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5 results on '"Micro-stretch model"'

1. Analytical solution of the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua (including full derivations).

Author

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

Subjects
*ANALYTICAL solutions, *PARAMETER identification
Abstract

We derive analytical solutions for the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua. These solutions may help in the identification of material parameters of generalized continua which are able to disclose size effects. [ABSTRACT FROM AUTHOR]

Published
2023
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2. Analytical solutions of the cylindrical bending problem for the relaxed micromorphic continuum and other generalized continua.

Author

Rizzi, Gianluca, Hütter, Geralf, Madeo, Angela, and Neff, Patrizio

Subjects
*ANALYTICAL solutions, *ELASTICITY, *MATHEMATICAL continuum
Abstract

We consider the cylindrical bending problem for an infinite plate as modeled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length scale effects in the sense that thinner specimens are comparatively stiffer. We provide the analytical solution for each case and exhibits the predicted bending stiffness. The relaxed micromorphic continuum shows bounded bending stiffness for arbitrary thin specimens, while classical micromorphic continuum or gradient elasticity as well as Cosserat models (Neff et al. in Acta Mechanica 211(3–4):237–249, 2010) exhibit unphysical unbounded bending stiffness for arbitrary thin specimens. This finding highlights the advantage of using the relaxed micromorphic model, which has a definite limit stiffness for small samples and which aids in identifying the relevant material parameters. [ABSTRACT FROM AUTHOR]

Published
2021
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3. Analytical solution of the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)

Author

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

Subjects
Micromorphic continuum, Micro-void model, Uniaxial extension stiffness, Micropolar, Mathematics::General Topology, Relaxed micromorphic model, Micro-stretch model, Generalized continua, Gradient elasticity, Micro-strain model, Couple stress model, Characteristic length, Bounded stiffness, Size effect, Uniaxial extension, Cosserat continuum
Abstract

We derive analytical solutions for the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua. These solutions may help in the identification of material parameters of generalized continua which are able to disclose size effects., Archive of applied mechanics; Vol. 93. 2023, Issue1, pp 5-21

Published
2021

4. Analytical solution of the cylindrical torsion problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)

Author

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

5. Analytical solutions of the cylindrical bending problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)

Author

Rizzi, Gianluca, Hütter, Geralf, Madeo, Angela, Neff, Patrizio, 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), and Universität Duisburg-Essen, Fakultät für Mathematik

Subjects
Quantitative Biology::Tissues and Organs, micro-void model, micromorphic continuum, generalized continua, micro-strain model, size-effect, Mathematics - Classical Analysis and ODEs, relaxed micromorphic model, bounded stiffness, cylindrical bending, micropolar, Classical Analysis and ODEs (math.CA), FOS: Mathematics, [SPI.MECA.SOLID] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph], bending stiffness, characteristic length, couple stress model, gradient elasticity, micro-stretch model, [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the solides [physics.class-ph], Cosserat continuum
Abstract

We consider the cylindrical bending problem for an infinite plate as modelled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length scale effects in the sense that thinner specimens are comparatively stiffer. We provide the analytical solution for each case and exhibit the predicted bending stiffness. The relaxed micromorphic continuum shows bounded bending stiffness for arbitrary thin specimens, while classical micromorphic continuum or gradient elasticity as well as Cosserat models [35] exhibit unphysical unbounded bending stiffness for arbitrary thin specimens. This finding highlights the advantage of using the relaxed micromorphic model, which has a definite limit stiffness for small samples and which aids in identifying the relevant material parameters., Comment: 50 pages, 28 figures (38 pictures)

Published
2020
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