Transverse isotropy

About: Transverse isotropy is a research topic. Over the lifetime, 6396 publications have been published within this topic receiving 134947 citations.

Effective Elastic Properties of Carbon Nanotube Reinforced Composites

Abstract: We seek to obtain continuum level elastic properties for carbon nanotubes and carbon nanotube reinforced composites through a variety of micromechanics techniques. Using the in-plane elastic properties of graphene sheets the effective properties of carbon nanotubes are calculated using a modified composite cylinders micromechanics technique to treat the hollow nanotube as a transversely isotropic solid cylinder. Effective properties found for single-walled carbon nanotubes in this fashion are found to be in good agreement with both experimentally and theoretically obtained results available in the literature. Having a solid fiber then allows for the calculation of an Eshelby tensor and hence, the use of additional more advanced micromechanics techniques to calculate carbon nanotube reinforced composite effective elastic properties. In what are termed two-step approaches, the generalized self-consistent and Mori-Tanaka micromechanics techniques are employed to obtain effective elastic properties of composites consisting of aligned single or multi-walled effective carbon nanotubes embedded in a polymer matrix of EPON 862 at various effective carbon nanotube volume fractions. These results are compared to a single step composite cylinders approach wherein an additional phase consisting of the polymer matrix is placed around the carbon nanotube prior to obtaining the effective carbon nanotube properties, thereby obtaining the effective composite properties in a single calculation. It is found that the two-step Mori-Tanaka results yield nearly identical results as the single step composites cylinders approach. Finally, it has been observed in the literature that electrostatic clumping of nanotubes into nanotube bundles complicates the adequate dispersion of the nanotubes within the polymer matrix. The quantification and modeling of this clustering in aligned nanotube composites is accomplished herein using Dirichlet tessellation in conjunction with an n-phase generalized self-consistent technique. It is observed that the effect of clustering is to reduce in magnitude only the transverse to fiber alignment properties of the transversely isotropic effective composite as compared to the randomly distributed aligned carbon nanotube composite’s effective elastic properties, and that this reduction in transverse elastic properties increases with increasing global volume fraction of effective carbon nanotubes. Results indicate that, while the clustering effect does contribute to some reduction in composite properties, other factors such as cluster misalignment and poor fiber-matrix bonding may play a significantly larger role. Nomenclature 11 E = the one-direction Young’s modulus 12 ν = the one-direction Poisson’s ratio 23 κ = the 2-3-plane bulk modulus 12 μ = the 1-2-plane shear modulus 23 μ = the 2-3 plane shear modulus A E = the axial Young’s modulus of a fiber

Anisotropic elasticity of a natural clay

Abstract: Lightly overconsolidated natural clays are commonly anisotropic because of their mode of deposition. They exhibit substantial ranges of approximately linear, reversible (elastic) behaviour at stress levels which do not produce yielding of the particle structure of the clay. The Paper examines the five elastic parameters needed to describe transverse isotropy, sometimes called crossanisotropy. Only three parameters can be measured in triaxial tests, and reasonable assumptions, with easily identifiable physical significance, are proposed which permit extrapolation from triaxial to more general stress conditions. Convenient parameters are identified such as the bulk modulus K, shear modulus G, and a cross modulus J which expresses the relationships in a transversely isotropic soil between mean stress and shear strain and between shear stress and volumetric strain. A least squares solution is used to evaluate these parameters from 76mm diameter triaxial tests on Lake Agassiz clay from Winnipeg, Canada. The so...

Properties and an Anisotropic Model of Cancellous Bone From the Proximal Tibial Epiphysis

Abstract: An investigation has been made of the source and magnitude of anisotropic material properties of cancellous bone in the proximal epiphysis of the human tibia. Results are reported for stiffness measurements made in three orthogonal directions on 21 cubes of cancellous bone before testing to failure along one of the three principal axes. The structure is approximately transversely isotropic. Strength and stiffness are linear with area fraction for loading along the isotropic axis. Strength is proportional to stiffness for all directions. A finite element model is proposed, based on experimental observations, which enables one to predict the elastic constants of cylindrically structured cancellous bone in the tibia from morphological measurements in the transverse plane.

Imaging anisotropic and viscous properties of breast tissue by magnetic resonance-elastography

Abstract: MR-elastography is a new technique for assessing the viscoelastic properties of tissue. One current focus of elastography is the provision of new physical parameters for improving the specificity in breast cancer diagnosis. This analysis describes a technique to extend the reconstruction to anisotropic elastic properties in terms of a so-called transversely isotropic model. Viscosity is treated as being isotropic. The particular model chosen for the anisotropy is appealing because it is capable of describing elastic shear anisotropy of parallel fibers. The dependence of the reconstruction on the particular choice of Poisson's ratio is eliminated by extracting the compressional displacement contribution using the Helmholtz-Hodge decomposition. Results are presented for simulations, a polyvinyl alcohol breast phantom, excised beef muscle, and measurements in two patients with breast lesions (invasive ductal carcinoma and fibroadenoma). The results show enhanced anisotropic and viscous properties inside the lesions and an indication for preferred fiber orientation.