Transverse isotropy

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

Passive material properties of intact ventricular myocardium determined from a cylindrical model.

Abstract: The equatorial region of the canine left ventricle was modeled as a thick-walled cylinder consisting of an incompressible hyperelastic material with homogeneous exponential properties. The anisotropic properties of the passive myocardium were assumed to be locally transversely isotropic with respect to a fiber axis whose orientation varied linearly across the wall. Simultaneous inflation, extension, and torsion were applied to the cylinder to produce epicardial strains that were measured previously in the potassium-arrested dog heart. Residual stress in the unloaded state was included by considering the stress-free configuration to be a warped cylindrical arc. In the special case of isotropic material properties, torsion and residual stress both significantly reduced the high circumferential stress peaks predicted at the endocardium by previous models. However, a resultant axial force and moment were necessary to cause the observed epicardial deformations. Therefore, the anisotropic material parameters were found that minimized these resultants and allowed the prescribed displacements to occur subject to the known ventricular pressure loads. The global minimum solution of this parameter optimization problem indicated that the stiffness of passive myocardium (defined for a 20 percent equibiaxial extension) would be 2.4 to 6.6 times greater in the fiber direction than in the transverse plane for a broad range of assumed fiber angle distributions and residual stresses. This agrees with the results of biaxial tissue testing. The predicted transmural distributions of fiber stress were relatively flat with slight peaks in the subepicardium, and the fiber strain profiles agreed closely with experimentally observed sarcomere length distributions. The results indicate that torsion, residual stress and material anisotropy associated with the fiber architecture all can act to reduce endocardial stress gradients in the passive left ventricle.

On elastic behaviour of fibre reinforced materials of arbitrary transverse phase geometry

Abstract: T he Plane strain bulk modulus and the two shear moduli of multiphase transversely isotropic fibre reinforced materials of arbitrary transverse phase geometry, are bounded from above and below in terms of phase moduli and phase volume fractions. Particular attention is given to the important special case of two-phase fibre reinforced materials.

Estimation of fracture parameters from reflection seismic data—Part I: HTI model due to a single fracture set

Abstract: The simplest effective model of a formation containing a single fracture system is transversely isotropic with a horizontal symmetry axis (HTI) Reflection seismic signatures in HTI media, such as NMO velocity and amplitude variation with offset (AVO) gradient, can be conveniently described by the Thomsen‐type anisotropic parameters e(V), δ(V), and γ(V) Here, we use the linear slip theory of Schoenberg and co‐workers and the models developed by Hudson and Thomsen for pennyshaped cracks to relate the anisotropic parameters to the physical properties of the fracture network and to devise fracture characterization procedures based on surface seismic measurements Concise expressions for e(V), δ(V), and γ(V) linearized in the crack density, show a substantial difference between the values of the anisotropic parameters for isolated fluid‐filled and dry (gas‐filled) penny‐sh aped cracks While the dry‐crack model is close to elliptical with e(V)≈δ(V), for thin fluid‐filled cracks e(V);≈0 and the absolute value

Elastic wave propagation in media with parallel fractures and aligned cracks

Abstract: A model of parallel slip interfaces simulates the behaviour of a fracture system composed of large, closely spaced, aligned joints. The model admits any fracture system anisotropy: triclinic (the most general), monoclinic, orthorhombic or transversely isotropic, and this is specified by the form of the 3 × 3 fracture system compliance matrix. The fracture system may be embedded in an anisotropic elastic background with no restrictions on the type of anisotropy. To compute the long wavelength equivalent moduli of the fractured medium requires at most the inversion of two 3 × 3 matrices. When the fractures are assumed on average to have rotational symmetry (transversely isotropic fracture system behaviour) and the background is assumed isotropic, the resulting equivalent medium is transversely isotropic and the effect of the additional compliance of the fracture system may be specified by two parameters (in addition to the two isotropic parameters of the isotropic background). Dilute systems of flat aligned microcracks in an isotropic background yield an equivalent medium of the same form as that of the isotropic medium with large joints, i.e. there are two additional parameters due to the presence of the microcracks which play roles in the stress-strain relations of the equivalent medium identical to those played by the parameters due to the presence of large joints. Thus, knowledge of the total of four parameters describing the anisotropy of such a fractured medium tells nothing of the size or concentration of the aligned fractures but does contain information as to the overall excess compliance due to the fracture system and its orientation. As the aligned microcracks, which were assumed to be ellipsoidal, with very small aspect ratio are allowed to become non-fiat, i.e. have a growing aspect ratio, the moduli of the equivalent medium begin to diverge from the standard form of the moduli for flat cracks. The divergence is faster for higher crack densities but only becomes significant for microcracks of aspect ratios approaching 0.3.