Analytic Solution for a Line Edge Dislocation in a Bimaterial System Incorporating Interface Elasticity

2018 ◽  
Vol 132 (2) ◽  
pp. 295-306 ◽  
Author(s):  
Ming Dai ◽  
Peter Schiavone
Keyword(s):  
Edge Dislocation ◽  
Analytic Solution ◽  
Interface Elasticity ◽  
Bimaterial System

Plane Deformations of an Inhomogeneity–Matrix System Incorporating a Compressible Liquid Inhomogeneity and Complete Gurtin–Murdoch Interface Model

2018 ◽  
Vol 85 (12) ◽  
Author(s):  
Ming Dai ◽  
Min Li ◽  
Peter Schiavone
Keyword(s):  
Analytic Solution ◽  
Elastic Solid ◽  
Compressible Liquid ◽  
External Loading ◽  
Interface Model ◽  
Interface Tension ◽  
Soft Solids ◽  
Remote Loading ◽  
Interface Elasticity ◽  
Plane Deformations

We consider the plane deformations of an infinite elastic solid containing an arbitrarily shaped compressible liquid inhomogeneity in the presence of uniform remote in-plane loading. The effects of residual interface tension and interface elasticity are incorporated into the model of deformation via the complete Gurtin–Murdoch (G–M) interface model. The corresponding boundary value problem is reformulated and analyzed in the complex plane. A concise analytical solution describing the entire stress field in the surrounding solid is found in the particular case involving a circular inhomogeneity. Numerical examples are presented to illustrate the analytic solution when the uniform remote loading takes the form of a uniaxial compression. It is shown that using the simplified G–M interface model instead of the complete version may lead to significant errors in predicting the external loading-induced stress concentration in gel-like soft solids containing submicro- (or smaller) liquid inhomogeneities.

scholarly journals Singularities interacting with interfaces incorporating surface elasticity under plane strain deformations

2014 ◽  
Vol 41 (4) ◽  
pp. 267-282 ◽  
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Plane Strain ◽  
Edge Dislocation ◽  
Surface Elasticity ◽  
Point Force ◽  
Interface Model ◽  
Interface Elasticity ◽  
Interface Parameters ◽  
Surface Mechanics ◽  
The Continuum

We consider problems involving singularities such as point force, point moment, edge dislocation and a circular Eshelby?s inclusion in isotropic bimaterials in the presence of an interface incorporating surface/interface elasticity under plane strain deformations and derive elementary solutions in terms of exponential integrals. The surface mechanics is incorporated using a version of the continuum-based surface/interface model of Gurtin and Murdoch. The results indicate that the stresses in the two half-planes are dependent on two interface parameters.

An Analytic Solution for the Noncoplanar P4P Problem with An Uncalibrated Camera

2011 ◽  
Vol 34 (4) ◽  
pp. 748-754 ◽  
Author(s):  
Yang GUO ◽  
Xiang-De ZHANG ◽  
Xin-He XU
Keyword(s):  
Analytic Solution ◽  
Uncalibrated Camera

On the convective diffusion under partial slip at wall

1989 ◽  
Vol 54 (4) ◽  
pp. 967-980 ◽  
Author(s):  
Ondřej Wein ◽  
Petr Kučera
Keyword(s):  
Mass Transfer ◽  
Numerical Solution ◽  
Analytic Solution ◽  
Convective Diffusion ◽  
Linear Velocity ◽  
Partial Slip ◽  
Accurate Calculation ◽  
Transfer Coefficients ◽  
Empirical Formulas ◽  
Mass Transfer Coefficients

Extended Leveque problem is studied for linear velocity profiles, vx(z) = u + qz. The existing analytic solution is reconsidered and shown to be inapplicable for the accurate calculation of mean mass-transfer coefficients. A numerical solution is reported and its accuracy is checked in detail. Simple but fairly accurate empirical formulas are suggested for the calculating of local and mean mass-transfer coefficients.

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