An extended exponentiated Hencky energy for transverse isotropy

The composite ceramics is composed of fiber-eutectics, transformation particles and matrix particles. First, the recessive expression between the effective stress in fiber-eutectic and the flexibility increment tensor is obtained according to the four-phase model. Second, the analytical formula which contains elastic constant of the fiber-eutectic is obtained applying Taylor’s formula. The eutectic is transverse isotropy, so there are five elastic constants. Third, the effective elastic constants of composite ceramics are predicted. The result shows that the elastic modulus of composite ceramic is reduced with the increase of fibers fraction and fibers diameter.

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Constitutive Laws for Biomechanical Modeling of Refractive Surgery

Journal of Biomechanical Engineering ◽

10.1115/1.2796033 ◽

1996 ◽

Vol 118 (4) ◽

pp. 473-481 ◽

Cited By ~ 122

Author(s):

Michael R. Bryant ◽

Peter J. McDonnell

Keyword(s):

Finite Element ◽

Material Properties ◽

Refractive Surgery ◽

Fiber Optic ◽

Transverse Isotropy ◽

Constitutive Laws ◽

Finite Element Models ◽

Corneal Refractive Surgery ◽

Best Fit ◽

Membrane Inflation

Membrane inflation tests were performed on fresh, intact human corneas using a fiber optic displacement probe to measure the apical displacements. Finite element models of each test were used to identify the material properties for four different constitutive laws commonly used to model corneal refractive surgery. Finite element models of radial keratotomy using the different best-fit constitutive laws were then compared. The results suggest that the nonlinearity in the response of the cornea is material rather than geometric, and that material nonlinearity is important for modeling refractive surgery. It was also found that linear transverse isotropy is incapable of representing the anisotropy that has been experimentally measured by others, and that a hyperelastic law is not suitable for modeling the stiffening response of the cornea.

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Numerical study of fractured rock masses: Transverse isotropy vs. implicit joint-continuum models

Computers and Geotechnics ◽

10.1016/j.compgeo.2021.104317 ◽

2021 ◽

Vol 138 ◽

pp. 104317

Author(s):

Hosung Shin ◽

J. Carlos Santamarina

Keyword(s):

Numerical Study ◽

Fractured Rock ◽

Transverse Isotropy ◽

Continuum Models ◽

Rock Masses ◽

Fractured Rock Masses

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Use of RTM full 3D subsurface angle gathers for subsalt velocity update and image optimization: Case study at Shenzi field

Geophysics ◽

10.1190/geo2011-0065.1 ◽

2011 ◽

Vol 76 (5) ◽

pp. WB27-WB39 ◽

Cited By ~ 8

Author(s):

Zheng-Zheng Zhou ◽

Michael Howard ◽

Cheryl Mifflin

Keyword(s):

Model Building ◽

Transverse Isotropy ◽

Velocity Model ◽

Reverse Time ◽

Reverse Time Migration ◽

Data Set ◽

Edge Diffraction ◽

Time Migration ◽

Image Optimization ◽

Free Generation

Various reverse time migration (RTM) angle gather generation techniques have been developed to address poor subsalt data quality and multiarrival induced problems in gathers from Kirchhoff migration. But these techniques introduce new problems, such as inaccuracies in 2D subsurface angle gathers and edge diffraction artifacts in 3D subsurface angle gathers. The unique rich-azimuth data set acquired over the Shenzi field in the Gulf of Mexico enabled the generally artifact-free generation of 3D subsurface angle gathers. Using this data set, we carried out suprasalt tomography and salt model building steps and then produced 3D angle gathers to update the subsalt velocity. We used tilted transverse isotropy RTM with extended image condition to generate full 3D subsurface offset domain common image gathers, which were subsequently converted to 3D angle gathers. The angle gathers were substacked along the subsurface azimuth axis into azimuth sectors. Residual moveout analysis was carried out, and ray-based tomography was used to update velocities. The updated velocity model resulted in improved imaging of the subsalt section. We also applied residual moveout and selective stacking to 3D angle gathers from the final migration to produce an optimized stack image.

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Three-dimensional time-harmonic elastodynamic Green ’ s functions for anisotropic solids

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1995.0052 ◽

1995 ◽

Vol 449 (1937) ◽

pp. 441-458 ◽

Cited By ~ 102

Keyword(s):

Differential Equations ◽

Radon Transform ◽

Transverse Isotropy ◽

Three Dimensional ◽

Surface Integral ◽

Line Integral ◽

Surface Integration ◽

Time Harmonic ◽

Inverse Radon Transform ◽

Eigenvectors And Eigenvalues

A method based on the Radon transform is presented to determine the displacement field in a general anisotropic solid due to the application of a time-harmonic point force. The Radon transform reduces the system of coupled partial differential equations for the displacement components to a system of coupled ordinary differential equations. This system is reduced to an uncoupled form by the use of properties of eigenvectors and eigenvalues. The resulting simplified system can be solved easily. A back transformation to the original coordinate system and a subsequent application of the inverse Radon transform yields the displacements as a summation of a regular elastodynamic term and a singular static term. Both terms are integrals over a unit sphere. For the regular dynamic term, the surface integration can be evaluated numerically without difficulty. For the singular static term, the surface integral has been reduced to a line integral over half a unit circle. Reductions to the cases of isotropy and transverse isotropy have been worked out in detail. Examples illustrate applications of the method.

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Radial vibration of a cylindrical shell having transverse isotropy

Pure and Applied Geophysics ◽

10.1007/bf00875040 ◽

1969 ◽

Vol 75 (1) ◽

pp. 42-46 ◽

Cited By ~ 1

Author(s):

N. Bhanja

Keyword(s):

Cylindrical Shell ◽

Transverse Isotropy ◽

Radial Vibration

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Wrinkling of a Fiber-Reinforced Membrane

Journal of Applied Mechanics ◽

10.1115/1.2967888 ◽

2008 ◽

Vol 76 (1) ◽

Author(s):

E. Shmoylova ◽

A. Dorfmann

Keyword(s):

Boundary Conditions ◽

Energy Function ◽

Mechanical Response ◽

Transverse Isotropy ◽

Base Material ◽

Strain Energy Function ◽

Transversely Isotropic ◽

Incompressible Material ◽

Fiber Reinforced ◽

Relaxed Energy

In this paper we investigate the response of fiber-reinforced cylindrical membranes subject to axisymmetric deformations. The membrane is considered as an incompressible material, and the phenomenon of wrinkling is taken into account by means of the relaxed energy function. Two cases are considered: transversely isotropic membranes, characterized by one family of fibers oriented in one direction, and orthotropic membranes, characterized by two family of fibers oriented in orthogonal directions. The strain-energy function is considered as the sum of two terms: The first term is associated with the isotropic properties of the base material, and the second term is used to introduce transverse isotropy or orthotropy in the mechanical response. We determine the mechanical response of the membrane as a function of fiber orientations for given boundary conditions. The objective is to find possible fiber orientations that make the membrane as stiff as possible for the given boundary conditions. Specifically, it is shown that for transversely isotropic membranes a unique fiber orientation exists, which does not affect the mechanical response, i.e., the overall behavior is identical to a nonreinforced membrane.

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Transverse isotropy of the upper mantle in the vicinity of Pacific fracture zones

Bulletin of the Seismological Society of America ◽

10.1785/bssa0590010059 ◽

1969 ◽

Vol 59 (1) ◽

pp. 59-72

Author(s):

Robert S. Crosson ◽

Nikolas I. Christensen

Keyword(s):

Upper Mantle ◽

Symmetry Axis ◽

Transverse Isotropy ◽

Transversely Isotropic ◽

Seismic Wave Propagation ◽

Fracture Zones ◽

Mantle Material ◽

Transversely Isotropic Media ◽

Horizontal Symmetry ◽

Isotropic Media

Abstract Several recent investigations suggest that portions of the Earth's upper mantle behave anisotropically to seismic wave propagation. Since several types of anisotropy can produce azimuthal variations in Pn velocities, it is of particular geophysical interest to provide a framework for the recognition of the form or forms of anisotropy most likely to be manifest in the upper mantle. In this paper upper mantle material is assumed to possess the elastic properties of transversely isotropic media. Equations are presented which relate azimuthal variations in Pn velocities to the direction and angle of tilt of the symmetry axis of a transversely isotropic upper mantle. It is shown that the velocity data of Raitt and Shor taken near the Mendocino and Molokai fracture zones can be adequately explained by the assumption of transverse isotropy with a nearly horizontal symmetry axis.

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