• Corpus ID: 249395381

Cosserat micropolar elasticity: classical Eringen vs. dislocation form

@inproceedings{Ghiba2022CosseratME,
  title={Cosserat micropolar elasticity: classical Eringen vs. dislocation form},
  author={Ionel‐Dumitrel Ghiba and Gianluca Rizzi and Angela Madeo and Patrizio Neff},
  year={2022}
}
In this paper we do 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… 

Tables from this paper

Size-effects of metamaterial beams subjected to pure bending: on boundary conditions and parameter identification in the relaxed micromorphic model

We devote this paper to model the size-effects of metamaterial beams under bending with the aid of the relaxed micromorphic continuum. We analyze first the size-dependent bending stiffness of

The consistent coupling boundary condition for the classical micromorphic model: existence, uniqueness and interpretation of parameters

We consider the classical Mindlin–Eringen linear micromorphic model with a new strictly weaker set of displacement boundary conditions. The new consistent coupling condition aims at minimizing

References

SHOWING 1-10 OF 67 REFERENCES

Torsion of a micropolar elastic prism of square cross-section

Existence of minimizers for a geometrically exact Cosserat solid

We study a geometrically exact Cosserat continuum model. The model is investigated in variational form as a two‐field minimization problem for the deformation φ and the independent microrotation

MICROSTRUCTURE IN LINEAR ELASTICITY

Abstract : A linear theory is formulated of a three-dimensional, elastic continuum which has some of the properties of a crystal lattice as a result of the inclusion, in the theory, of the idea of

Size effects and micromechanics of a porous solid

The rigidity of rods of a polymeric foam in bending and torsion is measured as a function of diameter. The dependence of rigidity upon specimen size is found to be inconsistent with a classically

A unifying perspective: the relaxed linear micromorphic continuum

We formulate a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force stresses and curvature contribution depending only on the micro-dislocation tensor. Our relaxed model is

Acceleration waves in micropolar elastic media

For nonlinearly elastic micropolar media, a condition of the existence of weak discontinuous solutions of equations of motion has been obtained. For these solutions, which constitute acceleration

Cosserat Media

The aim of this chapter consists of a brief presentation of basics of Cosserat continuum mechanics including kinematics, dynamics and constitutive modeling.

Theory of Micropolar Elasticity

In this article we present a self-contained account of the recent theory of micropolar elasticity. Micropolar elastic materials, roughly speaking, are the classical elastic materials with extra

Stability of Cosserat solids: size effects, ellipticity and waves

We consider stability in Cosserat solids. To obtain restrictions on elastic constants based on positive definite strain energy, energy terms are tacitly assumed to be independent. In finite size

Dislocation dispersion of elastic waves

...