Work

Explicit formula for the $$\Gamma $$-convergence homogenised quadratic curvature energy in isotropic Cosserat shell models

Year: 2025

Type: article

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

Source: Zeitschrift für angewandte Mathematik und Physik

DOI: 10.1007/s00033-024-02415-4

Authors: Maryam Mohammadi Saem, Emilian Bulgariu, Ionel-Dumitrel Ghiba, Patrizio Neff

Institutions: Witten/Herdecke University, University of Duisburg-Essen, Alexandru Ioan Cuza University, Romanian Academy

Language: English

Topic: Nonlocal and gradient elasticity in micro/nano structures

Subfield: Materials Chemistry

Field: Materials Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,590

Funder: Academia Româna