Elastic fields in rotating transversely isotropic media

Representation of elastic fields in terms of scalar functions, which permit reducing the problems of determining these fields to determining scalar potentials, are generalized to the case of transversely isotropic media rotating at a constant angular velocity. Relations for calculating the parameters of surface acoustic waves (SAW) propagating in a rotating transversely isotropic halfspace with various directions of the medium material symmetry axis with respect to the half-space surface are given.     

Elastic moduli of transversely isotropic graphite fibers and their composites

This paper demonstrates that it is possible to calculate the complete set of elastic mechanical properties for graphite-epoxy fiber-reinforced materials at any fiber-volume fraction by modifying equations previously developed to include transversely isotropic graphite-fiber properties. Experimental verification of the modified equations is demonstrated by using these equations to curve fit elastic-property data obtained ultrasonically over a range of fiber-volume fractions. Material systems under consideration are T300/5208, AS-3501 and Modomor II/LY558 graphite epoxy. Using the modified equations it is possible to extrapolate for fiber properties. From Modomor II/LY558 ultrasonic data, it is shown that five out of seven extrapolated graphite-fiber properties are consistent with the assumption that graphite fibers are transversely isotropic. Elastic properties for T300/5208 and AS-3501 are ultrasonically evaluated by propagating stress waves through six individual specimens but at various angles from a block of unidirectional material. Particular attention is devoted to specimen dimensions. To demonstrate the need for accurately calculating or experimentally measuring all lamina elastic properties, a brief discussion is included on the effect that variations in lamina elastic properties have on calculating interlaminar stresses.     

Love solutions in the linear inhomogeneous transversely isotropic theory of elasticity

A general Love solution for the inhomogeneous transversely isotropic theory of elasticity with the elastic constants dependent on the coordinate z is proposed. This result may be considered as a generalization of the Love solutions we recently derived for the inhomogeneous isotropic theory of elasticity. The key steps of deriving the Love solution for the classical linear homogeneous transversely isotropic theory of elasticity are described for further use of the derivation procedure, which is then generalized to the inhomogeneous transversely isotropic case. Some particular cases of inhomogeneity traditionally used in the theory of elasticity are also examined. The significance of the derived solutions and their importance for the modeling of functionally graded materials are briefly discussed     

Vibration of an infinite inhomogeneous transversely isotropic viscoelastic medium with cylindrical hole

This paper investigates the influences of higher order viscoelasticity and the inhomogeneities of the transversely isotropic elastic parameters on the disturbances in an infinite medium, caused by the presence of a transient radial force or twist on the surface of a cylindrical hole with circular cross section. Following Voigt＇s model for higher order viscoelasticity, the nonvanishing stress components valid for a transversely isotropic and higher order viscoelastic solid medium have been deduced in terms of radial displacement component. Considering the power law variation of elastic and viscoelastic parameters, the stress equation of motion has been developed. Solving this equation under suitable boundary conditions, due to transient forces and twists, radial displacement and relevant stress components have been determined in terms of modified Bessel functions. The problem for the presence of transient radial force has been numerically analysed. Modulations of displacement and stresses due to different order of viscoelasticity and inhomogeneity have been graphically depicted. The numerical study of the disturbance caused by the presence of twist on the surface may be similarly done but is not pursued in this paper.     

Elastic properties and long-term damage of transversely isotropic composites with stress-rupture microstrength described by a fractional-power function

The damage process is modeled by randomly dispersed micropores occurring in places of destroyed microvolumes according to the stress-rupture microstrength, which is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, according to the Huber–Mises criterion, and is a random function of coordinates. Given microstresses or microstrains, the equations of porosity balance at an arbitrary time are derived. Together with the macrostress–macrostrain relationships for a discrete fibrous composite with porous components, they describe the coupled processes of deformation and long-term damage. A specific problem with a bounded stress-rupture microstrength function is solved Translated from Prikladnaya Mekhanika, Vol. 45, No. 1, pp. 71–81, January 2009.     

Elastic contact between a sphere and a semi infinite transversely isotropic body

The problem is solved by using a Hankel transformation. The stress and displacement expressions are explicitly given for any point of the medium. Curves of numerical results are presented.     

Wave propagation in an inhomogeneous transversely isotropic material obeying the generalized power law model

The analytical solutions for body-wave velocity in a continuously inhomogeneous transversely isotropic material, in which Young’s moduli (E, E′), shear modulus (G′), and material density (ρ) change according to the generalized power law model, (a+b z) ^c , are set down. The remaining elastic constants of transversely isotropic media, ν, and ν′ are assumed to be constants throughout the depth. The planes of transversely isotropy are selected to be parallel to the horizontal surface. The generalized Hooke’s law, strain-displacement relationships, and equilibrium equations are integrated to constitute the governing equations. In these equations, utilizing the displacement components as fundamental variables, the solutions of three quasi-wave velocities (V _SV , V _P ,?V _SH ) are generated for the present inhomogeneous transversely isotropic materials. The proposed solutions are compared with those of Daley and Hron (Bull Seismol Soc Am 67:661–675, (1977)), and Levin (Geophysics 44:918–936, (1979)) when the inhomogeneity parameter c?=?0. The agreement between the present results and previously published ones is excellent. In addition, the parametric study results reveal that the magnitudes of wave velocity are remarkably affected by (1) the inhomogeneity parameters (a, b, c); (2) the type and degree of material anisotropy (E/E′, ν/ν′, G/G′); (3) the phase angle (θ); and (4) the depth of the medium (z). Consequently, it is imperative to consider the effects of inhomogeneity when investigating wave propagation in transversely isotropic media.     

Elastic state of a transversely isotropic piezoelectric body with an arbitrarily oriented elliptic crack

The elastic stress state in a piezoelectric body with an arbitrarily oriented elliptic crack under mechanical and electric loads is analyzed. The solution is obtained using triple Fourier transform and the Fourier-transformed Green’s function for an unbounded piezoelastic body. Solving the problem for the case of a crack lying in the isotropy plane, for which there is an exact solution, demonstrates that the approach is highly efficient. The distribution of the stress intensity factors along the front of a crack in a piezoelectric body under uniform mechanical loading is analyzed numerically for different orientations of the crack __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 39–48, February 2008.     

《Elaticity of Transversely Isotropic Materials》一书评介

浙江大学土木系丁皓江教授和陈伟球教授及澳大利亚悉尼大学航空、机械与机电工程学院章亮炽教授的专著“Elasticity of Transversely Isotropic Ma- terials”(ISBN：1-4020-4033-4),2006年由Springer公司出版,该书是加拿大著名力学家G．M．L．Gladwell     

Evolution of the fronts of quasi-compressional and quasi-shear discontinuous waves in inhomogeneous transversely isotropic elastic media

The propagation and evolution of the fronts of discontinuous waves in inhomogeneous transversely isotropic elastic media are studied. A method to draw evolving rays and fronts is proposed. Geometrical singularities on the fronts are studied for different parameters of anisotropy and inhomogeneity     

Representations for transversely hemitropic and transversely isotropic stress-strain relations

The sets of polynomial stress-strain relations for elastic points which are transversely hemitropic and transversely isotropic are presented as projections of free algebraic modules having 20 and 10 generators, respectively. Complete sets of relations for the projections are presented which allow the sets of interest to be identified as free submodules having 12 and 6 generators, respectively. The results are established using the Cartan decomposition of the representation of the adjoint action of the two-dimensional rotation and orthogonal groups on the space of three-by-three symmetric matrices. The results are compared to known representations for nonlinear transversely isotropic stress-strain relations and for linear, transversely hemitropic and transversely isotropic ones.Work supported in part by National Science Foundation Grant INT-9106519.     

Representations for transversely hemitropic and transversely isotropic stress-strain relations

The sets of polynomial stress-strain relations for elastic points which are transversely hemitropic and transversely isotropic are presented as projections of free algebraic modules having 20 and 10 generators, respectively. Complete sets of relations for the projections are presented which allow the sets of interest to be identified as free submodules having 12 and 6 generators, respectively. The results are established using the Cartan decomposition of the representation of the adjoint action of the two-dimensional rotation and orthogonal groups on the space of three-by-three symmetric matrices. The results are compared to known representations for nonlinear transversely isotropic stress-strain relations and for linear, transversely hemitropic and transversely isotropic ones.     

Shear modulus of transversely isotropic materials

A new and simple method is presented to determine the inde-pendent shear modulus of transversely isotropic material.Mathematical formulation,derivation and solution are given,and test apparatus and results are presented.The method wastested on one of such materials-Green River Formation oilshale.Comparisons wich other approximate results and acou-stical methods are made.Confirmation of the test methodwith materials having known shear moduli is also presented.     

The effective properties of piezoelectric composite materials with transversely isotropic spherical inclusions

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