Theory and experimental verification of thermal stresses in Cosserat medium

Sikoń, M.

doi:10.2478/v10175-010-0119-y

Cited by 2 publications

(4 citation statements)

References 3 publications

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“…These fields exactly satisfy all the equilibrium field equations (12,13). If on the beam ends the force and couple traction vectors are applied in accord with (14,19,20), the boundary conditions are exactly satisfied everywhere, except for the requirement of zero applied m yz on the beam's y = constant lateral surfaces. Eqs.…”

Section: Can the Classical Bending Solution Also Solve Cosserat Bending?mentioning

confidence: 97%

“…(24) the volume integral becomes an in-plane area integral and the surface integral an in-plane line integral with S now referring to the lateral surface of the bar. The lateral surface boundary conditions require t i = 0 and m i = 0 everywhere on S except, in accord with Eqs (14,22),. m z = ±(β + γν)/R on y = ±a, respectively.…”

mentioning

confidence: 91%

“…The Cosserat characteristic length was determined in a polymer honeycomb as a two dimensional system [13]. On smaller scales, asymmetric interatomic action was studied in magnetic media; the existence of non-central load was demonstrated with electron paramagnetic resonance [14].…”

Section: Introductionmentioning

confidence: 99%

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Bending of a Cosserat Elastic Bar of Square Cross Section: Theory and Experiment

Lakes

Drugan

2015

Journal of Applied Mechanics

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Pure bending experiments on prismatic bars of square cross section composed of reticulated polymer foam exhibit deformation behavior not captured by classical elasticity theory. Perhaps the clearest example of this is the observed sigmoidal deformation of the bars' lateral surfaces, which are predicted by classical elasticity theory to tilt but remain planar upon pure moment application. Such foams have a non-negligible length scale compared to the bars' cross-sectional dimensions, whereas classical elasticity theory contains no inherent length scale. All these facts raise the intriguing question: is there a richer, physically sensible, yet still continuum and relatively simple elasticity theory capable of modeling the observed phenomenon in these materials? This paper reports our exploration of the hypothesis that Cosserat elasticity can. We employ the principle of minimum potential energy for homogeneous isotropic Cosserat linear elastic material in which the microrotation vector is taken to be independent of the macrorotation vector (as prior experiments indicate that it should be in general to model such materials) to obtain an approximate three-dimensional solution to pure bending of a prismatic bar having a square cross section. We show that this solution, and hence Cosserat elasticity, captures the experimentally observed nonclassical deformation feature, both qualitatively and quantitatively, for reasonable values of the Cosserat moduli. A further interesting conclusion is that a single experiment—the pure bending one—suffices to reveal directly, via the observation of surface deformation, the presence of nonclassical elastic effects describable by Cosserat elasticity.

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Section: Can the Classical Bending Solution Also Solve Cosserat Bending?mentioning

confidence: 97%

mentioning

confidence: 91%

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Bending of a Cosserat Elastic Bar of Square Cross Section: Theory and Experiment

Lakes

Drugan

2015

Journal of Applied Mechanics

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“…The aim of the work is to describe the experimental parameters of the Cosserat medium in nano-scale and measure these parameters in EPR spectrometer. A system of molecular interactions (forces and couples) is interpreted as the result of non-central interaction and the additional motion of an electron is generated, and it leads to the precession of the electron orbits ω couple [8]. The final result of such interactions is appearance of the additional magnetic field B couple leading to magnetization G couple of the continuum [8].…”

Section: Introductionmentioning

confidence: 99%

Quantum analysis of the Cosserat media with application to paramagnetic resonance

Sikoń¹

2010

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. This work is a continuation of the investigation which first results were presented in the Bulletin of the Polish Academy of Sciences: Technical Sciences in 2009. In the work the Cosserat medium is defined there, where inter-atomic actions have non-central nature. Non-central potential energy is introduced. As regards the Schrödinger equation the energetic state of the atom is described in the field of the quantum mechanics. The analysis is carried out on the base of mechanical and magnetic properties of the atom. The obtained solution is applied to write the resonance condition in the EPR spectrometer. The spectra, obtained for a loaded hydrated copper sulfate, were interpreted from the point of view of the presented theory and experimental parameters of the Cosserat medium were written.

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Theory and experimental verification of thermal stresses in Cosserat medium

Cited by 2 publications

References 3 publications

Bending of a Cosserat Elastic Bar of Square Cross Section: Theory and Experiment

Bending of a Cosserat Elastic Bar of Square Cross Section: Theory and Experiment

Quantum analysis of the Cosserat media with application to paramagnetic resonance

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