Product: Abaqus/Standard
User subroutine UANISOHYPER_STRAIN:
can be used to define the strain energy potential of anisotropic hyperelastic materials as a function of the components of the Green strain tensor;
is called at all material calculation points of elements for which the material definition contains user-defined anisotropic hyperelastic behavior with a Green strain-based formulation (“Anisotropic hyperelastic behavior,” Section 18.5.3 of the Abaqus Analysis User's Manual);
can include material behavior dependent on field variables or state variables; and
requires that the values of the derivatives of the strain energy density function of the anisotropic hyperelastic material be defined with respect to the components of the modified Green strain tensor.
In the array of modified Green strain, EBAR, direct components are stored first, followed by shear components. There are NDI direct and NSHR engineering shear components. The order of the components is defined in “Conventions,” Section 1.2.2 of the Abaqus Analysis User's Manual. Since the number of active stress and strain components varies between element types, the routine must be coded to provide for all element types with which it will be used.
The array of first derivatives of the strain energy function, DU1, contains NTENS+1 components, with NTENS=NDI+NSHR. The first NTENS components correspond to the derivatives with respect to each component of the modified Green strain, 
. The last component contains the derivative with respect to the volume ratio, 
.
The array of second derivatives of the strain energy function, DU2, contains (NTENS+1)*(NTENS+2)/2 components. These components are ordered using the following triangular storage scheme:
Finally, the array of third derivatives of the strain energy function, DU3, also contains (NTENS+1)*(NTENS+2)/2 components, each representing the derivative with respect to 
of the corresponding component of DU2. It follows the same triangular storage scheme as DU2.
There are several special considerations that need to be noted.
When UANISOHYPER_STRAIN is used to define the material response of shell elements that calculate transverse shear energy, Abaqus/Standard cannot calculate a default value for the transverse shear stiffness of the element. Hence, you must define the element's transverse shear stiffness. See “Shell section behavior,” Section 25.6.4 of the Abaqus Analysis User's Manual, for guidelines on choosing this stiffness.
When UANISOHYPER_STRAIN is used to define the material response of elements with hourglassing modes, you must define the hourglass stiffness for hourglass control based on the total stiffness approach. The hourglass stiffness is not required for enhanced hourglass control, but you can define a scaling factor for the stiffness associated with the drill degree of freedom (rotation about the surface normal). See “Section controls,” Section 23.1.4 of the Abaqus Analysis User's Manual.
SUBROUTINE UANISOHYPER_STRAIN (EBAR, AJ, UA, DU1, DU2, DU3,
1 TEMP, NOEL, CMNAME, INCMPFLAG, IHYBFLAG, NDI, NSHR, NTENS,
2 NUMSTATEV, STATEV, NUMFIELDV, FIELDV, FIELDVINC,
3 NUMPROPS, PROPS)
C
INCLUDE 'ABA_PARAM.INC'
C
CHARACTER*80 CMNAME
C
DIMENSION EBAR(NTENS), UA(2), DU1(NTENS+1),
2 DU2((NTENS+1)*(NTENS+2)/2),
3 DU3((NTENS+1)*(NTENS+2)/2),
4 STATEV(NUMSTATEV), FIELDV(NUMFIELDV),
5 FIELDVINC(NUMFIELDV), PROPS(NUMPROPS)
user coding to define UA,DU1,DU2,DU3,STATEV
RETURN
ENDUA(1)
U, strain energy density function. For a compressible material at least one derivative involving J should be nonzero. For an incompressible material all derivatives involving J are ignored.
UA(2)
, the deviatoric part of the strain energy density of the primary material response. This quantity is needed only if the current material definition also includes Mullins effect (see “Mullins effect in rubberlike materials,” Section 18.6.1 of the Abaqus Analysis User's Manual).
DU1(NTENS+1)
Derivatives of strain energy potential with respect to the components of the modified Green strain tensor, , and with respect to the volume ratio, .
DU2((NTENS+1)*(NTENS+2)/2)
Second derivatives of strain energy potential with respect to the components of the modified Green strain tensor and the volume ratio (using triangular storage, as mentioned earlier).
DU3((NTENS+1)*(NTENS+2)/2)
Derivatives with respect to J of the second derivatives of the strain energy potential (using triangular storage, as mentioned earlier). This quantity is needed only for compressible materials with a hybrid formulation (when INCMPFLAG = 0 and IHYBFLAG = 1).
STATEV
Array containing the user-defined solution-dependent state variables at this point. These are supplied as values at the start of the increment or as values updated by other user subroutines (see “User subroutines: overview,” Section 14.2.1 of the Abaqus Analysis User's Manual) and must be returned as values at the end of the increment.
TEMP
Current temperature at this point.
NOEL
Element number.
CMNAME
User-specified material name, left justified.
NDI
Number of direct stress components at this point.
NSHR
Number of engineering shear stress components at this point.
NTENS
Size of the stress or strain component array (NDI + NSHR).
INCMPFLAG
Incompressibility flag defined to be 1 if the material is specified as incompressible or 0 if the material is specified as compressible.
IHYBFLAG
Hybrid formulation flag defined to be 1 for hybrid elements; 0 otherwise.
NUMSTATEV
User-defined number of solution-dependent state variables associated with this material (see “Allocating space” in “User subroutines: overview,” Section 14.2.1 of the Abaqus Analysis User's Manual).
NUMFIELDV
Number of field variables.
FIELDV
Array of interpolated values of predefined field variables at this material point at the end of the increment based on the values read in at the nodes (initial values at the beginning of the analysis and current values during the analysis).
FIELDVINC
Array of increments of predefined field variables at this material point for this increment, including any values updated by user subroutine USDFLD.
NUMPROPS
Number of material properties entered for this user-defined hyperelastic material.
PROPS
Array of material properties entered for this user-defined hyperelastic material.
EBAR(NTENS)
Modified Green strain tensor, 
, at each material point at the end of the increment.
AJ
J, determinant of deformation gradient (volume ratio) at the end of the increment.