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Cosserat micropolar elasticity: classical Eringen vs. dislocation form

Ionel-Dumitrel Ghiba, Gianluca Rizzi, Angela Madeo and Patrizio Neff

Vol. 18 (2023), No. 1, 93–123
Abstract

We give a comparative presentation of the linear isotropic Cosserat elastic model from two perspectives: the classical Mindlin–Eringen–Nowacki description in terms of a microrotation vector and a new formulation in terms of a skew-symmetric matrix and a curvature energy in dislocation form. We provide the reader with an alternative representation of the energy for the isotropic Cosserat model to ease the comparison with the relaxed micromorphic model and the geometrically nonlinear Cosserat elastic model.

Keywords
Cosserat micropolar model, relaxed micromorphic model, microrotation vector, Cosserat couple modulus, parameter identification, dislocation density tensor, Nye's formula
Milestones
Received: 11 July 2022
Revised: 18 November 2022
Accepted: 22 November 2022
Published: 24 March 2023
Authors
Ionel-Dumitrel Ghiba
Department of Mathematics
Alexandru Ioan Cuza University of Iaşi
Iaşi
Romania
Octav Mayer Institute of Mathematics of the Romanian Academy
Iaşi Branch
Iaşi
Romania
Gianluca Rizzi
Faculty of Architecture and Civil Engineering
Technische Universität Dortmund
Dortmund
Germany
Angela Madeo
Faculty of Architecture and Civil Engineering
Technische Universität Dortmund
Dortmund
Germany
Patrizio Neff
Faculty of Mathematics
Universität Duisburg-Essen
Essen
Germany