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arXiv · 2309.06032

Explicit formula for the Gamma-convergence homogenized quadratic curvature energy in isotropic Cosserat shell models

Maryam Mohammadi Saem·Emilian Bulgariu·Ionel-Dumitrel Ghiba·Patrizio Neff
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Abstract

We show how to explicitly compute the homogenized curvature energy appearing in the isotropic $\Gamma$-limit for flat and for curved initial configuration Cosserat shell models, when a parental three-dimensional minimization problem on $\Omega \subset \mathbb{R}^3$ for a Cosserat energy based on the second order dislocation density tensor $\alpha:=\overline{R} ^T {\rm Curl}\,\overline{R} \in \mathbb{R}^{3\times 3}$, $\overline{R}\in {\rm SO}(3)$ is used.

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Maryam Mohammadi Saem, Emilian Bulgariu, Ionel-Dumitrel Ghiba, Patrizio Neff. 2023-09-12. Explicit formula for the Gamma-convergence homogenized quadratic curvature energy in isotropic Cosserat shell models. https://arxiv.org/abs/2309.06032

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