 20.0 TOTAL ACCUMULATED TIME 20.0
ABAQUS VERSION: 5.4-1 DATE: 16-DEC-95 TIME: 17:34:10
STEP 1 INCREMENT 7
1
23
Figure �� Uniaxial Tension Test
ABAQUS
1
23 DISPLACEMENT MAGNIFICATION FACTOR = 1.00 ORIGINAL MESH DISPLACED MESH
TIME COMPLETED IN THIS STEP 20.0 TOTAL ACCUMULATED TIME 20.0
ABAQUS VERSION: 5.4-1 DATE: 16-DEC-95 TIME: 01:29:37
STEP 1 INCREMENT 7
1
23
Figure �� Shear Test
��
Pressurized Pipe
��� Model De�nition for One Layer of Elements
�HEADING
INF LONG CYLIN TUBE SUBJECTED TO INT PRESS � POWER LAW MAT� � LAYER �C�D
�R�
UNITS� N� mm
�RESTART�WRITE
�NODE
��
� �� � �
�� � ��
� �
�
�� ��� �� � �
�
�� � �� ��� �
�NGEN�LINE�C�NSET�Di
�� �� �� � � �� � �� � �
�NGEN�LINE�C�NSET�Do
�
�� �
�� �� � � �� � �� � �
�NFILL�NSET�Face�
Di� Do� �
� ��
�NCOPY�CHANGE NUMBER�
����OLD SET�Face��SHIFT�NEW SET�Face
� �� � �� ��� �
� ��
�NFILL�NSET�Nall
Face�� Face
�
� ����
�NSET�GENERATE�NSET�Xsymm
�� �
�� ��
����� ��
�� ��
����
�
�� ��
�NSET�GENERATE�NSET�Ysymm
�� �
�� ��
����� ��
�� ��
����
�
�� ��
�NSET�GENERATEN�NSET�Noutp
�� �
�� ��
��
�ELEMENT�TYPE�C�D
�R
�� �� �
�� �
�� ��
����
�
��
�
��
���� ��� �
� ���
�
����
�
�
����
��
� ����� ��
�� ��
�� ����
�ELGEN�ELSET�Eall
�
�� ��
� �
�ELSET�GENERATE�ELSET�Inside
�� �
�ELSET�ELSET�Eoutp
�
�SOLID SECTION�ELSET�Eall�MATERIAL�ALLE
�MATERIAL�NAME�ALLE
�USER MATERIAL�CONSTANTS��
�� E v POWER sig� eps� StTol Pnlt
�� E�� �� ��� �� �� E�
�� E
�USER SUBROUTINE
SUBROUTINE UMAT�STRESS�STATEV�DDSDDE�SSE�SPD�SCD�
END
�BOUNDARY
Xsymm�
Ysymm� �
Face�� �
Face
� �
�������������������
�STEP�PERTURBATION
�STATIC
�DLOAD
Inside� P
� �� �
�EL PRINT�ELSET�Eoutp
��
�������
��������������
�����������
COORD� S��� S
� S��
�EL PRINT�ELSET�Eoutp
���������
��
��
�
��
�
COORD� S��� S
� S��
�EL FILE
S� E
�NODE PRINT�NSET�Noutp
U��
�NODE FILE
U� RF
�END STEP
�
��� Model De�nition for Four Layers of Elements
�HEADING
INF LONG CYLIN TUBE SUBJECTED TO INT PRESS � POWER LAW MAT� � LAYERS �C�D
�R�
UNITS� N� mm
�RESTART�WRITE
�NODE
��
� �� � �
�� � ��
� �
�
�� ��� �� � �
�
�� � �� ��� �
�NGEN�LINE�C�NSET�Di
�� �� �� � � �� � �� � �
�NGEN�LINE�C�NSET�Do
�
�� �
�� �� � � �� � �� � �
�NFILL�NSET�Face�
Di� Do� �
� ��
�NCOPY�CHANGE NUMBER�
����OLD SET�Face��SHIFT�NEW SET�Face
� �� � �� ��� �
� ��
�NFILL�NSET�Nall
Face�� Face
�
� ����
�NSET�GENERATE�NSET�Xsymm
�� �
�� ��
����� ��
�� ��
����
�
�� ��
�NSET�GENERATE�NSET�Ysymm
�� �
�� ��
����� ��
�� ��
����
�
�� ��
�NSET�GENERATEN�NSET�Noutp
�� �
�� ��
��
�ELEMENT�TYPE�C�D
�R
�� �� ��� ��� ��
����
����
����
����
�� �
�
��
�
�
��
��
�
�
��
��
� ����� ����� ����� ����
�ELGEN�ELSET�Eall
�� ��
� �� �� ��� ��
�ELSET�GENERATE�ELSET�Inside
��
�� �
�ELSET�GENERATE�ELSET�Eoutp
�� ��� ��
�SOLID SECTION�ELSET�Eall�MATERIAL�ALLE
�MATERIAL�NAME�ALLE
�USER MATERIAL�CONSTANTS��
�� E v POWER sig� eps� StTol Pnlt
�� E�� �� ��� �� �� E�
�� E
�USER SUBROUTINE
SUBROUTINE UMAT�STRESS�STATEV�DDSDDE�SSE�SPD�SCD�
END
�BOUNDARY
Xsymm�
Ysymm� �
Face�� �
Face
� �
�������������������
�STEP�PERTURBATION
�STATIC
�DLOAD
Inside� P
� �� �
�EL PRINT�ELSET�Eoutp
��
�������
COORD� S��� S
� S��
�EL FILE
S� E
�NODE PRINT�NSET�Noutp
U�
�NODE FILE
U�RF
�END STEP
��
ABAQUS
1
2
3
1
2
3
4
5
6
789
81
83
85
8789
161
162
163
164
165
166
167
168169
1001
1003
1005
10071009
1161
1163
1165
11671169
2001
2002
2003
2004
2005
2006
200720082009
2081
2083
2085
20872089
2161
2162
2163
2164
2165
2166
2167
21682169
1
2
3
4
1
2
3
Figure �� Pressurized Pipe� One layer of elements� Power Law Material� Mesh�
ABAQUS
1
2
3
DISPLACEMENT MAGNIFICATION FACTOR = 1.126E+03 ORIGINAL MESH DISPLACED MESH
TIME COMPLETED IN THIS STEP 2.220E-16 TOTAL ACCUMULATED TIME 0.000E+00
ABAQUS VERSION: 5.4-1 DATE: 19-DEC-95 TIME: 15:01:21
STEP 1 INCREMENT 1
1
2
3
Figure � Pressurized Pipe� One layer of elements� Power Law Mate�
rial�Displacement�
��
ABAQUS
1
2
3 1
2
3
S22 VALUE
-3.06E+01
-2.30E+01
-1.54E+01
-7.80E+00
-1.85E-01
+7.43E+00
+1.50E+01
+2.26E+01
+3.03E+01
+3.79E+01
+4.55E+01
+5.31E+01
TIME COMPLETED IN THIS STEP 2.220E-16 TOTAL ACCUMULATED TIME 0.000E+00
ABAQUS VERSION: 5.4-1 DATE: 19-DEC-95 TIME: 15:01:21
STEP 1 INCREMENT 1
Figure
� Pressurized Pipe� One layer of elements� Power Law Material� �
��
�
ABAQUS
1
2
3 1
2
3
Figure �� Pressurized Pipe� Four layers of elements� Power Law Material� Mesh�
��
ABAQUS
1
2
3
DISPLACEMENT MAGNIFICATION FACTOR = 974. ORIGINAL MESH DISPLACED MESH
TIME COMPLETED IN THIS STEP 2.220E-16 TOTAL ACCUMULATED TIME 0.000E+00
ABAQUS VERSION: 5.4-1 DATE: 19-DEC-95 TIME: 15:09:03
STEP 1 INCREMENT 1
1
2
3
Figure �� Pressurized Pipe� Four layers of elements� Power Law Mate�
rial�Displacement�
ABAQUS
1
2
3 1
2
3
S22 VALUE
-4.11E+01
-3.16E+01
-2.21E+01
-1.25E+01
-3.04E+00
+6.48E+00
+1.60E+01
+2.55E+01
+3.50E+01
+4.46E+01
+5.41E+01
+6.36E+01
TIME COMPLETED IN THIS STEP 2.220E-16 TOTAL ACCUMULATED TIME 0.000E+00
ABAQUS VERSION: 5.4-1 DATE: 19-DEC-95 TIME: 15:09:03
STEP 1 INCREMENT 1
Figure �� Pressurized Pipe� Four layers of elements� Power Law Material� �
��
�
��
ABAQUS
1
2
3
DISPLACEMENT MAGNIFICATION FACTOR = 991. ORIGINAL MESH DISPLACED MESH
TIME COMPLETED IN THIS STEP 2.220E-16 TOTAL ACCUMULATED TIME 0.000E+00
ABAQUS VERSION: 5.4-1 DATE: 19-DEC-95 TIME: 14:40:29
STEP 1 INCREMENT 1
1
2
3
Figure �� Pressurized Pipe� Four layers of elements� Linear Material� Displacement�
ABAQUS
1
2
3 1
2
3
S22 VALUE
-4.11E+01
-3.16E+01
-2.21E+01
-1.25E+01
-3.04E+00
+6.48E+00
+1.60E+01
+2.55E+01
+3.50E+01
+4.46E+01
+5.41E+01
+6.36E+01
TIME COMPLETED IN THIS STEP 2.220E-16 TOTAL ACCUMULATED TIME 0.000E+00
ABAQUS VERSION: 5.4-1 DATE: 19-DEC-95 TIME: 14:40:29
STEP 1 INCREMENT 1
Figure ��� Pressurized Pipe� Four layers of elements� Linear Material��
��
�
��
本文档为【Power+Law+UMAT】,请使用软件OFFICE或WPS软件打开。作品中的文字与图均可以修改和编辑,
图片更改请在作品中右键图片并更换,文字修改请直接点击文字进行修改,也可以新增和删除文档中的内容。
该文档来自用户分享,如有侵权行为请发邮件ishare@vip.sina.com联系网站客服,我们会及时删除。
[版权声明] 本站所有资料为用户分享产生,若发现您的权利被侵害,请联系客服邮件isharekefu@iask.cn,我们尽快处理。
本作品所展示的图片、画像、字体、音乐的版权可能需版权方额外授权,请谨慎使用。
网站提供的党政主题相关内容(国旗、国徽、党徽..)目的在于配合国家政策宣传,仅限个人学习分享使用,禁止用于任何广告和商用目的。