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1

Earthquake fragmentation and slip processes: spin and shear-twist wave mosaic

Teisseyre R., Górski M.

Acta Geophysica

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2011

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Vol. 59, no. 3

453-469

EN

We followour former considerations on rotational processes and emission of rotation and shear-twist waves as occurring in earthquake source zones. A concise presentation of the motion and constitutive relations is given for each type of the four fundamental point deformations: displacements, rotations, point stretch/squeeze, and string-string point deformations (shear nuclei). We apply the Asymmetric Continuum Theory to the micro-fracture processes in an earthquake source zone: the fragmentation and slip processes are described by the linear and rotational transport fields incorporated in the motion equations. The advanced non-linear micro-fracture processes under high load are discussed.

2

Transport in fracture processes: Fragmentation and slip

Teisseyre R., Górski M.

Acta Geophysica

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2009

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Vol. 57, no. 3

583-599

EN

We present a new development in the asymmetric continuum theory with the shear oscillations (twist motions) and independent spin; these motions (displacement velocities and spin) can be shifted in phase to describe the independent rebound processes. Our approach provides an extension of the asymmetric continuum theory by including the microfragmentation processes with a double transport which may appear in an advanced fracture process under very high load. The related nonlinear equations, leading to soliton solutions, are derived.

3

Physics of basic motions in asymmetric continuum

Teisseyre R., Górski M.

Acta Geophysica

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2007

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Vol. 55, no. 2

119-132

EN

We consider the advantages of a formalism based on concept of the asymmetric continuum and we present some equivalence theorems relating it to the asymmetric elasticity and to micropolar and micromorphic theories as founded by Nowacki, Cosserats and Eringen. We consider the basic processes in an asymmetric continuum which could be reduced to the point basic motions/deformations. The coaction of spin and shear motions is assumed to play the main role in fracturing process, while the constitutive relation between the antisymmetric stresses and rotations replaces the friction constitutive law.

4

Asymmetric Continuum and Anisotropy

Teisseyre R.

Acta Geophysica

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2006

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Vol. 54, no. 3

225-238

EN

We present a relation between stress moments and antisymmetric part of stresses and the related constitutive law joining those stresses with the particle/point rotations. Correspondence of the asymmetric continuum theory to the micromorphic theory is considered. An extension of the asymmetric continuum theory for the case of 2D anisotropy for antisymmetric stresses leads us to the problems of friction ani-sotropy and fracture pattern.

5

Asymmetric continuum mechanics: deviations from elasticity and symmetry

Teisseyre R.

Acta Geophysica Polonica

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2005

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Vol. 53, nr 2

115-126

EN

The Kröner approach to continua with a distribution of self-field sources is applied to a wide class of deviations from the classical ideal elasticity; the same approach is applied to the theory of continua with asymmetric fields. The corresponding equations of motion are derived. Such an approach replaces other methods based on the constitutive relations specific for each type of the medium; here, the reference constitutive relation remains the same, but deviations from the classical ideal elasticity are attributed to different sources and defects introduced into continuum theory. Both methods lead to the expressions for the related currents. The nuclei responsible for the deviations from classical elasticity can be related to the defect distribution (dislocation and disclination densities), thermal excitation, some features of internal structure and different types of nuclei (e.g. electric nuclei, rotation nuclei); other deviations lead to an elastoplastic behavior. Our considerations extend also on deviations from the stress symmetry and related incompatibilities; we consider the resulting equations of motion.

6

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

Teisseyre R.

Acta Geophysica Polonica

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2004

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Vol. 52, nr 2

173-183

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.

7

Generalized continuum with defects and asymmetric stresses

Boratyński W., Teisseyre R.

Acta Geophysica Polonica

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2004

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Vol. 52, nr 2

185-195

EN

Consistent theory is presented of continuum with defect distribution: dislocation and disclination densities and the densities of rotation nuclei of two kinds. Special attention is paid to rotation and twist motions, and the two approaches to the definition of the twist-bend tensor are combined. The elastic and self fields of stresses and strains become asymmetric, while the total fields remain symmetric as required by the compatibility conditions. However, the tensor of incompatibility becomes asymmetric. The dislocation-stress relations and the equations of motion for symmetric and asymmetric parts of stresses are given and the wave equations for spin and twist are derived. Some applications are shortly discussed.

8

Continuum with self-rotation nuclei: Evolution of defect fields and equations of motion

Teisseyre R., Boratyński W.

Acta Geophysica Polonica

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2002

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Vol. 50, nr 2

223-229

EN

Asymmetric theory of elastic continuum with dislocations, disclinations and nuclei of rotations is extended; we study the evolution and flow of the defect fields and arrive at the equations of motion for the symmetric and antisymmetric parts. The total fields can be represented by its elastic and self parts and the respective equations can be split into its self part prevailing on the fracture plane and into its total part describing seismic radiation field in a surrounding space. Special attention is paid to the rotation and twist motions.

9

Continuum with defect and self-rotation fields

Teisseyre R.

Acta Geophysica Polonica

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2002

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Vol. 50, nr 1

51-68

EN

An elastic continuum containing dense distribution of internal nuclei (dislocations, disclinations, vacancies, thermal nuclei, or electric nuclei) are the objects/sources creating internal stresses (self stresses). We consider the rotation and twist fields and the internal nuclei generating these fields; in general an asymmetry of some fields shall be taken into account. We present total, self and elastic fields and the related compatibility conditions; the stress-defect density relations arc derived, proving the validity of our approach. The examples of experimental results are given to indicate the possibilities of recording the rotation and twist effects.