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Deduction of derivatives of free-energy density function in ABAQUS UHYPER

Submitted by Lianhua Ma on
research
Dear xuanhe and all,
I have reviewed the paper "Method to analyze programmable deformation of dielectric elastomer layers". (Xuanhe zhao, Zhigang Suo)
It is very insteresting.
I have one question you would like to ask you.  Hope to get your reply.
You put forward the free-energy function of ideal dielectric elastomer in this paper.

you noted "We embed this method in the commercial finite element software, ABAQUS, by coding

the free-energy function W(F E),  and its derivatives in a user-supplied subroutine, UMAT"
I think this dielectric elastomer can be ragarded as hyperelastic material,  I want to know you embed the free-energy function in ABAQUS by UMAT or UHYPER? CAN it be implemented only by UHYPER?
If the material model can be implemented only by UHYPER in ABAQUS, How can we code the third term of the free-energy function as shown in attached figure.  The UHYPER in abaqus requires that the values of the derivatives of the strain energy density function of the hyperelastic material be defined with respect to the strain invariants, but the third term of the proposed free-energy function W(F,E) is not the form of the strain invariants. How can get the the derivatives ?
I was tring to code only by UHYPER, but I can not succeed.
Hope for your kind help,  thank you very much.
Warm regards,

LH MA
Xuanhe Zhao

Lianhua,

Thank you for your interests in our work. We implemented the method via ABAQUS UMAT. The same principle has also been implemented with UHYPER by O’Brien et al in a very neat way. I think their paper will answer your question clearly.

Xuanhe 

Sat, 07/04/2009 - 20:56 Permalink