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Chloé Arson - One of the best experts on this subject based on the ideXlab platform.
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Anisotropic nonlocal damage model for materials with intrinsic Transverse Isotropy
International Journal of Solids and Structures, 2018Co-Authors: Jin Wencheng, Chloé ArsonAbstract:Abstract This paper presents the theoretical formulation and numerical implementation of an anisotropic damage model for materials with intrinsic Transverse Isotropy. Crack initiation and propagation are modeled by phenomenological damage evolution laws, controlled by four equivalent strain measures. The latter are constructed so as to distinguish the mechanical response of the material in tension and compression, along the direction perpendicular to the bedding plane and within the bedding plane. To avoid mesh dependency induced by softening, equivalent strains are replaced by nonlocal counterparts, defined as weighted averages over a neighborhood scaled by two internal length parameters. Finite Element equations are solved with a normal plane arc length control algorithm, which allows passing limit points in case of snap back or snap through. The model is calibrated against triaxial compression tests performed on shale, for different confinements and loading orientations relative to the bedding plane. Gauss point simulations confirm that the model successfully captures the variation of uniaxial tensile strength with respect to the bedding orientation. Finite Element simulations of three-point bending tests and compression splitting tests show that nonlocal enhancement indeed avoids mesh dependency, and that the axial and Transverse dimensions of the damage process zone are scaled by the two characteristic lengths. Results further show that the damage process zone is direction dependent both in tension and compression. The model can be used for any type of textured brittle material; it allows representing several concurrent damage mechanisms in the macroscopic response and interpreting the failure mechanisms that control the damage process zone.
Alan D Freed - One of the best experts on this subject based on the ideXlab platform.
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invariant formulation for dispersed Transverse Isotropy in aortic heart valves an efficient means for modeling fiber splay
Biomechanics and Modeling in Mechanobiology, 2005Co-Authors: Daniel R Einstein, Alan D Freed, Ivan VeselyAbstract:Most soft tissues possess an oriented architecture of collagen fiber bundles, conferring both anIsotropy and nonlinearity to their elastic behavior. Transverse Isotropy has often been assumed for a subset of these tissues that have a single macroscopically-identifiable preferred fiber direction. Micro-structural studies, however, suggest that, in some tissues, collagen fibers are approximately normally distributed about a mean preferred fiber direction. Structural constitutive equations that account for this dispersion of fibers have been shown to capture the mechanical complexity of these tissues quite well. Such descriptions, however, are computationally cumbersome for two-dimensional (2D) fiber distributions, let alone for fully three-dimensional (3D) fiber populations. In this paper, we develop a new constitutive law for such tissues, based on a novel invariant theory for dispersed Transverse Isotropy. The invariant theory is derived from a novel closed-form 'splay invariant' that can easily handle 3D fiber populations, and that only requires a single parameter in the 2D case. The model fits biaxial data for aortic valve tissue as accurately as the standard structural model. Modification of the fiber stress-strain law requires no reformulation of the constitutive tangent matrix, making the model flexible for different types of soft tissues. Most importantly, the model is computationally expedient in a finite-element analysis, demonstrated by modeling a bioprosthetic heart valve.
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invariant theory for dispersed Transverse Isotropy an efficient means for modeling fiber splay
ASME 2004 International Mechanical Engineering Congress and Exposition, 2004Co-Authors: Daniel R Einstein, Alan D Freed, I VesleyAbstract:Most soft tissues possess an oriented architecture of collagen fiber bundles, conferring both anIsotropy and nonlinearity to their elastic behavior. Transverse Isotropy has often been assumed for a subset of these tissues that have a single macroscopically-identifiable preferred fiber direction. Micro-structural studies, however, suggest that, in some tissues, collagen fibers are approximately normally distributed about a mean preferred fiber direction. Structural constitutive equations that account for this dispersion of fibers have been shown to capture the mechanical complexity of these tissues quite well. Such descriptions, however, are computationally cumbersome for two-dimensional (2D) fiber distributions, let alone for fully three-dimensional (3D) fiber populations. In this paper, we develop a new constitutive law for such tissues, based on a novel invariant theory for dispersed Transverse Isotropy. The invariant theory is based on a novel closed-form splay invariant that can easily handle 3D fiber populations, and that only requires a single parameter in the 2D case. The model is polyconvex and fits biaxial data for aortic valve tissue as accurately as the standard structural model. Modification of the fiber stress-strain law requires no re-formulation of the constitutive tangent matrix, making the model flexible for different types of soft tissues. Most importantly, the model is computationally expedient in a finite-element analysis.
H Xiao - One of the best experts on this subject based on the ideXlab platform.
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on scalar vector and second order tensor valued anisotropic functions of vectors and second order tensors relative to all kinds of subgroups of the Transverse Isotropy group cinfinityh
Philosophical transactions - Royal Society. Mathematical physical and engineering sciences, 1998Co-Authors: H XiaoAbstract:Scalar–, vector– and second order tensor–valued functions of any finite number of vector and second order tensor variables are considered, which are required to possess invariance or form–invariance under the action of any given subgroup of the Transverse Isotropy group C ∞h . Irreducible functional bases and irreducible generating sets are presented to determine general reduced forms of the anisotropic functions just indicated. The results given are derived in the sense of non–polynomial representation.
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on anisotropic functions of vectors and second order tensors all subgroups of the Transverse Isotropy group c h
Archives of Mechanics, 1998Co-Authors: H XiaoAbstract:A UNIFIED PROCEDURE for constructing both the generating sets and the functional bases is suggested, which reduces the representation problem for anisotropic functions of any finite number of vector and second order tensor variables under any subgroup g ⊆ C∞ h , to that for the same types of anisotropic functions of not more than two vector and/or second order tensor variables. By using this procedure and new results for isotropic extension of anisotropic functions, simple irreducible generating sets and functional bases in unified forms are presented to determine general reduced forms of scalar-, vector-, and second order tensor-valued anisotropic functions of any finite number of vectors and second order tensors, under all kinds of subgroups of the Transverse Isotropy group C∞ h . The results given are derived in the sense of nonpolynomial representation.
Hitoshi Kawakatsu - One of the best experts on this subject based on the ideXlab platform.
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a new fifth parameter for Transverse Isotropy ii partial derivatives
Geophysical Journal International, 2016Co-Authors: Hitoshi KawakatsuAbstract:Kawakatsu etal. and Kawakatsu introduced a new fifth parameter, η κ , to describe Transverse Isotropy (TI). Considering that η κ characterizes the incidence angle dependence of body wave phase velocities for TI models, its relevance for body wave seismology is obvious. Here, we derive expressions for partial derivatives (sensitivity kernels) of surface wave phase velocity and normal mode eigenfrequency for the new set of five parameters. The partial derivative for η κ is about twice as large as that for the conventional η, indicating that η κ should be more readily resolved. While partial derivatives for S velocities are not so changed, those for P velocities are significantly modified; the sensitivity for anisotropic P velocities is greatly reduced. In contrary to the suggestion by Dziewonski & Anderson and Anderson & Dziewonski, there is not much control on the anisotropic P velocities. On the other hand, the significance of η κ for long-period seismology has become clear.
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a new fifth parameter for Transverse Isotropy
Geophysical Journal International, 2016Co-Authors: Hitoshi KawakatsuAbstract:S U M M A R Y Properties of a new parameter, ηκ , that is recently introduced by Kawakatsu et al. for Transverse Isotropy are examined. It is illustrated that the parameter nicely characterizes the incidence angle dependence of bodywave phase velocities for vertical Transverse Isotropy models that share the same Pand S-wave anIsotropy. When existing models of upper-mantle radial anIsotropy are compared in terms of this new parameter, PREM shows a distinct property. Within the anisotropic layer of PREM (a depth range of 24.4–220 km), ηκ 1 in the lower half. If ηκ > 1, anIsotropy cannot be attributed to a layering of homogeneous isotropic layers, and thus requires the presence of intrinsic anIsotropy.
Edward J Garnero - One of the best experts on this subject based on the ideXlab platform.
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Isotropy or weak vertical Transverse Isotropy in d beneath the atlantic ocean
Journal of Geophysical Research, 2004Co-Authors: Edward J Garnero, Melissa M Moore, Thorne Lay, Matthew J FouchAbstract:[1] Shear velocity properties of D″ beneath the central Atlantic Ocean are explored using predominantly European seismic recordings of intermediate and deep focus (>100 km) South American earthquakes. Broadband data are analyzed and, when possible, corrected for upper mantle models of receiver-side anisotropic structure. Regional shear velocity heterogeneity in D″ is mapped by analysis of 306 S-SKS differential times that have been corrected for three-dimensional seismic velocity structure above D″ using a whole mantle tomographic model. This correction yields modest (less than ±2%) estimates of seismic velocity heterogeneity in D″, with a transition from high to low seismic velocities traversing from west to east beneath the central Atlantic, in agreement with global tomographic models. Additionally, shear wave splitting of S and Sdiff for the same recordings was analyzed to assess seismic anIsotropy in D″. The highest-quality data provide 105 splitting times between SH and SV onsets that are mostly within the ±1 s uncertainty level. The few larger values generally exhibit SV delayed relative to SH. Assuming an anIsotropy geometry involving vertical Transverse Isotropy (VTI), as preferred in most regions of D″ that have been studied to date, <0.5% anIsotropy strength within a 100 km thick layer, or <0.25% anIsotropy within a 300 km thick layer are compatible with the data. These values are low in comparison to those found in high-velocity regions beneath the circum-Pacific Ocean or in the low-velocity region beneath the central Pacific, and many observations are, in fact, consistent with isotropic structure. The lack of strong VTI relative to other regions may be due to (1) the absence of stress from overlying midmantle downwelling, (2) relatively weaker shear flow in the D″ boundary layer, and/or (3) lack of chemical heterogeneity that could develop either lattice-preferred orientation or shape-preferred orientation. The azimuthal sampling of this region of D″ is quite limited; thus the precise geometry and mechanism of any anIsotropy are difficult to constrain. It remains possible that this region may contain subtle azimuthal anIsotropy that could couple the SV and SH signals; however, amplitude observations suggest that any such coupling is minor.
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shear wave splitting and waveform complexity for lowermost mantle structures with low velocity lamellae and Transverse Isotropy
Journal of Geophysical Research, 2004Co-Authors: Melissa M Moore, Edward J Garnero, Thorne Lay, Quentin WilliamsAbstract:[1] Shear waves that traverse the lowermost mantle exhibit polarization anomalies and waveform complexities that indicate the presence of complex velocity structure above the core-mantle boundary. Synthetic seismograms for horizontally and vertically polarized shear waves (SH and SV, respectively) are computed using the reflectivity method for structures with low-velocity sheets (“lamellae”), and for comb-like models approximating long wavelength vertical Transverse Isotropy (VTI). Motivated by evidence for partial melt in the deep mantle, lamella parameter ranges include (1) δVP from −5 to −10%, δVS = 3δVP; (2) 100 to 300 km thickness of vertical stacks of lamella; (3) lamella spacing and thickness varying from 0.5 to 20 km; and (4) lamellae concentrated near the top, bottom, or throughout the D″ region at the base of the mantle. Such lamellae represent, in effect, horizontally emplaced dikes within D″. Excessively complex waveforms are produced when more than ∼20% of D″ volume is comprised of low-velocity lamellae. Many lamellae models can match observed Sdiff splitting (1–10 s delays of SVdiff), but typically underpredict ScS splitting (1–4 s delays of ScSV). VTI model parameters are selected to address D″ observations, and include (1) 0.5 to 3% anIsotropy; (2) discontinuous D″ shear velocity increases up to 3%; (3) D″ thicknesses from 100 to 300 km; and (4) VTI concentrated at the top, bottom, or throughout D″. VTI models readily match observed splits of ScS and Sdiff. We discuss lamellae and VTI model attributes in relationship to waveform complexities, splitting magnitude, triplications from a high-velocity D″ discontinuity, and apparently reversed polarity SVdiff onsets. The possible presence of melt-filled lamellae indicates that local chemical or thermal perturbations can produce regions that exceed the solidus within D″. Such melt could occur in the bulk of D″ because the melt is either close to neutral buoyancy, advective velocities exceed percolative velocities, or both.
