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

被引：0
作者：
Gianluca Rizzi
Geralf Hütter
Angela Madeo
Patrizio Neff
机构：
[1] Université de Lyon,GEOMAS, INSA
[2] Institute of Mechanics and Fluid Dynamics,Lyon
[3] Universität Duisburg-Essen,TU Bergakademie Freiberg
来源：
Continuum Mechanics and Thermodynamics | 2021年 / 33卷
关键词：
Generalized continua; Cylindrical bending; Bending stiffness; Characteristic length; size effect; Micromorphic continuum; Cosserat continuum; Couple stress model; Gradient elasticity; Micropolar; Relaxed micromorphic model; Micro-stretch model; Micro-strain model; Micro-void model; Bounded stiffness;
D O I：
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学科分类号：
摘要：
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.
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页码：1505 / 1539
页数：34
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