Hello everyone,
My ultimate aim is to write a UMAT based on Schapery's Integral equation and verify it in Abaqus. I am pretty much a newbie in UMAT. So decided to start off by working on a linear viscoelastic UMAT that of a simple Kelvin model (linear spring and dashpot in parallel). The constitutive law is known.
sigma_total = (E * epsilon) + (eta * d(epsilon)/dt)
Discretised constitutive law is of the form
sigma(t+1) = {E * epsilon(t+1)} + {eta * (del_epsilon)/del_time}
In abaqus will it suffiient to just code this as
dstress(k1) = {E * stran(k1)} + {eta * dstran(k1) / dtime}
and to find the jacobian as
ddsdde(k2,k1) = E + (eta/dtime)
IS this the way to go.. I am a real newbie and I hope somebody helps me out to start with the work
Thanks for your time
Shree
UPDATE 1 : Thanks a lot guys for all the responses.. I could code UMAT for linearviscoelasticity finally.
Hello,
The above mentioned constitutive law is respected to the 1D stress that you can assume in the 1D element as a spring/dashpot . In addition the Frank UMAT subroutin also is represented the stress tensor for the element with 3 DOF. So if this is appropriate for your model you can use it as a guide line for your reseach but I am not sure that its for calculation of linear viscoelastic behavior.
you may find the '' Example: Simple linear viscoelastic material'' in abaqus documentation and also using the CREEP subroutine may be can be helpfull for your work.
Try with that: (find on internet)
SUBROUTINE UMAT(STRESS,STATEV,DDSDDE,SSE,SPD,SCD,
1 RPL,DDSDDT,DRPLDE,DRPLDT,
2 STRAN,DSTRAN,TIME,DTIME,TEMP,DTEMP,PREDEF,DPRED,CMNAME,
3 NDI,NSHR,NTENS,NSTATV,PROPS,NPROPS,COORDS,DROT,PNEWDT,
4 CELENT,DFGRD0,DFGRD1,NOEL,NPT,LAYER,KSPT,KSTEP,KINC)
C
INCLUDE 'ABA_PARAM.INC'
C
CHARACTER*80 CMNAME
DIMENSION STRESS(NTENS),STATEV(NSTATV),
1 DDSDDE(NTENS,NTENS),
2 DDSDDT(NTENS),DRPLDE(NTENS),
3 STRAN(NTENS),DSTRAN(NTENS),TIME(2),PREDEF(1),DPRED(1),
4 PROPS(NPROPS),COORDS(3),DROT(3,3),DFGRD0(3,3),DFGRD1(3,3)
C
C
INTEGER i, j
REAL Y, n, eta
REAL lambda, thetalambda, mu, thetamu
REAL A, B, C, D, F, G
C
REAL, DIMENSION(NTENS,NTENS):: DDSDE
REAL, DIMENSION(NTENS,NTENS):: DDSDS
REAL, DIMENSION(NTENS):: SIGold
C
Y = PROPS(1)
n = PROPS(2)
eta = PROPS(3) ! shear viscosity
C
lambda = Y*n/((1.0d0+n)*(1.0d0-2.0d0*n))
mu = Y/(2.0d0*(1.0d0+n))
thetalambda = 3.0d0*eta/Y
thetamu = eta/mu
C
A = lambda*(1.0d0 + thetalambda/DTIME) +
1 2.0d0*mu*(1.0d0 + thetamu/DTIME)
B = lambda*(1.0d0 + thetalambda/DTIME)
C = lambda + 2.0d0*mu
D = lambda
F = 2.0d0*mu*(1.0d0 + thetamu/DTIME)
G = 2.0d0*mu
C
DO i = 1,NTENS
DO j = 1,NTENS
DDSDDE(i,j) = 0.0d0
DDSDE(i,j) = 0.0d0
DDSDS(i,j) = 0.0d0
END DO
END DO
C
C DEFINE TENSOR COEFFICIENTS RELATED TO NORMAL STRESSES
C
DO i = 1,NDI
DO j = 1,NDI
DDSDDE(i,j) = B
DDSDE(i,j) = D
DDSDS(i,j) = 0.0d0
END DO
DDSDDE(i,i) = A
DDSDE(i,i) = C
DDSDS(i,i) = -1.0d0
END DO
C
C DEFINE TENSOR COEFFICIENTS RELATED TO SHEAR STRESSES
C
DO i = NDI+1,NTENS
DDSDDE(i,i) = F/2.0d0
DDSDE(i,i) = G/2.0d0
DDSDS(i,i) = - 1.0d0
END DO
C
C STORE PRESENT STRESS STATE IN ARRAY SIGold
C
DO i= 1,NTENS
SIGold(i) = STRESS(i)
END DO
C
C UPDATE STRESSES
C
DO i = 1,NTENS
DO j = 1,NTENS
STRESS(i) = STRESS(i) + DDSDDE(i,j)*DSTRAN(j) +
1 DDSDE(i,j)*STRAN(j) +
2 DDSDS(i,j)*SIGold(j)
END DO
END DO
C
RETURN
END
Hello Franck,
Thanks for that UMAT. I will check it out. Btw, I just wanted to know if my approach was ok..
Thanks and Regards
Shree
Hello,
The above mentioned constitutive law is respected to the 1D stress that you can assume in the 1D element as a spring/dashpot . In addition the Frank UMAT subroutin also is represented the stress tensor for the element with 3 DOF. So if this is appropriate for your model you can use it as a guide line for your reseach but I am not sure that its for calculation of linear viscoelastic behavior.
you may find the '' Example: Simple linear viscoelastic material'' in abaqus documentation and also using the CREEP subroutine may be can be helpfull for your work.
I am the author of the above code. Mode on
http://imechanica.org/node/12702
Schapery:
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Int. J. Numer. Meth. Engng 2004; 59:25–45 (DOI: 10.1002/nme.861)
Numerical nite element formulation of the Schapery
non-linear viscoelastic material model
Rami M. Haj-Ali ; and Anastasia H. Muliana
The constants in the example in the subroutine manual are a great pain. How do you relate these constants to the coefficients of the springs and dashpot ? That example is totally cryptic.
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