Spin and twist motions in a homogeneous elastic continuum and cross-band geometry of fracturing

• Autorzy: Teisseyre R.
• Języki publikacji: EN

Abstrakty

EN

A uniform continuum with rotation motions of spin and twist type is presented; in this approach we supplement the ideal elasticity constitutive law, the strain-stress relation, by the rotation-asymmetric stress relation. In such a way, we can evade an influence of the Hook law, which, when used as the unique law in the ideal elasticity, rules out an existence of rotation waves. Thus, in the ideal elastic continuum the rotation vibrations can propagate and are not attenuated. The asymmetric elastic rotation fields and their relation to asymmetric elastic stresses are proposed and discussed, under the condition that the total fields with the elastic and self parts remain symmetric or antisymmetric as required by the compatibility conditions. The tensor of incompatibility splits into the symmetric or antisymmetric parts. The conservation and balance laws for spin and twist fields and the stress -related equations of motion for symmetric and antisymmetric parts of stresses are given. The relations obtained for elastic fields, expressed by difference of the total and self-fields, can be split into the self-parts prevailing on the fracture plane and the total parts describing seismic radiation field in a surrounding space. The role of rotation processes in premonitory and rebound time domains is considered in estimating the most effective fracture patterns.

Słowa kluczowe

EN

asymmetric stresses; spin and twist motions; equations of motion; rotation waves; fracture pattern

• Wydawca: Instytut Geofizyki PAN
• Czasopismo: Acta Geophysica Polonica
• Rocznik: 2004
• Tom: Vol. 52, nr 2
• Strony: 173--183
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Teisseyre R.

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

Bibliografia

• 1. Dietrich, J.H.J., 1978, Preseismic fault slip and earthquakes prediction, J. Geophys. Res. 83, B8, 3940-3954.
• 2. Kröner, E., 1982, Continuum theory of defects. In: Balian et al. (eds.), "Les Houches, Session XXXV, 1980, Physique des Defaults/Physics of Defects", North Holland Publ. Comp., Dordrecht.
• 3. Shimbo, M., 1975, A geometrical formulation of asymmetric features in plasticity, Bull. Fac. Eng., Hokkaido Univ. 77, 155-159.
• 4. Shimbo, M., 1995, Non-Riemannian geometrical approach to deformation and friction. In: R. Teisseyre (ed.), 'Theory of Earthquake Premonitory and Fracture Processes", PWN, Warszawa, 520-528.
• 5. Teisseyre, R., 2002, Continuum with defect and self-rotation fields, Acta Geophys. Pol. 50, l, 51-68.
• 6. Teisseyre, R., and W. Boratyński, 2002, Continuum with self-rotation nuclei: evolution of defect fields and equations of motion, Acta Geophys. Pol. 50, 2, 223-229.
• 7.Teisseyre, R., R., and W. Boratyński, 2003, Continua with self-rotation nuclei: evolution of asymmetric fields, Mech. Res. Commun. 30, 235-240.
• 8. Teisseyre, R., and W. Boratyński, 2004, Generalized continuum with defects and asymmetric stresses, Acta Geophys. Pol. 52, 185-195.
• 9. Teisseyre, R., and T. Yamashita, 1999, Splitting stress motion equation into seismic wave and fault-related fields, Acta Geophys. Pol. 47, 2, 135-147.
• 10. Teisseyre, R., K.P. Teisseyre and M. Górski, 2001, Earthquake fracture-band theory, Acta Geophys. Pol. 49, 4, 463-479.