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arXiv · 2209.02563

A degenerating Robin-type traction problem in a periodic domain

Matteo Dalla Riva·Gennady Mishuris·Paolo Musolino
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Abstract

We consider a linearly elastic material with a periodic set of voids. On the boundaries of the voids we set a Robin-type traction condition. Then we investigate the asymptotic behavior of the displacement solution as the Robin condition turns into a pure traction one. To wit, there will be a matrix function {$b[k](\cdot)$ that depends analytically on a real parameter $k$ and vanishes for $k=0$ and we multiply the Dirichlet-like part of the Robin condition by $b[k](\cdot)$}. We show that the displacement solution can be written in terms of power series of $k$ that converge for $k$ in a whole neighborhood of $0$. For our analysis we use the Functional Analytic Approach.

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Matteo Dalla Riva, Gennady Mishuris, Paolo Musolino. 2022-09-06. A degenerating Robin-type traction problem in a periodic domain. https://arxiv.org/abs/2209.02563

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