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Jacobian matrix for External material model
Posted Jan 29, 2020, 10:39 a.m. EST Structural & Acoustics, Geomechanics, Structural Mechanics Version 5.5 0 Replies
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Dear all:
I developed an external material model in which the stress was updated incrementally, which is differnt from the stress update algorithm in the BLOG which is defined by total value. Now I have a problem about the calculation of Jacobian matrix. According to the HELP document, the Jacobian is defined as: 
, where ds and de are the derivatives with respect to total value. However, for the incremental stress update algorithm, this Jacobian definition seems difficult to be determined. It may be calculated as: d(s_pre+delta_s)=Jacd(e_pre+delta_e), where _pre means the value at previous converged step and delta means the incremental values. As the s_pre and e_pre are constants at current step, this defination may be simplified as: d(delta_s)=Jacd(delta_e) , which is similar to the first one, i.e. “delta_s = Jac * delta_e”. I have tried this defination, but it does not work well. So I think it may be better to use the Jacobian defined with respect to total value.
Could you please share me some ideas how to determine the Jacobian matrix?
Thanks a lot.
-------------------Yu Zhang
Hello Yu Zhang
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