A Circular Inclusion With Imperfect Interface: Eshelby’s Tensor and Related Problems

1995 ◽  
Vol 62 (4) ◽  
pp. 860-866 ◽  
Author(s):  
Zhanjun Gao
Keyword(s):  
Closed Form Solution ◽  
Subsequent Development ◽  
Physical Nature ◽  
Circular Inclusion ◽  
Imperfect Interface ◽  
Form Solution ◽  
Normal Displacement ◽  
Tangential Displacement ◽  
Shear Stresses ◽  
Eshelby’S Tensor

Eshelby’s tensor for an ellipsoidal inclusion with perfect bonding at interface has proven to have a far-reaching influence on the subsequent development of micromechanics of solids. However, the condition of perfect interface is often inadequate in describing the physical nature of the interface for many materials in various loading situations. In this paper, Airy stress functions are used to derive Eshelby’s tensor for a circular inclusion with imperfect interface. The interface is modeled as a spring layer with vanishing thickness. The normal and tangential displacement discontinuities at the interface are proportional to the normal and shear stresses at the interface. Unlike the case of the perfectly bonded inclusion, the Eshelby’s tensor is, in general, not constant for an inclusion with the spring layer interface. The normal stresses are dependent on the shear eigenstrain. A closed-form solution for a circular inclusion with imperfect interface under general two-dimensional eigenstrain and uniform tension is obtained. The possible normal displacement overlapping at the interface is discussed. The conditions for nonoverlapping are established.

Closed-form solution for a coated circular inclusion under uniaxial tension

2012 ◽  
Vol 223 (5) ◽  
pp. 937-951 ◽  
Author(s):  
Y. E. Pak ◽  
D. Mishra ◽  
S. -H. Yoo
Keyword(s):  
Closed Form ◽  
Uniaxial Tension ◽  
Closed Form Solution ◽  
Circular Inclusion ◽  
Form Solution

Effect of temperature variation on the plate-end debonding of FRP-strengthened beams: A theoretical study

2021 ◽  
pp. 136943322110463
Author(s):  
Dong Guo ◽  
Wan-Yang Gao ◽  
Dilum Fernando ◽  
Jian-Guo Dai
Keyword(s):  
Temperature Variation ◽  
Thermal Loading ◽  
Closed Form Solution ◽  
Form Solution ◽  
Effect Of Temperature ◽  
Shear Stresses ◽  
Limited Information ◽  
Element Analysis ◽  
Bond Slip ◽  
Loading Effects

Steel/concrete structures strengthened with externally bonded FRP plates may be subjected to significant temperature variations during their service time. Such temperature variation (i.e., thermal loading) may significantly influence the debonding mechanism in FRP-strengthened structures due to the thermal incompatibility between the FRP plate and the substrate as well as the temperature-induced bond degradation at the FRP-to-steel/concrete interface. However, limited information is available on the effect of temperature variation on the debonding failure in FRP-strengthened beams. This paper presents a new and closed-form solution to investigate the plate-end debonding failure of the FRP-strengthened beam subjected to combined thermal and mechanical (i.e., flexural) loading. A bilinear bond-slip model is used to describe the bond behavior of the FRP-to-substrate interface. The analytical solution is validated through comparisons with finite element analysis results regarding the distributions of the interfacial shear stresses, the interfacial slips and the axial stresses of the FRP plate. Given that a constant bond-slip relationship is adopted, it is observed that an increase in service temperature will lead to an increased interfacial slip at the plate end and consequently a reduced plate-end debonding load, and vice versa. Further parametric studies have indicated that the thermal loading effects become more significant when shorter and stiffer FRP plates are applied for strengthening.

Closed Form Solution of the Exterior-Point Eshelby Tensor for an Elliptic Cylindrical Inclusion

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
B. R. Kim ◽  
H. K. Lee
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Eshelby Tensor ◽  
Cylindrical Inclusion ◽  
Normal Vector ◽  
Eshelby’S Tensor ◽  
Cylindrical Inclusions ◽  
Outward Unit ◽  
Outward Unit Normal Vector

With the help of the I-integrals expressed by Mura (1987, Micromechanics of Defects in Solids, 2nd ed., Martinus Nijhoff, Dordrecht) and the outward unit normal vector introduced by Ju and Sun (1999, “A Novel Formulation for the Exterior-Point Eshelby’s Tensor of an Ellipsoidal Inclusion,” ASME Trans. J. Appl. Mech., 66, pp. 570–574), the closed form solution of the exterior-point Eshelby tensor for an elliptic cylindrical inclusion is derived in this work. The proposed closed form of the Eshelby tensor for an elliptic cylindrical inclusion is more explicit than that given by Mura, which is rough and unfinished. The Eshelby tensor for an elliptic cylindrical inclusion can be reduced to the Eshelby tensor for a circular cylindrical inclusion by letting the aspect ratio of the inclusion α=1. The closed form Eshelby tensor presented in this study can contribute to micromechanics-based analysis of composites with elliptic cylindrical inclusions.

Gravity-Driven Granular Flows of Smooth, Inelastic Spheres Down Bumpy Inclines

1990 ◽  
Vol 57 (4) ◽  
pp. 1036-1043 ◽  
Author(s):  
M. W. Richman ◽  
R. P. Marciniec
Keyword(s):  
Solid Fraction ◽  
Constitutive Relations ◽  
Closed Form Solution ◽  
Form Solution ◽  
Shear Stresses ◽  
Steady Flows ◽  
Mean Velocity ◽  
Flow Rates ◽  
Gravity Driven ◽  
Fast Flow

We employ a kinetic constitutive theory that includes the effects of particle transport and collisions to analyze steady, fully developed, gravity-driven flows of smooth, inelastic spheres down bumpy inclines. By replacing the solid fraction by its depth-averaged value wherever it occurs in the balance equations, we obtain a closed-form solution for the granular temperature profile, which when employed in the constitutive relations for the normal and shear stresses determines the solid fraction and mean velocity profiles. The solutions ensure that the stresses and energy flux vanish at the free surface and that the balance of momentum and energy are satisfied at the base. We also determine for fixed flow rates the ranges of inclinations within which steady flows are possible, and for fixed inclinations the depths of the resulting flows. Most striking are the inclinations and flow rates at which both a dilute, fast flow and a dense, slow flow are possible.

Transient Response of an Infinite Elastic Medium Containing a Spherical Cavity Subjected to Torsion

1999 ◽  
Vol 67 (2) ◽  
pp. 282-287 ◽  
Author(s):  
U. Zakout ◽  
Z. Akkas ◽  
G. E. Tupholme
Keyword(s):  
Elastic Medium ◽  
Transient Response ◽  
Spherical Cavity ◽  
Laplace Transformation ◽  
Closed Form Solution ◽  
Form Solution ◽  
Shear Stresses ◽  
Surface Loading ◽  
Transformation Techniques ◽  
Isotropic Elastic Medium

An exact closed-form solution is obtained for the transient response of an infinite isotropic elastic medium containing a spherical cavity subjected to torsional surface loading using the residual variable method. The main advantage of the present approach is that it eliminates the computational problems arising in the existing methods which are primarily based on Fourier or Laplace transformation techniques. Extensive numerical results for the circumferential displacements and shear stresses at various locations are presented graphically for Heaviside loadings. [S0021-8936(00)01102-8]

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

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