Dear Benhour,
 

> These are 9 concepts, in 9 lines of text, all without any kind of 
> elaboration. 
> In other words, we have no real idea what you are doing, and equally 
> important, we have no idea what is actually wrong. When debugging problems 
> like yours, you need to learn to reduce things to the minimal case that 
> shows 
> the problem, and to look for the *first sign* where something seems to be 
> going wrong. 


Prof Bangerth has succinctly stated why I'm having such difficulties in 
helping you. 

I, like him, would encourage you to take your code and strip out as many of 
the complexities as possible, and produce some test cases that convince you 
that each part of your code is working as expected. This is exactly how I 
build up any of my codes that tackle complex problems. For this you often 
need to test your implementation of each "feature" against a really simple 
problem that you can hand calculate a comparison result for, or otherwise 
some benchmark in the literature.

Thats really the best advice we can give you in this instance. So, for 
example, coming back to your question of the implementation of the traction 
boundary condition: you could easily test this by considering a distributed 
load on a bar (inducing uni-axial tension) or perhaps the result shown in 
step-44 <https://www.dealii.org/8.4.1/doxygen/deal.II/step_44.html> or one 
of the more simple code-gallery examples 
<https://dealii.org/developer/doxygen/deal.II/code_gallery_Quasi_static_Finite_strain_Compressible_Elasticity.html>
.

Regards,
Jean-Paul

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