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arXiv · 2305.02168

Curvature-dependent Eulerian interfaces in elastic solids

Katharina Brazda·Martin Kružík·Fabian Rupp·Ulisse Stefanelli
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Abstract

We propose a sharp-interface model for a hyperelastic material consisting of two phases. In this model, phase interfaces are treated in the deformed configuration, resulting in a fully Eulerian interfacial energy. In order to penalize large curvature of the interface, we include a geometric term featuring a curvature varifold. Equilibrium solutions are proved to exist via minimization. We then utilize this model in an Eulerian topology optimization problem that incorporates a curvature penalization.

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Katharina Brazda, Martin Kružík, Fabian Rupp, Ulisse Stefanelli. 2023-05-03. Curvature-dependent Eulerian interfaces in elastic solids. https://doi.org/10.1098/rsta.2022.0366

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