scholarly journals Analytical solutions of the cylindrical bending problem for the relaxed micromorphic continuum and other generalized continua

2021 ◽  
Author(s):  
Gianluca Rizzi ◽  
Geralf Hütter ◽  
Angela Madeo ◽  
Patrizio Neff
Keyword(s):  
Analytical Solutions ◽  
Cylindrical Bending ◽  
Generalized Continua ◽  
Micromorphic Continuum

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

2021 ◽  
Author(s):  
Gianluca Rizzi ◽  
Hassam Khan ◽  
Ionel-Dumitrel Ghiba ◽  
Angela Madeo ◽  
Patrizio Neff
Keyword(s):  
Analytical Solution ◽  
Analytical Solutions ◽  
Size Effects ◽  
Uniaxial Extension ◽  
Extension Problem ◽  
Generalized Continua ◽  
Material Parameters ◽  
Micromorphic Continuum

AbstractWe 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.

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

2021 ◽  
pp. 108128652110235
Author(s):  
Gianluca Rizzi ◽  
Geralf Hütter ◽  
Hassam Khan ◽  
Ionel-Dumitrel Ghiba ◽  
Angela Madeo ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Torsion Problem ◽  
Generalized Continua ◽  
Material Parameters ◽  
Micromorphic Continuum

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, because slender specimens are, in general, described as stiffer.

Cosserat Modeling of Size Effects in Crystalline Solids

2000 ◽  
Vol 653 ◽  
Author(s):  
Samuel Forest
Keyword(s):  
Stress State ◽  
Size Effects ◽  
Elastic Inclusion ◽  
Characteristic Size ◽  
Infinite Matrix ◽  
Crystalline Solids ◽  
Generalized Continua ◽  
Absolute Size ◽  
Kink Bands ◽  
The Matrix

AbstractThe mechanics of generalized continua provides an efficient way of introducing intrinsic length scales into continuum models of materials. A Cosserat framework is presented here to descrine the mechanical behavior of crystalline solids. The first application deals with the problem of the stress field at a crak tip in Cosserat single crystals. It is shown that the strain localization patterns developping at the crack tip differ from the classical picture : the Cosserat continuum acts as a bifurcation mode selector, whereby kink bands arising in the classical framework disappear in generalized single crystal plasticity. The problem of a Cosserat elastic inclusion embedded in an infinite matrix is then considered to show that the stress state inside the inclusion depends on its absolute size lc. Two saturation regimes are observed : when the size R of the inclusion is much larger than a characteristic size of the medium, the classical Eshelby solution is recovered. When R is much small than the inclusion, a much higher stress is reached (for an inclusion stiffer than the matrix) that does not depend on the size any more. There is a transition regime for which the stress state is not homogeneous inside the inclusion. Similar regimes are obtained in the study of grain size effects in polycrystalline aggregates of Cosserat grains.

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