Novice's question on UMAT in Abaqus

[CF]

I am currently trying to code a UMAT routine for an orthotropic hyperelastic model applicable for biological tissues. I am using the UMAT routine instead of UHYPER as I want to implement time-dependent effects into the model later on. I am having some trouble with this and I believe it is to do with my specification of DDSDDE.

As I understand it, DDSDDE is the tangent of the Jaumann rate of Cauchy stress (DJC). Using index notation:

DDSDDE=DJC(ijkl) = 1 / J DJK(ijkl) - cauchy_stress(ij) * kronecker_delta(kl) (1)

DJK(ijkl) = DTK(ijkl) + 1 / 2 (tau(il) * kronecker_delta(jk) + tau(jl) * kronecker_delta(ik) + tau(ik) * kronecker_delta(jl) + tau(jk) * kronecker_delta(il)) (2)

(where tau is the kirchoff stress)

DTK(ijkl) = F(ia) * F(jb) * F(kc) * F(ld) * DK2(abcd) (3)

where F is the deformation gradient and DK2 is the derivative of the second-piola kirchoff stress wrt strain.

Am I on the right track here?

Thanks in advance for any help.

Regards,
Cormac

[Jorgen]

Hello Cormac,

You seem to be on the right track, but your equations almost seem too cumbersome. According to the ABAQUS manuals the Jacobian for large deformations is given by:
1/J {partial Delta Sigma_Kirchhoff} / {partial Delta Strain}

Without knowing more about your consitututive theory I don't see the need to switch over to 2nd Piola Kirchhoff stress in your equations for DDSDDE.

As an another hint, for small problems and during subroutine development, I have had very good sucess using a finite difference numerical approximation of DDSDDE. Note, an approximate Jacobian will not change the accuracy of the solution, only the convergence properties of the Newton solution scheme.

Or as another alternative, you can start by writing a VUMAT for ABAQUS/Explicit and debug that code first. Note, a VUMAT does not need the Jacobian and is hence easier to code.

Best of luck,
Jorgen

[CF]

Jorgen,

Thanks very much for the help. Seems I was over-complicating things for myself. All works fine now.

Regards,

Cormac