Grioli's theorem with weights and the relaxed-polar mechanism of optimal Cosserat rotations

DOI10.4171/RLM/777zbMath1386.74009arXiv1701.08150OpenAlexW2583606141MaRDI QIDQ2408733

Andreas Fischle, Patrizio Neff

Publication date: 13 October 2017

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.08150

zbMATH Keywords

CosseratGrioli's theorempolar mediaEuclidean distance to \(SO(n)\)zero Cosserat couple modulus

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Energy minimization in equilibrium problems in solid mechanics (74G65) Matrix equations and identities (15A24) Analysis on real and complex Lie groups (22E30) Polar materials (74A35) Nonsimple materials (74A30) Explicit solutions of equilibrium problems in solid mechanics (74G05) Analysis of microstructure in solids (74N15) Qualitative behavior of solutions of equilibrium problems in solid mechanics (74G55)

Related Items (6)

A geometrically nonlinear Cosserat shell model for orientable and non-orientable surfaces: discretization with geometric finite elements ⋮ Soliton solutions in geometrically nonlinear Cosserat micropolar elasticity with large deformations ⋮ Optimality of the relaxed polar factors by a characterization of the set of real square roots of real symmetric matrices ⋮ Explicit Global Minimization of the Symmetrized Euclidean Distance by a Characterization of Real Matrices with Symmetric Square ⋮ Characterization of the critical points for the shear-stretch strain energy of a Cosserat problem ⋮ Compatibility conditions of continua using Riemann–Cartan geometry

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