Finite deformations of a hyperelastic, compressible and fibre reinforced tube

Finite torsion and axial stretch of a long, hyperelastic, compressible and circular tube is studied for the design of a prototype of small diameter vascular prosthesis. The analysis is carried out in the context of the finite elasticity theory by using a class of Ogden strain energy function augmented with unidirectional reinforcing that is characterized by a single additional constitutive parameter for strength of reinforcement. The highly non-linear differential equations with variable coefficients governing the problem are solved numerically using a Runge–Kutta method. For different prestresses supported by the tube, the effects of the combined deformation on the stress distributions are presented.     

Transversely isotropic viscoplasticity model for a directionally solidified Ni-base superalloy

A transversely isotropic continuum viscoplasticity model has been formulated to capture the fatigue and creep responses of a directionally solidified (DS) polycrystalline Ni-base superalloy used mainly in turbine blades. This model has been implemented as an ABAQUS User MATerial (UMAT) subroutine using a semi-implicit integration scheme. Isothermal uniaxial fatigue data from tests conducted with and without hold times and creep data are used to characterize the stress–strain response at temperatures ranging from 427 °C to 1038 °C. The scheme leads to reduction of the associated computational costs when compared to a crystal viscoplasticity model that explicitly considers 3-D grain structure. The macroscopic elastoviscoplastic model is shown to simulate the homogenized deformation response of the polycrystalline DS alloy for various isothermal histories. The predictive capability of this model is verified using both in-phase and out-of-phase TMF data, and is compared to the results of analysis of a single crystal in terms of stress concentration and stress distribution for a model problem of a plate with a central hole.     

Evaluation of Failure Behavior of Transversely Loaded Unidirectional Model Composites

A leading reason for the limited use of laminated composite materials in primary structural applications is that the failure initiates in the ply oriented transverse to the direction of the applied load at a much lower strain level than that which would cause the ultimate failure of the laminate. Previous studies indicate that transverse failure is manifested as either cavitation-induced failure of the matrix system or fiber-matrix debonding. The mechanism causing the failure initiation event is not decidedly known and depends on the local stress field of the constrained matrix that is a function of fiber spacing. In the present study a model composite system using a transparent matrix is employed in a cruciform-shaped specimen to evaluate the viability of several transverse failure theories. The cruciform-shaped specimen utilizes a low strain-to-failure 828/D230 RT cured epoxy and stainless steel wires arranged such that a fiber is placed at the intersection of face diagonals of four remaining fibers located at corners of a square. The transverse failure mechanism is observed in-situ via the reflected light method and recorded utilizing high resolution, high magnification microscope cameras. A parametric study is conducted using three dimensional finite element models to analyze the stress state in the cruciform specimen as a function of fiber spacing. The result of the 3-D FE models in conjunction with experimental observations are used to evaluate the transverse failure theories suggested in the literature. In addition this data will be used to develop a comprehensive failure criterion for transversely loaded multi-fiber composites that encompasses the dependence on fiber spacing.     

Three-dimensional analytical solution for a rotating disc of functionally graded materials with transverse isotropy

Based on the basic equations for axisymmetric problems of transversely isotropic elastic materials, the displacement components are expressed in terms of polynomials of the radial coordinate with the five involved coefficients, named as displacement functions in this paper, being undetermined functions of the axial (thickness) coordinate. Five equations governing the displacement functions are then derived. It is shown that the displacement functions can be found through progressive integration by incorporating the boundary conditions. Thus a three-dimensional analytical solution is obtained for a transversely isotropic functionally graded disc rotating at a constant angular velocity.The solution can be degenerated into that for an isotropic functionally graded rotating disc. A prominent feature of this solution is that the material properties can be arbitrary functions of the axial coordinate. Thus, the solution for a homogeneous transversely isotropic rotating disc is just a special case that can be easily derived. An example is finally considered for a special functionally graded material, and numerical results shows that the material inhomogeneity has a remarkable effect on the elastic field.     

三峡库区巴东组地层的发育特征及其空间变化规律

根据大量的野外实际观察、室内岩石标本的薄片鉴定及化学成分分析结果,作者详细论述了三峡库区巴东组地层(T2b)的发育特征及其空间变化的规律性。巴东组地层在秭归、巴东、巫山、奉节等4个地区的总厚度最小约为830m,最大约为1420m,自东而西地层总厚度具有逐渐增大的趋势。红色与灰色是巴东组地层的两大基本色调,红色系列的岩层(第二、四段),多见为碎屑或砂泥质岩类,而灰色系列的岩层(第一、三、五段),多见为碳酸盐岩类。由其发育特征可知,巴东组为典型的易滑岩组。     

Increased torque transducer sensitivity via oversampling

The sensitivity of a commercial torque transducer under oscillatory shear conditions is extended by about a factor 3–5 into the small torque region. This increased sensitivity is a result of a straightforward data treatment in the time domain termed “on the fly oversampling”. This method is enabled by the emergence of modern ADC-cards. The underlying ideas of oversampling together with a first experimental verification of this method are described in detail. Received: 22 August 2000 Accepted: 14 November 2000     

Asymmetric vibrations and stability of a rotating annular plate loaded by a torque

The paper investigates transverse vibration of a thin annular plate clamped at its inner edge to a rigid shaft, while its outer edge is clamped to a rigid cylinder. The shaft and the outer edge of the plate are loaded by torques of the same intensity, but of opposite directions. The whole structure rotates at a constant angular speed. The solution has been determined using Galerkin’s method. The obtained results illustrate the impact of the torque, angular speed and inner and outer radia ratio to transverse asymmetric vibration frequency of the plate. Stability of the plate has been examined and critical values of angular speed and torque leading to the loss of stability of the plate have been determined. Some mode shapes have been drawn and the influence of torque and angular speed on nodal lines has been shown.     

Transverse isotropic poroelastic osteon model under cyclic loading

The poroelastic problem associated with a hollow cylinder under cyclic loading is solved. This cylinder models an osteon, basic unit of cortical bone. Both fluid and solid phases are supposed compressible. Solid matrix is modeled as an elastic transverse isotropic material. An explicit close-form solution for the steady state is obtained. Fluid flow distribution as a function of poroelastic properties and cyclic loading is discussed as it could influence bone remodeling. Strain rate of loading is shown to play a significant role in mass flux in the porous material.     

M-shaped Specimen for the High-strain Rate Tensile Testing Using a Split Hopkinson Pressure Bar Apparatus

An experimental technique is proposed to determine the tensile stress–strain curve of metals at high strain rates. An M-shaped specimen is designed which transforms a compressive loading at its boundaries into tensile loading of its gage section. The specimen can be used in a conventional split Hopkinson pressure bar apparatus, thereby circumventing experimental problems associated with the gripping of tensile specimens under dynamic loading. The M-specimen geometry provides plane strain conditions within its gage section. This feature retards necking and allows for very short gage sections. This new technique is validated both experimentally and numerically for true equivalent plastic strain rates of up to 4,250/s.     

Surface effect on free transverse vibrations and dynamic instability of current-carrying nanowires in the presence of a longitudinal magnetic field

Free transverse vibration and instability of current-carrying nanowires immersed in a longitudinal magnetic field are of concern. On the basis of the surface elasticity theory, a model is developed to investigate the problem. The analytical expressions of dynamic transverse displacements as well as natural frequencies of the magnetically affected nanowire for carrying electric current are obtained. The influences of the surface effect, initial tensile force within the nanowire, strength of the longitudinal magnetic field, and electric current on the natural frequencies as well as dynamic displacements are examined. The obtained results reveal that the transverse stiffness of the nanostructure is enhanced by the surface effect and the initial tensile force, while electric current or longitudinal magnetic field reduces the nanowire's stiffness. The condition which leads to the dynamic instability of the nanostructure is obtained. Further, the roles of the influential parameters on its stability are inclusively discussed.