Effective shear modulus of piezoelectric film embedded with square nano-fibers under anti-plane shear waves

AbstractIt has been shown that uncoupled surface waves of SH type can be propagated without any dispersion in an electrically conducting semi-infinite elastic medium provided a uniform magnetic field acts non-aligned to the direction of wave propagation. In general, the velocity of propagation will be slightly greater than that of plane shear waves in the medium.

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Exact equations for fluid and solid substitution

Geophysics ◽

10.1190/geo2013-0187.1 ◽

2014 ◽

Vol 79 (3) ◽

pp. L21-L32 ◽

Cited By ~ 36

Author(s):

Nishank Saxena ◽

Gary Mavko

Keyword(s):

Shear Stress ◽

Shear Modulus ◽

Bulk Modulus ◽

Fluid Substitution ◽

Pore Shape ◽

Effective Shear Modulus ◽

Stiffness Measurement ◽

Saturated Rock ◽

Mean Stresses

We derived exact equations, elastic bulk and shear, for fluid and solid substitution in monomineralic isotropic rocks of arbitrary pore shape and suggested methods to obtain the required substitution parameters. We proved that the classical Gassmann’s bulk modulus equation for fluid-to-fluid substitution is exact for solid-to-solid substitution if compression-induced mean stresses (pressure) in initial and final pore solids are homogeneous and either the shear modulus of the substituted solid does not change or no shear stress is induced in pores. Moreover, when compression-induced mean stresses in initial and final pore solids are homogeneous, we evaluated exact generalizations of Gassmann’s bulk modulus equation, which depend on usually known parameters. For the effective shear modulus, we found general exactness conditions of Gassmann and other approximations. Using the new exact substitution equations, we interpreted that predicting solid-filled rock stiffness from a dry rock stiffness measurement requires more information (i.e., assumptions about the pore shape) compared to predicting the same from a fluid-saturated rock stiffness.

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Discussion of “ Evaluation of In Situ Effective Shear Modulus from Dispersion Measurements ” by Christos Vrettos and Bernd Prange (October, 1990, Vol. 116, No. 10)

Journal of Geotechnical Engineering ◽

10.1061/(asce)0733-9410(1992)118:7(1122.2) ◽

1992 ◽

Vol 118 (7) ◽

pp. 1122-1122 ◽

Cited By ~ 1

Author(s):

Glenn J. Rix

Keyword(s):

Shear Modulus ◽

Effective Shear Modulus

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Features of nonlinear in-plane shear deformation of a unidirectional and orthogonally reinforced polymer sheets of composite materials

Industrial laboratory Diagnostics of materials ◽

10.26896/1028-6861-2021-87-5-47-55 ◽

2021 ◽

Vol 87 (5) ◽

pp. 47-55

Author(s):

A. O. Polovyi ◽

N. V. Matiushevski ◽

N. G. Lisachenko

Keyword(s):

Experimental Data ◽

Composite Materials ◽

Shear Modulus ◽

Maximum Deviation ◽

Linear Section ◽

Stress Strain ◽

Plane Shear ◽

End Point ◽

Reinforced Polymer ◽

Failure Point

A comparative analysis of typical stress-strain diagrams obtained for in-plain shear of the 25 unidirectional and cross-ply reinforced polymer matrix composites under quasi-static loading was carried out. Three of them were tested in the framework of this study, and the experimental data on other materials were taken from the literature. The analysis of the generalized shear-strength curves showed that most of the tested materials exhibit the similar deformation pattern depending on their initial shear modulus: a linear section is observed at the beginning of loading, whereas further increase of the load decreases the slope of the curve reaching the minimum in the failure point. For the three parameters (end point the linear part, maximum reduced deviation of the diagram, tangent shear modulus at the failure point) characterizing the individual features of the presented stress-strain diagrams, approximating their dependences on the value of the reduced initial shear modulus are obtained. At the characteristic points of the deformation diagrams, boundary conditions are determined that can be used to find the parameters of the approximating functions. A condition is proposed for determination of the end point of the linear section on the experimental stress-strain curve, according to which the maximum deviation between the experimental and calculated (according to Hooke’s law) values of the shear stress in this section is no more than 1%, thus ensuring rather high accuracy of approximation on the linear section of the diagram. The results of this study are recommended to use when developing universal and relatively simple in structure approximating functions that take into account the characteristic properties of the experimental curves of deformation of polymer composite materials under in-plane shear of the sheet. The minimum set of experimental data is required to determine the parameters of these functions.

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