I want to know which one is computationally more expensive than the other and why?

Thank you.

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If you are interested in knowing more about them, please read the following if it is possible for you:

http://rspa.royalsocietypublishing.org/content/464/2089/117.short

And here are, to compare, a paper and a PhD thesis (go to page 66) which have solved a problem but using different approaches.

http://link.springer.com/article/10.1007%2Fs00161-008-0067-z#page-1

Junker, P., Simulation of shape memory alloys - material modeling using the principle of maximum dissipation, PhD-Thesis, urn:nbn:de:hbz:294-33862 (2011)