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jacobian matrix caculation
Dear friends
Hi. I'm working on multiscale modeling of soft tissues. In my research I faced with a problem about computing the jacobian matrix in ABAQUS UMAT. In my model the material properties are function of external parameter like ef (ef is kind of strain and obtained from loading conditions) and relation between the "ef" and the strin in the model in unkown. Now, i want to calculate the jacubian matrix for this material, as you konw, the jacobian is defined as delta_sigma/delta_epsilon.
I have two question;
1- Is this true that i compute the jacobian without considering the relation between the ef and strain . In other words, since the material propertis is not directly function of strain is it true that the jacobian matrix meembers are constants?
2-which strain must be used in the jacobian derivation? small strain? logarithmic? green?(My model is subjected to large rotation but small strain and i turned on the NLGEOM optin in ABAQUS)
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Dear afallah,
Dear afallah,
An exact jacobian matrix can accelarate the speed of convergence. If you can't derive a precise form for the jacobian matrix, it may require more iterations or more increments to achieve convergence. Sometimes an elastic stiffness matrix can also work well.
If you check the Abaqus documentation, DSTRAN passing into UMAT is the logarithmic strain. You need to derive the function between DSTRSS and DSTRAN before you get the jacobian.
Because my major is not soft tissues, please note that my answer may be not correct.
I hope my answer may be helpful to you.
ِDear Han Shiwei
ِDear Han Shiwei
Thanks for your quick and fruitful answer. As I found from your answer you said that jacobian matrix only affects the convergence rate and does not influence on the result accuracy. But my question is if it is true then where do the different material models play their role? As you mentioned in some cases elastic stiffness matrix leads to acceptable results. If i use elastic stiffness matrix for material with nonlinear behaviour like sigma= C*epsilon^n , where this model enter in the solution process and affects the resluts.
Thank you again.
Dear afallah,
Dear afallah,
Jacobian is derive from the function of DSTRSS and DSTRAN in the current configuration. Because my major is about crystal plasticity which maitains elastic during finite strain, I am not familiar with the constitutive relation in soft tissue. Sorry for can't help you more.
Good Luck!