Journal ArticleDOI
A unifying treatise of variational principles for two types of micropolar continua
Paul Steinmann,Erwin Stein +1 more
Reads0
Chats0
TLDR
In this article, a variational formulation for micropolar continua with constrained and non-constrained rotations is presented and the interrelation between the different formulations is highlighted.Abstract:
The objective of this work is to elaborate upon the variational setting for micropolar continua withconstrained andunconstrained rotations. To this end, several mixed variational principles and their regularizations are considered for both the geometrically linear and nonlinear case. The interrelation between the different formulations are highlighted. The most advantageous result is obtained by translating the insight gained for the geometrically linear case to the geometrically nonlinear case involving large strains and large rotations. It turns out that a particular micropolar description involves standard constitutive models for the symmetric stress part together with a nonsymmetric penalty stress thus circumventing to describe the constitutive law in terms of a nonsymmetric strain measure.read more
Citations
More filters
Journal ArticleDOI
On generalized Cosserat-type theories of plates and shells: a short review and bibliography
TL;DR: In this article, the Cosserat-type theories of plates and shells are discussed as a special application of this model, and the authors show that they can explain additional effects in solid and fluid mechanics in a more satisfying manner.
Journal ArticleDOI
On natural strain measures of the non-linear micropolar continuum
TL;DR: In this article, three different ways of defining the strain measures in the non-linear micropolar continuum are discussed: (a) by a direct geometric approach, (b) considering the strain measure as the fields required by the structure of local equilibrium conditions, and (c) requiring the strain energy density of the polar-elastic body to satisfy the principle of invariance under superposed rigid-body deformations.
Journal ArticleDOI
A Geometrically Exact Micromorphic Model for Elastic Metallic Foams Accounting for Affine Microstructure. Modelling, Existence of Minimizers, Identification of Moduli and Computational Results
Patrizio Neff,Samuel Forest +1 more
TL;DR: In this article, a geometrically exact generalized continua of micromorphic type in the sense of Eringen for the phenomenological description of metallic foams was investigated in a variational form.
Journal ArticleDOI
A finite-strain elastic–plastic Cosserat theory for polycrystals with grain rotations
TL;DR: In this paper, a geometrically exact generalized continua of Cosserat micropolar type was investigated and a variational form of these models was recalled and extended to finite-strain elasto-plasticity based on the multiplicative decomposition of the deformation gradient.
Journal ArticleDOI
Linear plane wave propagation and normal transmission and reflection at discontinuity surfaces in second gradient 3D continua
TL;DR: In this paper, the balance of mechanical energy valid for second gradient continua is deduced for plane wave propagation in Cauchy continua and the reflection and transmission at plane displacement discontinuity surfaces.
References
More filters
Journal ArticleDOI
Strain gradient plasticity: Theory and experiment
TL;DR: In this paper, a deformation theory of plasticity is introduced to represent in a phenomenological manner the relative roles of strain hardening and strain gradient hardening, which is a non-linear generalization of Cosserat couple stress theory.
Journal ArticleDOI
Elastic materials with couple-stresses
TL;DR: HAL as discussed by the authors is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not, which may come from teaching and research institutions in France or abroad, or from public or private research centers.
Journal ArticleDOI
Effects of couple-stresses in linear elasticity
Théorie des corps déformables
TL;DR: Cosserat and Hermann as mentioned in this paper discussed the kinematical and dynamical theories of the flexible line, the flexible surface, and the deformable three-dimensional medium in great detail.