The Cosserat couple modulus for continuous solids is zero viz the linearized Cauchy‐stress tensor is symmetric

By Patrizio Neff. 2006

121 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/c868326772fade5d5563ff4f21e22f3b0e007c7e

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In Biomedical Engineering

In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

A unifying perspective: the relaxed linear micromorphic continuum (2013, unknown): “The model of Eringen and Claus [32,33,49] contains the linear Cosserat model [82,121,129,131] with asymmetric force stresses upon suitable restriction.”
Elliptic and parabolic regularity for second‐ order divergence operators with mixed boundary conditions (2013, background): “If in addition to (A1), the domain is a Lipschitz domain and if for the Lamé-constants , , the Cosserat couple modulus c and the parameter , it holds > 0, 2 C3 > 0, c 0 and > 0, then condition (A2) is satisfied [49, 50], where also more general situations are discussed.”
On the linear theory of micropolar plates (2009, unknown): “(23), λ, μ, κ, α, β, γ are the elastic moduli which satisfy the inequalities [25, 50] 2μ + κ ≥ 0, κ ≥ 0, 3λ + 2μ + κ ≥ 0, β + γ ≥ 0, γ − β ≥ 0, 3α + β + γ ≥ 0.”
At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola (2013, result): “Some examples of mathematical results which exploit in an efficient way the power of variational methods are those presented in Neff [74–76].”
Micropolar elasticity theory: a survey of linear isotropic equations, representative notations, and experimental investigations (2017, background): “Indeed, in this regard, it has been noted by Neff [42] that ‘‘as often the case, notation is a nightmare’’.”
On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush (2016, unknown): “1) = 2μ ‖sym∇u‖(2) + λ [tr(∇u)](2) + μc ‖ skew∇u−A‖(2) + 2μL(2)c ‖curl axl(A)‖(2) for the Cosserat model, where μc ≥ 0 is the (difficult to interpret [38]) Cosserat couple modulus [33].”
Material symmetry group and constitutive equations of micropolar anisotropic elastic solids (2016, unknown): “A similar model for infinitesimal strains was discussed in [38, 39].”
A finite-strain elastic–plastic Cosserat theory for polycrystals with grain rotations (2006, background): “In a series of papers [90,87,84,83,88,93,89,94] the author has investigated the mathematical and physical aspects of generalized microcontinuum theories in the elastic case.”