1. Analytical solution of the cylindrical torsion problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)
- Author
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Gianluca Rizzi, Geralf Hütter, Hassam Khan, Ionel-Dumitrel Ghiba, Angela Madeo, Patrizio Neff, Rizzi, Gianluca, Géomécanique, Matériaux et Structures (GEOMAS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA), Institute of Mechanics and Fluid Dynamics - Institut für Mechanik und Fluiddynamik [Freiberg] (IMFD), Technishe Universität Bergakademie Freiberg (TU Bergakademie Freiberg), Universität Duisburg-Essen, Fakultät für Mathematik, Universitatea Alexandru Ioan Cuza din Iași, and Octav Mayer Institute of Mathematics of the Romanian Academy
- Subjects
General Mathematics ,02 engineering and technology ,generalized continua ,01 natural sciences ,micro-strain model ,size-effect ,0203 mechanical engineering ,size effect ,Classical Analysis and ODEs (math.CA) ,FOS: Mathematics ,[SPI.MECA.SOLID] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph] ,General Materials Science ,Fakultät für Mathematik ,ddc:510 ,0101 mathematics ,characteristic length ,couple stress model ,gradient elasticity ,[SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the solides [physics.class-ph] ,Cosserat continuum ,micro-void model ,torsion ,micromorphic continuum ,torsional stiffness ,010101 applied mathematics ,020303 mechanical engineering & transports ,Mathematics - Classical Analysis and ODEs ,Mechanics of Materials ,relaxed micromorphic model ,bounded stiffness ,Mathematik ,micropolar ,micro-stretch model - Abstract
We solve the St.Venant torsion problem for an infinite cylindrical rod whose behaviour is described by a family of isotropic generalized continua, including the relaxed micromorphic and classical micromorphic model. The results can be used to determine the material parameters of these models. Special attention is given to the possible nonphysical stiffness singularity for a vanishing rod diameter, since slender specimens are in general described as stiffer., 41 pages, 29 figures
- Published
- 2021