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11.11.2014
1
||Institute for Building Materials
Mechanics of Building MaterialsABAQUS UMAT Implementation
F. Wittel
09.09.2013 1
||Institute for Building Materials
Overview on ABAQUS structures How subroutines interact with ABAQUS Calling subroutines inside a model Writing of subroutines UMAT and VUMAT UMAT in some detail Examples of UMATs for plasticity
Material implementation in ABAQUS
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User Subroutines:
Extension of the functionality and applicability of ABAQUS beyond thecurrent implementation.
Offers a powerful, flexible analysis tool by adaptation to individual needs.
Are typically written in Fortran77 code, that needs to be included into amodel for the calculation.
Can call utility routines to simplify coding.
ABAQUS User Subroutine Reference Manual describes (55) differentuser subroutines for Abaqus/Standard, (21) Abaqus/Explicit subroutines,and all available utility routines (18) in detail.
Material implementation in ABAQUS: structures
||Institute for Building Materials
Popular user subroutines for ABAQUS/Standard (for material behavior)
CREEP: Definition of time dependent, visko-plastic material behavior. Deformations with decomposition into deviatoric(creep) and volumetric c(swelling) part.
DLOAD: Definition of non-uniformly, distributed mechanical loads in form of surface or volumetric loads.
UEL: Definition of own finite elements, that are not contained in the element library.
URDFIL: Input of data from result files (*.fil) at the end of the increment.
USDFLD: Definition of filed properties directly at the integration point of elements. Those can depend on stresses andstrains.
DISP: Definition of boundary conditions.
ORIENT: Definition of material orientations.
UMAT: Definition of own, complex constitutive material models, that are not part of the material library of ABAQUS.
Material implementation in ABAQUS: structures
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Popular user subroutines for ABAQUS/Explicit for material behavior
VDISP: Definition of displacement boundary conditions.
VDLOAD: Definition of non-uniform loads.
VUEL: Element definition.
VUFIELD: Definition of field variables.
VUHARD: Definition of yield surfaces and hardening rules for isotropic plasticity or combined hardening models.
VUSDFLD: Definition of new field variables at the material point.
VUMAT: Definition of own, complex constitutive material models, not included in the material library of ABAQUS.
Utility routines: Obtaining values of ABAQUS environment variables, Job name, path name, output path, parallelization information, part information, information at material points and node averages, node information, element information, stress-/strain invariants and rotation tensor. Output to message file, and more
Material implementation in ABAQUS: structures
||Institute for Building Materials
Material implementation in ABAQUS: Interaction with ABAQUS
Analysis start
Definition of initial conditions
Initiation of step
Initiation of increment
Initiation of iteration
Definition of global stiffness matrix [K]
Definition of loads {F}
UEXTERNALDB
CREEP, FRIC, UEL,UEXPAN, UGENS,UMAT, USDFLD
DLOADFILM,
HETVAL,UWAVE
HARDINISDVINI
UPOREPSIGINIVOIDRI
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Did it converge?
End of step?
Go to iteration startsolve[K]{U}={F}
Write outputGo to next step
Go to next increment start
Yes
No
YesNo
Material implementation in ABAQUS: Interaction with ABAQUS
||Institute for Building Materials
Analysis start
Initial conditions
Step initiation
Increment initiation
Iteration start
System stiffness matrix [K]
Load definition{F}
Increment start
Calculation of field properties at integration points from node values
Iteration start
calculate
calculate ,
defineload
Px
CREEP
UEXPAN
FRIC
UGENS
,c r sw th
/ /N E
UEL
UMATUSDFLD
FILM
HETVAL/d h d /r
Material implementation in ABAQUS: Interaction with ABAQUS
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Before you can start you have to
Install Microsoft Visual Studio
Install a FORTRAN compiler
Set environment variable
Change starting propertiesstart of a calculation by giving the name of the user subroutine with the User parameter in the ABAQUS command shell.
Input file usage: Abaqus job=job-name User={Source-file | Object-file}Abaqus job=Analysis User=Sample _subroutine.for
Material implementation in ABAQUS: Using subroutines in ABAQUS
||Institute for Building Materials
Great care while programming Conventions and guidelines have to be followed!
INCLUDE call for FORTRAN compiler and linker. Always the first statement after the argument list:
ABAQUS/STANDARD: 'ABA_PARAM.INC /EXPLICIT: 'VABA_PARAM.INC Has to be stated in all main and sub routines.
'INCLUDE ABA_PARAM.INC' is the first statement after the argument list.
Include call in sub routines
Material implementation in ABAQUS: Using subroutines in ABAQUS
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Naming conventions:For name of COMMON blocks or called subroutines the initial letter K is reserved (Example: SUBROUTINE KS_Eff(D_f,Eff_val)).
Overwriting of variables:User subroutines are not allowed to overwrite other parts of ABAQUS. Passed in variables are:
already declared variables. Variables that need to be declares. Variables passed in for information purposes (do not overwrite).
Output of variables (debugging): Into the message file (*.msg) handler 7 or output file (*.dat) handler 6. handler 15-18 and > 100 can also be used for reading/writing into files.
Write statement to standard out goes into the *.log file in the cwd.
Material implementation in ABAQUS: Using subroutines in ABAQUS
||Institute for Building Materials
Golden rules:
Develop user routines always with the smallest meaningful model and singular elements inits simplest form (no contact ..).
Adding and modifying models requires tests before and after modification..
If possible test subroutines in a way that only node DOFs are specified. In a next steptests of combinations e.g. with volumetric forces and node values can be made.
Attention when assigning the number of solution dependent variables (SDV) with the*Depvar keyword. It 20 are needed but only 18 SDVs specified the consequences areunpredictable.
Material implementation in ABAQUS: Using subroutines in ABAQUS
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Interface for defining own, complicated constitutive material laws that are not part of the material library of ABAQUS-
ABAQUS/Standard UMAT ABAQUS/Explicit VUMAT
What you need for UMATs Explicit (total) stress Stress rate (only in co-rotational framework) Definition of time-, temperature- or field property dependence (if defined) Definition of solution dependent state variables (SDV if defined) Transformation of rate dependent constitutive models into incremental form with integration method (Forward
Euler (explicit); Backward Euler (implicit); Mid-point method (Semi implicit) Incremental statement for internal SDV Conventions of FORTRAN have to be followed correct variable declaration and initiation Memory allocation for SDV with *DEPVAR statement Calculation of a consistent Jacobian matrix (UMAT)
Material implementation in ABAQUS: UMAT and VUMAT
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Consistent Jacobian matrix (DDSDDE):For small deformations or large deformations with small volumetric change (plasticity) the Jacobian is:
CAUCHY stress increment; strain increment.Stain increments are approximated for small strains as logarithmic strain.Jacobian can be non-symmetric, depending on the constitutive model or integration scheme.For complicated constitutive models the Jacobian is only approximated loss of quadratic convergence.
D D SD D E J :
Material implementation in ABAQUS: UMAT and VUMAT
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Verification of implementations
on the simplest case: one or a few elements with input.
on calculations with prescribed displacements to test the integration algorithm for stress- and state variables..
for representative cases: Uni-axial, uniaxial under an angle, uniaxial with rotation, shear.
on calculations with prescribed load to test the accuracy of the Jacobian.
by comparing with analytical solutions or material models from ABAQUS.
Material implementation in ABAQUS: UMAT and VUMAT
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UMAT Variables stresses (STRESS), strains (STRAN), and solution dependent state variables (SDVs) (STATEV) at the start of the increment. Strain increment (DSTRAN), rotation increment (DROT(3,3)), deformation gradient at the increment start (DFGRD0(3,3)) and (DFGRD1(3,3))
Increment end. Total time (TIME(1)) and incremental time (DTIME), temperature (TEMP and DTEMP), and user defined field properties (PREDEF and
DPRED). Material constants (PROPS), material point positions (COORDS) and char. element length (CELENT). Element number (NOEL), integration point (NPT) and composite layer number for shell and layered bodies (LAYER). Present step (KSTEP) and increment number (KINC).
Hast to be updated by the UMAT: Stress (STRESS), SDVs (STATEV), and Jacobian (DDSDDE). Specific elastic strain energy (SSE), plastic dissipation (SPD) , creep dissipation (SCD). Predicted new (reduced) time increment (PNEWDT).
Utility Routines: SINV returns the fist and second invariant of a tensor. SPRINC returns principal values of a tensor. SPRIND returns principal orientations and values of a tensor. ROTSIG rotates a tensor with a rotation matrix. XIT terminates the calculation and closed all files.
Material implementation in ABAQUS: UMAT variables
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Units: ABAQUS has no fixed unit system except for rotations (rad). Units have to be self- consitent.
Stresses and strains are stored in vectorial form:
Plane stress state (PS):
Plane strain state (PE)/ axisymmetric:
3D elements:
Shear strain: ABAQUS always uses engineering strains.
Deformation gradient: The deformation gradient is always stored as a 3x3 matrix.
1 1 2 2 1 2, , 1 1 2 2 3 3 1 2, , ,
1 1 2 2 3 3 1 2 1 3 2 3, , , , , 2i j i j j i i j
i jF
Material implementation in ABAQUS: UMAT variables
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ABAQUS CAE Part Module: Define part Property module:
Define material. With General>Depvar number of SDVs isdefined
General>User define material parameter forUser Subroutine.
Material implementation in ABAQUS: UMAT usage
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Job module: Job definition with correct path to user subroutine.
Material implementation in ABAQUS: UMAT usage
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The Jaumann incremental form is integrated into the scheme of corotational formulation:
, : Lames constants
Material implementation in ABAQUS: UMAT for kinematic hardening
Constitutive relationsElasticity:
In Jaumann (Corotational) rate form:
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:y Yield stress
:h Material property
, i j i jS : Deviatoric stress and strain tensor (back stress)
Constitutive Relation Plasticity:Loading function with von MISES stress (J2)
Equivalent plastic strain rate
Plastic flow rule
Prager-Ziegler linear kinematic hardening in rate form:
Material implementation in ABAQUS: UMAT for kinematic hardening
||Institute for Building Materials
Back stress tensor at increment start0 :i j
Integration procedure:1. Elastic predictor: equivalent stress with purely elastic deformation is calculated:
2. If the equivalent predictor stress > yield stress plastic low sets in.The backward Euler integration scheme is used for integration of the equations.
3. Equivalent plastic strain increment:
Material implementation in ABAQUS: UMAT for kinematic hardening
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1 ( )e l e l e l e l p ln n n 1 1e l e ln n C
Cel : Elastic stiffness matrix
Update of back stress, stress and strain tensor:
Direction of the plastic strain increment (normality condition)
Back stress tensor increment Plastic strain increment
Stress at increment end
Material implementation in ABAQUS: UMAT for kinematic hardening
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Definition of a consistent Jacobian
Detailed documentation in the ABAQUS Users manual
D D SD D E J :
3 (1 2 )Ek k: bulk modulus
Jacobian matrix
Material implementation in ABAQUS: UMAT for kinematic hardening
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User Subroutine UMAT header and argument list:
Material implementation in ABAQUS: UMAT for kinematic hardening
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Definition and memory allocation for local variables:
Material implementation in ABAQUS: UMAT for kinematic hardening
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Definition of LAMEs constants and of the stiffness matrix (=Jacobian for elastic deformation):
Material implementation in ABAQUS: UMAT for kinematic hardening
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Calling and rotating strain tensors (elastic and plastic) and of back stress tensors for large displacementsand deformations.
Renaming initial values for stress and strains (el. + pl.). Calculation of predictor stress and elastic strain.
Material implementation in ABAQUS: UMAT for kinematic hardening
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Calculation of equivalent von MISES stress based on predictor stress. Comparison of equivalent von MISES stress with yield surface.
Material implementation in ABAQUS: UMAT for kinematic hardening
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Calculation of deviatoric part of the predictor stress. Calculation of direction of the plastic strain increment with normality condition. Calculation of equivalent plastic strain increment with consistency condition ( equivalent stress
= yield stress).
Material implementation in ABAQUS: UMAT for kinematic hardening
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Update of back stress tensor, elastic and plastic strain tensors and stress tensor for incremnt end. (Note *2for shear stain components since engineering definition is used in ABAQUS).
Calculation of plastic work or dissipation:11 2 ( )( )
p ln nS P D
Material implementation in ABAQUS: UMAT for kinematic hardening
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Calculation of the consistent Jacobian (material tangent stiffness matrix):
Material implementation in ABAQUS: UMAT for kinematic hardening
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Update of SDVs with values at the increment end. Output request write to *.log file(optional for debugging)
Material implementation in ABAQUS: UMAT for kinematic hardening
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The Jaumann incremental form is integrated into the scheme of corotational formulation:
, : Lames constants
Material implementation in ABAQUS: UMAT for isotropic hardening
Constitutive relationsElasticity:
In Jaumann (Corotational) rate form:
no difference to kinematic hardening
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Loading function with vonMISES stress (J2):
equivalent plastic strain in rate form:
Yield rate:
:y Yield stress:i jS Deviatoric stress
constitutive relation plasticity:
Material implementation in ABAQUS: UMAT for isotropic hardening
||Institute for Building Materials
Hardening rule( ) :p ly p l
( ) 0p lp lff d
Yield function:f
Integration procedure:1. Elastic predictor: equivalent stress calculated with purely elastic deformation:
2. If the equivalent predictor stress > yield stress plastic flow.The backward Euler integration scheme is used for integration the equation.
3. In general non-linear equation in e.g. solved via Newton method
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Algorithms for solving non-linear equations
1( )( )
nn n
n
f xx xf x
Newton Raphson method:Newton Raphson method multi dimensional:
11 ( ( ) ) ( )n n n nx x J x f x
1 1 1
1 2
2 2 1
1 2 1
1
1 1
( ) : ( )
n
n n
n
f f fx x x
f f fx x xi
nj
f ffx x x
fJ x f xx
1: ( ( ) ) ( )n n nx J x f x
( ) ( )n n nJ x x f x
1n n nx x x
Jacobian-matrix:
LES:
||Institute for Building Materials
1( )( )
nn n
n
f xx xf x
Newton Raphson method: Quasi Newton method:Modifizierte Newton Raphson method:
Iterative solution with identical tangent (from predictor step) in each increment.
Accurate results. Low computational cost within one
iteration.
Slow convergence. high number of iterations needed.
Very accurate results. Close to the solution quadratic
convergence. Only few iterations needed. Iterative solution with adapted tangent. Large computational cost within one
iteration.
1( )( )
nn n
o
f xx xf x
Inverse of the Hesse matrix is only
approximated. low computational cost Good convergence. Approximation of the Hesse matrix can
be costly. Diverse approaches for the
approximation.
1( )( )
nn n
n
f xx xB x
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Arc-length method
Usable for calculating snap-through and snap-back problems. Also fro singular tangent stiffness matrices in buckling / post-buckling Fast convergence for implicit solution and autonomous control. Can work deal with local and global extreme without stopping. More complicated solution, since the equation system becomes unsymmetrical band structure gets lost. Unusable for contact problems, visko-elastic material and bifurcation problems.
Extension of the classical Newton-Raphson method.Usage of arc-length for the approximation progress.Introduction of a loading parameter as pre-factor (Load step control)Displacements and loads are iterated simultaneously.
Algorithms for solving non-linear equations
||Institute for Building Materials
1 ( )e l e l e l e l p ln n n 1 1e l e ln n C
Cel : Elastic stiffness matrix
1( ) ( ) ( ( ) )p l k p l k p ld
Update of stress and strain tensorDirection of the plastic strain increment (normality condition):
Equivalent plastic strain increment:
Plastic strain increment:
Stress at increment end:
Material implementation in ABAQUS: UMAT for isotropic hardening
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D D SD D E J :
3 (1 2 )Ek k: bulk modulus
Definition if the consistent Jacobian
Detailed documentation in ABAQUS Users manual
Jacobian
Material implementation in ABAQUS: UMAT for isotropic hardening
||Institute for Building Materials
User Subroutine UMAT header and argument list:
Material implementation in ABAQUS: UMAT for isotropic hardening
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Definition and memory allocation for local variables:
Material implementation in ABAQUS: UMAT for isotropic hardening
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Definition of LAMEs constants and the stiffness matrix (=Jacobian for elastic deformations)
Material implementation in ABAQUS: UMAT for isotropic hardening
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Materialimplementierungen in ABAQUS
Calling and rotating strain tensors (elastic and plastic) for large displacements and deformations. Calculating predictor stress and elastic strain Calculation of equivalent vonMises stress from predictor stress
||Institute for Building Materials
Calculation of yield stress that correspond to the present equivalent plastic strain via the UHARD subroutine. Comparison of equivalent vonMISES stress with the present yield stress to check for yielding. Calculation of the flow direction.
Material implementation in ABAQUS: UMAT for isotropic hardening
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UHARD: User subroutine for defining yield surfaces and hardening parameters for isotropic or combined hardeningmodels.
User Subroutine UHARD header and arguments
(1)
( 2 )
( 3 )
yp l
yp l
y
H a rd h
H a rd
H a rd
Material implementation in ABAQUS: UMAT for isotropic hardening
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Definition of present yield values as function of the equivalent plastic strain and isotropic hardening parameters.
Material implementation in ABAQUS: UMAT for isotropic hardening
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Calculation of equivalent plastic strain increments and extension of consecutive yield surfaces with the iterative NEWTONMethod and UHARD.
Plastic material behavior is defined as multi-linear curve by pairs of material strength and corresponding equivalent plasticstrain.
( ) 0plplff d
Material implementation in ABAQUS: UMAT for isotropic hardening
||Institute for Building Materials
11 2 ( )( )p l
n nS P D S y S y Update of the stress tensors, elastic and plastic strain tensor and equivalent plastic strain at increment
end. Calculation of plastic work or dissipation:
Material implementation in ABAQUS: UMAT for isotropic hardening
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Calculation of the consistent Jacobian (material tangent stiffness matrix)
Material implementation in ABAQUS: UMAT for isotropic hardening
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Update of SDVs with values at the increment end. Output request output to *.log file (optional for debugging purposes)
Radial return mapping
Material implementation in ABAQUS: UMAT for isotropic hardening
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Thank you for your attention.
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