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Power+Law+UMAT

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Power+Law+UMAT 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�� � � � ...

Power+Law+UMAT
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�� �� � ��
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上传时间:2011-10-28
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