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1.
A novel method is proposed to design neutral N-phase (N ? 3) elliptical inclusions with internal uniform hydrostatic stresses. We focus on the study of the internal and external stress states of an N-phase elliptical inclusion which is bonded to an infinite matrix through (N ? 2) interphase layers. The interfaces of the N-phase elliptical inclusion are (N ? 1) confocal ellipses. The design of the resulting overall composite material consists of four stages: (i) an inner perfectly bonded interphase/inclusion interface which is necessary to make the internal uniform stress state hydrostatic; (ii) outer imperfect interphase layers properly designed to make the coated inclusion harmonic (i.e., the uniform mean stress of the original field within the matrix is unperturbed); (iii) the aspect ratio of the elliptic inclusion uniquely chosen for a given material and thickness parameters to make the resulting coated inclusion neutral (i.e., the prescribed uniform stress field in the matrix remains undisturbed); and finally (iv) the derivation of a simple condition relating the remote uniform stresses and the thickness parameters of the (N ? 2) interphase layers for given material parameters which lead to internal uniform hydrostatic stresses. We note that another interesting feature of the present results is that the mean stress is found to be constant within each interphase layer, and the hoop stress in the innermost interphase layer is uniform along the entire interphase/inclusion interface. 相似文献
2.
对非理想界面的三相复合材料,提出了计算弹性应力场的微观力学模型,在适当的简化假设下,对带界相的颗粒增强和纤维增强复合材料,得到了应力场的计算公式。以剪切载荷为例给出了数值例子。给出的数值结果表明非理想界面对三相复合材料应力场的影响。 相似文献
3.
Interaction between an edge dislocation and a circular inclusion with an inhomogeneously imperfect interface 总被引:2,自引:0,他引:2
This research presents an analytical study of the interaction problem of an edge dislocation with a circular inclusion with a circumferentially inhomogeneously imperfect interface. The interface, which is modeled as a spring (interphase) layer with vanishing thickness, is characterized by that in which there is a displacement jump across the interface in the same direction as the corresponding tractions, and the same degree of imperfection is realized in both the normal and tangential directions. Furthermore, the interface parameter is nonuniform along the interface. In order to arrive at an elementary form solution, we introduce a conformal mapping function. Then the stress field as well as the Peach–Koehler force acting on the edge dislocation can be obtained from the derived complex potentials. Calculations demonstrate that the nonuniform interface parameter has a significant influence on the stress field. 相似文献
4.
Gerald H. Meeten 《Rheologica Acta》2000,39(4):399-408
Various structured fluids were placed between the parallel circular plates of a squeeze-flow rheometer and squeezed by a
force F until the fluid thickness h was stationary. Fluid thickness down to a few microns could be measured. Most fluids showed two kinds of dependence of f on h according to an experimentally-determined thickness h
*. If h > h
* then F varied in proportion to h
−1 as predicted by Scott (1931) for a fluid with a shear yield stress τ0. The magnitude of τ0 from squeeze-flow data in this region was compared with the yield stress measured by the vane method. For some fluids τ0 measured by squeeze flow was less than the vane yield stress, suggesting that the yield stress of fluid in contact with the
plates was less than the bulk yield stress. If h < h
* then F varied approximately as h
−5/2 and the squeeze-flow data in this region analysed with Scott's relationship gave a yield stress which increased as the fluid
thickness decreased. This previously unreported effect may result from unconnected regions of large yield stress in the fluid
of size similar to h
* which are not sensed by the vane and which become effective in squeeze flow only when h < h
*.
Received: 13 December 1999/Accepted: 4 January 2000 相似文献
5.
A general method is presented for the rigorous solution of a circular inclusion embedded within an infinite matrix in plane
elastostatics. The bonding at the inclusion-matrix interface is considered to be imperfect with the assumption that the interface
imperfections are circumferentially inhomogeneous. Using analytic continuation, the basic boundary value problem for four
analytic functions is reduced to two coupled first order differential equations for two analytic functions. The resulting
closed-form solutions include a finite number of unknown constants determined by analyticity and certain other auxiliary conditions.
The method is illustrated using a particular class of inhomogeneous interface. The results from these calculations are compared
to the corresponding results when the imperfections in the interface are circumferentially homogeneous. These comparisons
illustrate, for the first time, how the circumferential variation of the parameter describing the imperfection has a pronounced
effect on the average stresses induced within the inclusion.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
6.
7.
8.
In this paper, we show that a three-phase elliptic inclusion under uniform remote stress and eigenstrain in anti-plane shear
admits an internal uniform stress field provided that the interfaces are two confocal ellipses. The exact closed-form solution
is used to quantify the effect of the interphase layer on the residual stresses within the inclusion and the dependency of
this effect on the aspect ratio of the elliptic inclusion.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
9.
Gerald Henry Meeten 《Rheologica Acta》2001,40(3):279-288
Experiments are described in which a constant force F squeezed a fluid, either between two parallel circular plates, or between a plate and convex spherical lens. Newtonian fluids
obeyed the relation of Stefan (1874) for plates, and the relation of Adams et al. (1994) for plate and lens. The non-Newtonian
yield stress fluids Brylcreem, Laponite and Sephadex were squeezed between plates of various diameter D to attain a stationary separation h. Only for separations greater than h
* (which depended on the fluid) did Brylcreem and Laponite obey the relation F/D
3 ∝ h
−1 of Scott (1931) and give a yield stress in agreement with the vane method. For Sephadex the dependence of F/D
3 on h disagreed with Scott's relation, but varied as h
−5/2 for h > 0.6 mm and h
−3/2 for h < 0.6 mm. On rotating one plate in its plane the yield stress fluids at a fixed F suffered a marked decrease of h. This, and the existence of h
*, are discussed in terms of the soft glassy material model of Sollich et al. (1997) and Sollich (1998). Brylcreem and Laponite
were squeezed between a plate and lenses of various curvature and their yield stress obtained using the relation of Adams
et al. (1994) was compared with measurements by plate-plate squeeze-flow and vane methods.
Received: 12 April 2000 Accepted: 26 October 2000 相似文献
10.
陈宜周 《应用数学和力学(英文版)》2014,35(7):863-874
This paper presents a closed form solution and numerical analysis for Es- helby's elliptic inclusion in an infinite plate. The complex variable method and the confor- real mapping technique are used. The continuity conditions for the traction and displace- ment along the interface in the physical plane are reduced to the similar conditions along the unit circle of the mapping plane. The properties of the complex potentials defined in the finite elliptic region are analyzed. From the continuity conditions, one can separate and obtain the relevant complex potentials defined in the inclusion and the matrix. From the obtained complex potentials, the dependence of the real strains and stresses in the inclusion from the assumed eigenstrains is evaluated. In addition, the stress distribution on the interface along the matrix side is evaluated. The results are obtained in the paper for the first time. 相似文献
11.
Dynamic Crack Growth Past a Stiff Inclusion: Optical Investigation of Inclusion Eccentricity and Inclusion-matrix Adhesion Strength 总被引:2,自引:1,他引:1
Interactions between a dynamically growing matrix crack and a stationary stiff cylindrical inclusion are studied optically.
Test specimens with two different bond strengths (weak and strong) and three crack-inclusion eccentricities (e = 0, d/2 and 3d/4, d being inclusion diameter) are studied using reflection mode Coherent Gradient Sensing (CGS) and high-speed photography. These
variants produce distinct dynamic crack trajectories and failure behaviors. A weaker inclusion-matrix interface attracts a
propagating crack while a stronger one deflects the crack away. The former results in a propagating crack lodging (‘key-hole’)
into the inclusion-matrix interface whereas in the latter the crack tends to circumvent the inclusion. When the inclusion
is in the prospective crack path, the maximum attained crack speed is much higher in the weakly bonded inclusion cases relative
to the strongly bonded counterparts. For a crack propagating towards a weakly bonded inclusion, the effective stress intensity
factor (K
e) value remains constant for each inclusion eccentricity considered. But these constant K
e values increase with increasing eccentricity. A distinct drop in K
e occurs when the crack is near the inclusion. In strongly bonded inclusion cases, on the other hand, monotonically increasing
K
e before the crack reaches the inclusion is observed. A drop in K
e is seen just before the crack reaches the inclusion. The mode-mixity estimates are of opposite signs for weakly and strongly
bonded inclusions in case of the largest eccentricity studied, confirming the observed crack attraction and deflection mechanisms.
相似文献
H. V. Tippur (SEM member)Email: |
12.
We study the plane deformation of an elastic composite system made up of an anisotropic elliptical inclusion and an anisotropic foreign matrix surrounding the inclusion. In order to capture the influence of interface energy on the local elastic field as the size of the inclusion approaches the nanoscale, we refer to the Gurtin-Murdoch model of interface elasticity to describe the inclusion-matrix interface as an imaginary and extremely stiff but zero-thickness layer of a finite stretching modulus. As opposed to isotropic cases in which the effects of interface elasticity are usually assumed to be uniform (described by a constant interface stretching modulus for the entire interface), the anisotropic case considered here necessitates non-uniform effects of interface elasticity (described by a non-constant interface stretching modulus), because the bulk surrounding the interface is anisotropic. To this end, we treat the interface stretching modulus of the anisotropic composite system as a variable on the interface curve depending on the specific tangential direction of the interface. We then devise a unified analytic procedure to determine the full stress field in the inclusion and matrix, which is applicable to the arbitrary orientation and aspect ratio of the inclusion, an arbitrarily variable interface modulus, and an arbitrary uniform external loading applied remotely. The non-uniform interface effects on the external loading-induced stress distribution near the interface are explored via a group of numerical examples. It is demonstrated that whether the nonuniformity of the interface effects has a significant effect on the stress field around the inclusion mainly depends on the direction of the external loading and the aspect ratio of the inclusion. 相似文献
13.
Stress analysis in two dimensional electrostrictive material with an elliptic rigid conductor 总被引:2,自引:0,他引:2
This paper presents the governing equations of electrostrictive materials. The stress and electric field solutions for an infinite plate with a rigid elliptic conductor under applied load at infinity are given. The asymptotic expansions of the solution for a narrow elliptic conductor show that the stresses and the electric fields near the end of a narrow elliptic conductor possess r−1 and r−1/2 forms respectively in a local coordinate system with the origin at its focus. 相似文献
14.
Thin interphase/imperfect interface in elasticity with application to coated fiber composites 总被引:3,自引:0,他引:3
The imperfect interface conditions which are equivalent to the effect of a thin elastic interphase are derived by a Taylor expansion method in terms of interface displacement and traction jumps. Plane and cylindrical interfaces are analyzed as special cases. The effective elastic moduli of a unidirectional coated fiber composite are obtained on the basis of the derived imperfect interface conditions. High accuracy of the method is demonstrated by comparison of solutions of several problems in terms of the imperfect interface conditions or explicit presence of interphase as a third phase. The problems considered are transverse shear of a coated infinite fiber in infinite matrix and effective transverse bulk and shear moduli and effective axial shear modulus of a coated fiber composite. Unlike previous elastic imperfect interface conditions in the literature, the present ones are valid for the entire range of interphase stiffness, from very small to very large. 相似文献
15.
Using a normal mode analysis, we predict the infinite dilution linear viscoelastic properties of single-strand (ss) DNA molecules
and compare the results to the linear viscoelastic data of Shusterman et al. (Phys Rev Let 92(4):048303, 2004) obtained by
monitoring the diffusion of a fluorescently labeled terminus of the molecule. To compute the overall best global fit, we constrain
the hydrodynamic interaction parameter, h*, equilibrium root mean square spring extension, b, and the number of Kuhn steps per spring, N
K,S, to be equal for the strands compared. The fits using the bead-spring model for all but 23,100 base ss-DNA strands match
the experimental data at long times with significant deviations at intermediate and short times. However, parameters fitted
separately to all individual strand lengths predict results well. The best fits to data for 2,400 and 6,700 base pairs yield
N
K,S ∼12 and h* = 0.12. These values are similar to those found for conventional polymers such as polystyrene which have been successfully
modeled with N
K,S ∼7 and h* = 0.15, indicating ss-DNA and polystyrene exhibit analogous hydrodynamic behavior. 相似文献
16.
In the following analysis, we present a rigorous solution for the problem of a circular elastic inclusion surrounded by an infinite elastic matrix in finite plane elastostatics. The inclusion and matrix are separated by a circumferentially inhomogeneous imperfect interface characterized by the linear spring-type imperfect interface model where the interface is such that the same degree of imperfection is realized in both the normal and tangential directions. Through the use of analytic continuation, a set of first-order coupled ordinary differential equations with variable coefficients are developed for two analytic potential functions. The unknown coefficients of the potential functions are determined from their analyticity requirements and some additional problem-specific constraints. An example is then presented for a specific class of interface where the inclusion mean stress is contrasted between the homogeneous interface and inhomogeneous interface models. It is shown that, for circumstances where a homogeneously imperfect interface may not be warranted, the inhomogeneous model has a pronounced effect on the mean stress within the inclusion. 相似文献
17.
《International Journal of Solids and Structures》2014,51(15-16):2865-2877
This paper proposes a procedure to deal with n-layered inclusion based composites with imperfect interfaces (which conditions consist of displacement or stress vector jumps) respecting spherical symmetry. For that purpose, “discontinuity matrices” have been introduced. These matrices have been derived for several classical interface-models and an asymptotic method has been used to determine some of them. A self-consistent condition based on a strain-energy equivalence in the case of inclusion-matrix type composite materials is restated for n-layered inclusions with imperfect interfaces and applied to get estimates of such composites materials. The remarkable feature of the presently self consistent approach is that it does not need any tedious algebra providing the attached interface models respect the spherical symmetry. The present Generalized Self Consistent Model (GSCM) is then used to study size effects and mismatch in composites reinforced by coated inclusions. 相似文献
18.
Stress–Strain State of a Ferromagnetic with a Paraboloidal Inclusion in a Homogeneous Magnetic Field
The stress–strain state of an infinite elastic soft ferromagnetic medium with an elliptic paraboloidal inclusion is analyzed. The material of the inclusion is a soft ferromagnetic too. The medium is in a magnetic field directed along the minor axis of the elliptic section of the paraboloid by a plane perpendicular to its axis. The main characteristics of the stress–strain state and induced magnetic fields in the medium and inclusion are determined. The features of the stress distribution over the inclusion boundary are studied 相似文献
19.
Nonsimilarity solutions for non-Darcy mixed convection from a vertical impermeable surface embedded in a saturated porous
medium are presented for variable surface heat flux (VHF) of the power-law form. The entire mixed convection region is divided
into two regimes. One region covers the forced convection dominated regime and the other one covers the natural convection
dominated regime. The governing equations are first transformed into a dimensionless form by the nonsimilar transformation
and then solved by a finite-difference scheme. Computations are based on Keller Box method and a tolerance of iteration of
10−5 as a criterion for convergence.
Three physical aspects are introduced. One measures the strength of mixed convection where the dimensionless parameter Ra*
x
/Pe3/2
x
characterizes the effect of buoyancy forces on the forced convection; while the parameter Pe
x
/Ra*2/3
x
characterizes the effect of forced flow on the natural convection. The second aspect represents the effect of the inertial
resistance where the parameter K′U
∞/ν is found to characterize the effect of inertial force in the forced convection dominated regime, while the parameter (K′U
∞/ν)(Ra*2/3
x
/Pe
x
) characterizes the effect of inertial force in the natural convection dominated regime. The third aspect is the effect of
the heating condition at the wall on the mixed convection, which is presented by m, the power index of the power-law form heating condition.
Numerical results for both heating conditions are carried out. Distributions of dimensionless temperature and velocity profiles
for both Darcy and non-Darcy models are presented.
Received on 26 May 1997 相似文献
20.
MOTIONS, FORCES AND MODE TRANSITIONS IN VORTEX-INDUCED VIBRATIONS AT LOW MASS-DAMPING 总被引:8,自引:0,他引:8
These experiments, involving the transverse oscillations of an elastically mounted rigid cylinder at very low mass and damping, have shown that there exist two distinct types of response in such systems, depending on whether one has a low combined mass-damping parameter (low m*ζ), or a high mass-damping (highm*ζ ). For our low m*ζ, we find three modes of response, which are denoted as an initial amplitude branch, an upper branch and a lower branch. For the classical Feng-type response, at highm*ζ , there exist only two response branches, namely the initial and lower branches. The peak amplitude of these vibrating systems is principally dependent on the mass-damping (m*ζ), whereas the regime of synchronization (measured by the range of velocity U*) is dependent primarily on the mass ratio, m*ζ. At low (m*ζ), the transition between initial and upper response branches involves a hysteresis, which contrasts with the intermittent switching of modes found, using the Hilbert transform, for the transition between upper–lower branches. A 180° jump in phase angle φ is found only when the flow jumps between the upper–lower branches of response. The good collapse of peak-amplitude data, over a wide range of mass ratios (m*=1–20), when plotted against (m*+CA) ζ in the “Griffin” plot, demonstrates that the use of a combined parameter is valid down to at least (m*+CA)ζ 0·006. This is two orders of magnitude below the “limit” that had previously been stipulated in the literature, (m*+CA) ζ>0·4. Using the actual oscillating frequency (f) rather than the still-water natural frequency (fN), to form a normalized velocity (U*/f*), also called “true” reduced velocity in recent studies, we find an excellent collapse of data for a set of response amplitude plots, over a wide range of mass ratiosm* . Such a collapse of response plots cannot be predicted a priori, and appears to be the first time such a collapse of data sets has been made in free vibration. The response branches match very well the Williamson–Roshko (Williamson & Roshko 1988) map of vortex wake patterns from forced vibration studies. Visualization of the modes indicates that the initial branch is associated with the 2S mode of vortex formation, while the Lower branch corresponds with the 2P mode. Simultaneous measurements of lift and drag have been made with the displacement, and show a large amplification of maximum, mean and fluctuating forces on the body, which is not unexpected. It is possible to simply estimate the lift force and phase using the displacement amplitude and frequency. This approach is reasonable only for very low m*. 相似文献