One-dimensional von K\'arm\'an models for elastic ribbons

Lorenzo Freddi; Peter Hornung; Maria Giovanna Mora; Roberto Paroni

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arXiv · 1701.02721

One-dimensional von K\'arm\'an models for elastic ribbons

Lorenzo Freddi·Peter Hornung·Maria Giovanna Mora·Roberto Paroni

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Abstract

By means of a variational approach we rigorously deduce three one-dimensional models for elastic ribbons from the theory of von K\'arm\'an plates, passing to the limit as the width of the plate goes to zero. The one-dimensional model found starting from the "linearized" von K\'arm\'an energy corresponds to that of a linearly elastic beam that can twist but can deform in just one plane; while the model found from the von K\'arm\'an energy is a non-linear model that comprises stretching, bendings, and twisting. The "constrained" von K\'arm\'an energy, instead, leads to a new Sadowsky type of model.

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Lorenzo Freddi, Peter Hornung, Maria Giovanna Mora, Roberto Paroni. 2017-01-10. One-dimensional von K\'arm\'an models for elastic ribbons. https://arxiv.org/abs/1701.02721

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