My question is simple.. Why do we need wing bending tests, what can we learn from them and how can this help us evolve the product?
It ensures that the theoretical assumptions are correct in practice.
Therefore it save our lives.
Transport category airplanes, which includes most aircraft in commercial passenger service, must meet the FAA regulations in 14 CFR Part 25. Some relevant excerpts are as follows:
The structure must be able to support ultimate loads without failure
Structural analysis may be used only if the structure conforms to that for which experience has shown this method to be reliable. In other cases, substantiating tests must be made to load levels that are sufficient to verify structural behavior
Ultimate loads are the absolute maximum loads that a structure must carry without failure. These are loads will be extremely rare and result in permanent damage to the structure, but with the structure still intact the aircraft should still be able to land safely.
The FAA will not certify the design if the manufacturer cannot prove that the structure is capable of meeting these requirements. One option is using computational simulations. Modern analysis techniques are very powerful. However, analysis is useless if you can't show that it is also reliable. Structures like wings are extremely complicated. Once the materials become permanently deformed, the behavior changes and the analysis becomes even more complicated.
So if you can't prove that computational methods will work, you have to do a test of the structure. Fatigue is similarly difficult to predict, so aircraft are generally subjected to multiple lifetimes worth of load cycles with special test rigs to understand how the parts will hold up.
When the Boeing 777 wing was tested, it failed at 4% over the required load. This shows that even the limited analysis capabilities (compared to today) were very accurate, but the only way to find out for sure is to test it. Analysis will always have some amount of error. If the analysis had been a few percent off the wing would have failed the test.
So the analysis for the 777 was shown to be reliable, but only in the case they tested. If a new design differs significantly, this adds some uncertainty into the analysis. Will it still be reliable in the new case? The only way to know for sure is to test it.
Computational models are only as good as the assumptions you made when setting up your model. The physical world in general, and the mechanical behaviour of your wing, is quite difficult to describe mathematically. Even if we mastered the mathematical description, we can only describe what we know of the world. A good example is Newtonian mechanics, it was derived at a time when we knew nothing about relativistic mechanics. Now we know Newtonian mechanics is not the complete picture, but we also know, when it is good enough. Engineers do the same all the time, e.g. is steel or aluminium a linear material (strain vs. stress)?
Therefore, good engineering practice is to validate and verify your mathematical models. The worse the consequences of failure, the more testing is done. This is why aircraft parts are extensively tested, apart from regulations.
The complete test of an aircraft wing is the very end of the mechanical testing regime. It starts from the materials involved, goes over single components and their connections, to end at the level of sub-assemblies and the complete wing.