Hi, I wrote some on arclength but did not find now. Here in an article and  from a book

https://books.google.se/books?id=rWvefGICfO8C&pg=PA763&lpg=PA763&dq=arclength+klaus+jurgen+baathe&source=bl&ots=gFLHBNwsK2&sig=RiumFfTnhL-ZhnvIiLJ31xwTx6g&hl=no&sa=X&ved=0ahUKEwjtnM6o_eXUAhXhApoKHRGhCTMQ6AEIIDAB#v=onepage&q=arclength%20klaus%20jurgen%20baathe&f=false

Here, in Section 5.3, is another kind. You prescribe displacement in one dof, and calculate the equivalent body force, because that is input control, but not (lost the word 'iso-growing')

Thesis Nonlocal plasticity models applied to localisation and compa...

penalty is a sort of friction coefficient, at least in Abaqus

I thought it was e.g. arclength method to control input in nonlinear modeling, when the main control variable is not monoton. Or otherwise improve robustness. 

 Thanks For the help, i really appreciate it  :) ...I have used different approach, which does not demand for Penalty Approach.

Please check references below.. hope it will be helpful for you… Regards…

https://www.math.u-psud.fr/~maury/Files/FEpen.pdf