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Elastodynamic fundamental solutions for anisotropic solids
PROPERTIES:SURFACES matrix representations of stress-displacement relations on the interface for the decomposed symmetric and anti-symmetric elastic motions are derived. The applicability of the stiffnessmatrix approach to the layer model is analysed by numerical comparison between the approximate and exact solutions. (from Authors) 952150 Interfneini waves in the presence of areas of slip G. A. Maugin, Y. Chevalier & M. Louzar, Geophysical Journal International, 118(2), 1994, pp 305-316. Interracial waves are considered propagating along, or incident upon, an interface between two orthotropic elastic materials which presents special mechanical matching conditions, involving elastic slip along the whole of the interface or in localized areas. The study is made with a view to applications in geophysics and dynamical non-destructive evaluation techniques. The work highlights those results which will be useful in a qualitative and quantitative characterization of the interface, especially concerning the presence of cracks and the quality of the bond. (from Authors) 952151 Ray method of calculating the intensity of wavefronts in the ease of a heterogeneous, sntqotropic, elastic medium V. M. Babich, Geophysical Journal International, 118(2), 1994, pp 379-383. In this paper, the basic formulae of the ray method of calculating the intensity of wavefronts are applied to the case of a heterogeneous, anisotropic, elastic body. (Author) 952152 Elasto4yaamle fundamental suindom for am~otropie solids C.-Y. Wang & J. D. Achenbach, Geophysical Journal International, 118(2), 1994, pp 384-392.
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propagation direction of the energy flux vector and the energy density are derived for each individual wave. Finally, periodic transverse waves are considered. (from Authors)
952154 Wave propagation in polar elastic superlattlees W. A. Green & E. R. Green, Geophysical Journal International, 118(2), 1994, pp 459-465. T~s paper examines the passband and stop band regions for time-periodic waves travelling normal to the layering through an infinite medium composed of alternating layers of two different elastic materials. The materials are such that the elastic energy density is a function of the straim and the strain gradients and, in consequence, a deformation gives rise to both the usual Cauchy stress and to a hyperstress or couplestress. The periodic layering gives rise to displacements which are periodic with a frequency-dependent wave number, the Floquet wave number. Dispersion curves, relating circular frequency to the Floquet wave numbeer, are obtained for different ratios of the layer depth to the natural length ! and for different values of the elastic interface coupling parameters. (from Authors)
Surface properties
952155 An assessment of field evidence for 'Byedee' friction R. H. Sibson, Pure & Applied Geophysics, 142(3-4), 1994, pp 645-662.
3-D and 2-D time-domain elastodynamic fundamental solutions (or Green's functions) for linearly elastic anisutropic materials are obtained by the Radon transform. Fundamental solutions in the frequency domain follow directly by a subsequent evaluation of the Fourier transforms of the time-domain solutions. The wavefields can be separated into singular and regular parts. The singular parts correspond to the elastostatic fundamental solutions. The regular parts are bounded continuous functions. The integrals h a v e been evaluated numerically for several examples. The results presented in this paper have direct applications to the formulation of boundary-integrai equations for bodies of anisotropic materials and for the subsequent solution of these equations by the boundary-element method. (from Authors)
Structural analyses of the angles of frictional 'lock-up' for fault sets that have become progressively misoriented, together with field observations, suggest that Byerlee friction coefficients (0.6 < Ix < 0.85) are widely applicable to natural sliding surfaces with displacements of up to a few kilomettes in the upper crust, from the surface of the earth to seismogenic depths. However, extensional detachments which appear to have formed and remained active at very low dips ( < 15°) lie well outside the dip range of currently active normal faults, requiring stress trajectories that deviate significantly from the vertical and horizontal during their initiation and perhaps also during their continued reactivation. On the basis of the evidence afforded by the lower displacement faults, the apparent weakness of such structures seems most likely to arise from locally elevated fluid pressure, rather than from the presence of anomalously low-friction material within the fault zones. (from Author)
952153 Finite-amplitude plane waves in deformed Hadamard elastic materials P. Boulanger, M. Hayes & C. Trimarco, GeophysicalJournal International, 118(2), 1994, pp 447-458.
952156 The mieromeehanles of friction in n g r n u l a r layer C. O. Sammis & S. J. Steacy, Pure & Applied Geophysics, 142(3-4), 1994, pp 777-794.
It has been shown previously that Hadamard compressible elastic materials are the only ones for which three linearly polarized finite-amplitude plane waves, one longitudinal and two transverse, may propagate in any direction when the material is maintained in a state of arbitrary static finite homogeneous deformation. Simple explicit expressions are obtained for the three wave speeds and a simple characterization of the polarization directions of the transverse waves. Results are expressed in terms of the angles that the propagation direction makes with the acoustic axes. Then, the energy flux and energy density of the waves are considered. Relations between the projection on to the
A grain bridge model is used to provide a physical interpretation of the rate- and state-dependent friction parameters for the simple shear of a granular layer. This model recognizes the difference between the fracture of a grain and the fracture of an adhesion between grains, and it explicitly accounts for dilation in the granular layer. The observed evolution from velocity strengthening to velocity weakening with displacement is interpreted as being due to the change in the micromechanics of strain accommodation from grain crushing to slip between adjacent grains; this change is associated with the observed evolution of a fractal grain structure. (from Authors)
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propagation direction of the energy flux vector and the energy density are derived for each individual wave. Finally, periodic transverse waves are considered. (from Authors)
952154 Wave propagation in polar elastic superlattlees W. A. Green & E. R. Green, Geophysical Journal International, 118(2), 1994, pp 459-465. T~s paper examines the passband and stop band regions for time-periodic waves travelling normal to the layering through an infinite medium composed of alternating layers of two different elastic materials. The materials are such that the elastic energy density is a function of the straim and the strain gradients and, in consequence, a deformation gives rise to both the usual Cauchy stress and to a hyperstress or couplestress. The periodic layering gives rise to displacements which are periodic with a frequency-dependent wave number, the Floquet wave number. Dispersion curves, relating circular frequency to the Floquet wave numbeer, are obtained for different ratios of the layer depth to the natural length ! and for different values of the elastic interface coupling parameters. (from Authors)
Surface properties
952155 An assessment of field evidence for 'Byedee' friction R. H. Sibson, Pure & Applied Geophysics, 142(3-4), 1994, pp 645-662.
3-D and 2-D time-domain elastodynamic fundamental solutions (or Green's functions) for linearly elastic anisutropic materials are obtained by the Radon transform. Fundamental solutions in the frequency domain follow directly by a subsequent evaluation of the Fourier transforms of the time-domain solutions. The wavefields can be separated into singular and regular parts. The singular parts correspond to the elastostatic fundamental solutions. The regular parts are bounded continuous functions. The integrals h a v e been evaluated numerically for several examples. The results presented in this paper have direct applications to the formulation of boundary-integrai equations for bodies of anisotropic materials and for the subsequent solution of these equations by the boundary-element method. (from Authors)
Structural analyses of the angles of frictional 'lock-up' for fault sets that have become progressively misoriented, together with field observations, suggest that Byerlee friction coefficients (0.6 < Ix < 0.85) are widely applicable to natural sliding surfaces with displacements of up to a few kilomettes in the upper crust, from the surface of the earth to seismogenic depths. However, extensional detachments which appear to have formed and remained active at very low dips ( < 15°) lie well outside the dip range of currently active normal faults, requiring stress trajectories that deviate significantly from the vertical and horizontal during their initiation and perhaps also during their continued reactivation. On the basis of the evidence afforded by the lower displacement faults, the apparent weakness of such structures seems most likely to arise from locally elevated fluid pressure, rather than from the presence of anomalously low-friction material within the fault zones. (from Author)
952153 Finite-amplitude plane waves in deformed Hadamard elastic materials P. Boulanger, M. Hayes & C. Trimarco, GeophysicalJournal International, 118(2), 1994, pp 447-458.
952156 The mieromeehanles of friction in n g r n u l a r layer C. O. Sammis & S. J. Steacy, Pure & Applied Geophysics, 142(3-4), 1994, pp 777-794.
It has been shown previously that Hadamard compressible elastic materials are the only ones for which three linearly polarized finite-amplitude plane waves, one longitudinal and two transverse, may propagate in any direction when the material is maintained in a state of arbitrary static finite homogeneous deformation. Simple explicit expressions are obtained for the three wave speeds and a simple characterization of the polarization directions of the transverse waves. Results are expressed in terms of the angles that the propagation direction makes with the acoustic axes. Then, the energy flux and energy density of the waves are considered. Relations between the projection on to the
A grain bridge model is used to provide a physical interpretation of the rate- and state-dependent friction parameters for the simple shear of a granular layer. This model recognizes the difference between the fracture of a grain and the fracture of an adhesion between grains, and it explicitly accounts for dilation in the granular layer. The observed evolution from velocity strengthening to velocity weakening with displacement is interpreted as being due to the change in the micromechanics of strain accommodation from grain crushing to slip between adjacent grains; this change is associated with the observed evolution of a fractal grain structure. (from Authors)