On generalized Cosserat-type theories of plates and shells: a short review and bibliography

By J. Altenbach, Holm Altenbach, Victor A. Eremeyev. 2010

411 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Control and Systems Engineering, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/b2e9969b54dd4b2db5b1f13ffec0ea0598a5423c

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In Biomedical Engineering

In Control and Systems Engineering

In Materials Chemistry

Citations in the corpus

Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models (2016, background): “, [59–62] or [63–65] for 2D or 1D generalized continua characterized by a specific microstructure).”
On the shell theory on the nanoscale with surface stresses (2011, methodology): “In some references this variant of the theory of shells is also named the micropolar shell theory (Altenbach et al., 2010) because it is kinematically equivalent to the 2D Cosserat (micropolar) continuum, i.e. 2D medium with independent translations and rotations which origins are stresses and…”
Wave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gaps (2013, background): “We finally remark that there are some similarities between dispersion relations for micromorphic continua (including the proposed relaxed model) and dispersion relations of various types of plates models, see [1,2] where Kirchhoff, Mindlin, and Reissner types of plates including consideration of rot”
Generalized continua and non‐homogeneous boundary conditions in homogenisation methods (2011, methodology): “Homogenization techniques already exist to construct 1D Cosserat beam models and 2D Mindlin plate models [1].”
Dynamic finite element formulation for Cosserat elastic plates (2015, background): “In this case, an isotropic micropolar material require the definition of six parameters, whereas a classical solid would only demand two moduli [23].”
Micropolar elasticity theory: a survey of linear isotropic equations, representative notations, and experimental investigations (2017, background): “In the context of theoretical (non-experimental) efforts for characterization of the constitutive equations corresponding to generalized continuum theories one can generally distinguish two types of approaches; homogenization methods used to replace composite materials, granular media, lattices, and”
Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”** by E. Hellinger (2017, background): “Again the ideas presented by Hellinger have been continued after many years of apparent neglect: among those papers which seems to us have been animated by Hellinger’s spirit we found particularly interesting: [5, 7, 10, 27, 39, 59, 73–75, 83, 90] for the generalized theory of beams and [6, 8, 13, 1”