Hi All:

Here is my 2 cents on the convergence issues:

1) As Stablguru mentioned, strain energy function needs to satisfy the ellipticity condition, it is essential for material stability.

2) Condition number of stiffness matrix, high condition number will cause difficulty in the inverse of stiffness matrix and I guess it will also lead to slower convergence rate, which may require more iterations than ABAQUS allows. For soft tissue, this may be more relevant as the bulk modulus is much higher than shear modulus due the incompressibility.

3) For low stiffness strain region for soft tissue, my understanding is:

Collagenous tissues usually exhibits strain-stiffnessing J-shaped stress-strain curves, ie., an initial large extension is achieved with relatively low levels of stress. This low stiffness of the material at the low strain region could cause convergence problems in the iterations. Say, for a given load increment dF(n+1) at increment step n+1, the predicted displacement increment is dU(n+1)=K{-1}dF(n+1) , where K is the stiffness matrix. dU(n+1) could be large due to the low stiffness, and thus the total displacement U(n)+ dU(n+1) may be out off the stress-strain range encompassed by J shape curve, this will lead to the difficulty in calculating F(U(n)+dU(n+1)) from the constitutive law and cause the convergence problems.

4) I doubt UMAT can handle the mixed formulation, wonder if anyone has successfully done it

5)To check if fiber is under compression, what I did is to see if I4 or I6<1, if so then set Sfiber=0. Physically it makes sense, however, I wonder if it will make energy discontinuity and cause numerical problems.

Thanks,

Wei