Degenerated mechanics in a homogeneous continuum: potentials for spin and twist

• Autorzy: Teisseyre R. , Białecki M. , Górski M.
• Języki publikacji: EN

Abstrakty

EN

In this paper we extend our considerations on the spin and twist motions in a homogenous continuum. Refering to our former results, we define the degenerated mechanics as that in which the displacement motions vanish while rotation motions, as the independent elastic fields, do exist. This is exactly the opposite case to the classic ideal elastic continuum in which only displacement motions are taken into account, while any independent rotation motions are excluded because of a lack of the appriopriate constitutive laws supporting the existence of an elastic response due to the rotational deformations of bonds in a lattice network. We propose a system of potentials which would help us to understand the waves and geometrical features of degenerated mechanics and its Riemannian geometry.

Słowa kluczowe

EN

spin and bend-twist motion; degenerated mechanics; rotation rigidity modulus; Riemannian geometry

• Wydawca: Instytut Geofizyki PAN
• Czasopismo: Acta Geophysica Polonica
• Rocznik: 2005
• Tom: Vol. 53, nr 3
• Strony: 219--230
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Teisseyre R.

• Institute of Geophysics, Polish Academy of Sciences, Księcia Janusza 64, 01-452 Warszawa, Poland

autor

Białecki M.

• Institute of Geophysics, Polish Academy of Sciences, Księcia Janusza 64, 01-452 Warszawa, Poland

autor

Górski M.

• Institute of Geophysics, Polish Academy of Sciences, Księcia Janusza 64, 01-452 Warszawa, Poland

Bibliografia

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• Shimbo, M., 1975, A geometrical formulation of asymmetric features in plasticity. Bull. Fac. Eng.,HokkaidoUniv. 77, 155-159.
• Shimbo, M., 1995, Non-Riemannian geometrical approach to deformation and friction. In: R. Teisseyre (ed.), "Theory of Earthquake Premonitory and Fracture Processes", 520--, 528, Polish Scientific Publishers PWN, Warszawa.
• Teisseyre, R., 2001, Evolution, propagation and diffusion of dislocation fields. In: R. Teisseyre and E. Majewski (eds.), "Earthquake Thermodynamics and Phase Transformations in the Earth's Interior" (vol. 76 of International Geophysical Series), 167-198, Academic Press, San Diego.
• Teisseyre, R., 2002, Continuum with defect and self-rotation nuclei, Acta Geophys. Pol. 50, 1, 51-68.
• Teisseyre, R., 2004, Spin and twist motions in a homogeneous elastic continuum and cross-band geometry of fracturing. Acta Geophys. Pol. 52, 2, 173-183.
• Teisseyre, R., 2005, Asymmetric continuum mechanics: deviations from elasticity and symmetry. Acta Geophys. Pol. 53, 2, 115-126.
• Teisseyre, R., and M. Białecki, 2005, Complex relativity: gravity and electromagnetic fields, arXiv:physics/0506033.
• Teisseyre, R., and W. Boratyński, 2003, Continua with self-rotation nuclei: evolution of asymmetric fields. Mech. Res. Commun. 30, 235-240.