This is an attempt to contribute to bring the discussion on non-linear issues in Continuum Mechanics (CM) under the comprehensive supervision of modern differential geometry (DG). Some people would say that engineers do not need so much mathematics, but such an opinion is a sure indicator of lack of knowledge of the matter. In fact I am an engineer, a University teacher and a designer in Structural Engineering and my experience is that a lot of troubles would have been saved to me by a basic training in DG.
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