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

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...

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Bibliographic Details
Published in:arXiv.org 2023-09
Main Authors: Maryam Mohammadi Saem, Bulgariu, Emilian, Ionel-Dumitrel Ghiba, Neff, Patrizio
Format: Article
Language:English
Subjects:
Curvature
Dislocation density
Tensors
Online Access:Get full text
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Summary: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.
ISSN:2331-8422