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Mathematical methods in classical mechanics, classical and quantum field theory, quantum mechanics, statistical mechanics, condensed matter, nuclear and atomic physics.

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Bending an elastic, inextensible sheet of paper into a teardrop shape

All in here (if using Euler Bernoulli beam theory) http://sci-toys.com/bent_paper_problem.pdf (Added by Joseph O'Rourke). Here is Fig.1 from the paper by Antoni Colom, "Analysis of the shape of a …
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Is there a maximum principle for stress in continuum mechanics?

In hertzian contacts (the archetype for linear elastic contact mechanics) the maximum Von Mises stress is subsurface (not on the boundary).
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