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61.
Zaoyang Guo Ferhun Caner Xiongqi Peng Brian Moran 《Journal of the mechanics and physics of solids》2008,56(6):2338-2357
In this paper a hyperelastic constitutive model is developed for neo-Hookean composites with aligned continuous cylindrical pores in the finite elasticity regime. Although the matrix is incompressible, the composite itself is compressible because of the existence of voids. For this compressible transversely isotropic material, the deformation gradient can be decomposed multiplicatively into three parts: an isochoric uniaxial deformation along the preferred direction of the material (which is identical to the direction of the cylindrical pores here); an equi-biaxial deformation on the transverse plane (the plane perpendicular to the preferred direction); and subsequent shear deformation (which includes “along-fibre” shear and transverse shear). Compared to the multiplicative decomposition used in our previous model for incompressible fibre reinforced composites [Guo, Z., Peng, X.Q., Moran, B., 2006, A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus. J. Mech. Phys. Solids 54(9), 1952–1971], the equi-biaxial deformation is introduced to achieve the desired volume change. To estimate the strain energy function for this composite, a cylindrical composite element model is developed. Analytically exact strain distributions in the composite element model are derived for the isochoric uniaxial deformation along the preferred direction, the equi-biaxial deformation on the transverse plane, as well as the “along-fibre” shear deformation. The effective shear modulus from conventional composites theory based on the infinitesimal strain linear elasticity is extended to the present finite deformation regime to estimate the strain energy related to the transverse shear deformation, which leads to an explicit formula for the strain energy function of the composite under a general finite deformation state. 相似文献
62.
We consider the problem of finding the transversely isotropic elasticity tensor closest to a given elasticity tensor with
respect to the Frobenius norm. A similar problem was considered by other authors and solved analytically assuming a fixed
orientation of the natural coordinate system of the transversely isotropic tensor. In this paper we formulate a method for
finding the optimal orientation of the coordinate system—the one that produces the shortest distance. The optimization problem
reduces to finding the absolute maximum of a homogeneous eighth-degree polynomial on a two-dimensional sphere. This formulation
allows us a convenient visualization of local extrema, and enables us to find the closest transversely isotropic tensor numerically.
相似文献
63.
This article presents a general theory on indentation over a multiferroic composite half-space. The material is transversely isotropic and magneto-electro-elastic with its axis of symmetry normal to the surface of the half-space. Based on the corresponding half-space Green’s functions to point sources applied on the surface, explicit expressions for the generalized pressure vs. indentation depth are derived for the first time for the three common indenters (flat-ended, conical, and spherical punches). The important multiphase coupling issue is discussed in detail, with the weak and strong coupling being correctly revisited. The derived analytical solutions of indentation will not only serve as benchmarks for future numerical studies of multiphase composites, but also have important applications to experimental test and characterization of multiphase materials, in particular, of multiferroic properties. 相似文献
64.
V. A. Osinov 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(1):69-80
It is known that a high degree of anisotropy in the constitutive behaviour of a solid may result in the loss of hyperbolicity
of the dynamic equations in the form of either complex-conjugate or purely imaginary characteristic wave speeds (flutter ill-posedness
and shear band formation, respectively). In the present paper we investigate the characteristic wave speeds in the dynamic
problem for a transversely isotropic fluid-saturated porous solid. Three cases are considered: a dry solid and a saturated
solid under locally undrained and drained conditions. It is shown that, for given constitutive parameters of the solid skeleton,
the dynamic problem for a drained solid may become ill-posed due to the flutter-type loss of hyperbolicity, while the dynamic
equations for a dry and an undrained solids remain hyperbolic. For a given solid skeleton, the characteristic wave speeds
are strongly influenced by the pore fluid compressibility which, in turn, is extremely sensitive to the presence of a small
amount of free gas. 相似文献
65.
66.
67.
William Basener 《Topology and its Applications》2006,153(18):3627-3632
Our main result is that for a minimal flow φ on a compact manifold M, either M is a torus and the flow is topologically conjugate to an irrational flow, or M is not a torus and every parametrization of φ has sensitive dependence on initial conditions. Our results depend heavily on the work of Lopez and Candel. 相似文献
68.
This paper gives an overview of the methods developed for tissue motion estimation using transverse oscillation images (TO). TO images are specific radiofrequency ultrasound images featuring oscillations in both spatial directions. The initial studies on TO were published in the late 1990s. This paper reviews the main ideas and applications behind this motion estimation approach. First the origin and motivation of TO is briefly reviewed. Then the beamforming methods that lead to TO images are given, detailing the receive-only approach and the transmit-and-receive approach using synthetic aperture data. The different medical applications where TO has been used are discussed (blood flow, elastography and echocardiography), showing how it can improve motion estimation. Finally, the future perspectives of TO are outlined. 相似文献
69.
70.
T. Kaneyoshi 《Journal of magnetism and magnetic materials》2010,322(20):3014-3703
Phase diagrams of a cylindrical nanowire described by the transverse Ising model are investigated by the use of two theoretical frameworks, namely the mean field theory and the effective field theory with correlations. The phase diagram of the system is strongly affected by the surface situations. Some characteristic phenomena are found in the phase diagram, depending on the ratio of the physical parameters in the surface shell and the core. 相似文献