scholarly journals Complex variable formulation for non-slipping plane strain contact of two elastic solids in the presence of interface mismatch eigenstrain

2012 ◽  
Vol 49 (9) ◽  
pp. 1177-1188 ◽  
Author(s):  
Lifeng Ma ◽  
Alexander M. Korsunsky
Keyword(s):  
Plane Strain ◽  
Complex Variable ◽  
Elastic Solids ◽  
Slipping Plane

Exact determination of gravity stresses in finite elastic slopes: Part I. Theoretical considerations

1983 ◽  
Vol 20 (1) ◽  
pp. 47-54 ◽  
Author(s):  
V. Silvestri ◽  
C. Tabib
Keyword(s):  
Plane Strain ◽  
Half Plane ◽  
Inclination Angle ◽  
Complex Variable ◽  
Earth Pressure ◽  
Exact Distributions ◽  
Exact Determination ◽  
Upper Half Plane ◽  
Theoretical Considerations

The exact distributions of gravity stresses are obtained within slopes of finite height inclined at various angles, −β (β = π/2, π/3, π/4, π/6, and π/8), to the horizontal. The solutions are obtained by application of the theory of a complex variable. In homogeneous, isotropic, and linearly elastic slopes under plane strain conditions, the gravity stresses are independent of Young's modulus and are a function of (a) the coordinates, (b) the height, (c) the inclination angle, (d) Poisson's ratio or the coefficient of earth pressure at rest, and (e) the volumetric weight. Conformal applications that transform the planes of the various slopes studied onto the upper half-plane are analytically obtained. These solutions are also represented graphically.

scholarly journals Plane-strain waves in nonlinear elastic solids with softening

Wave Motion ◽  
2019 ◽  
Vol 89 ◽  
pp. 65-78 ◽  
Author(s):  
Harold Berjamin ◽  
Bruno Lombard ◽  
Guillaume Chiavassa ◽  
Nicolas Favrie
Keyword(s):  
Plane Strain ◽  
Elastic Solids ◽  
Strain Waves ◽  
Nonlinear Elastic

Thermal Stresses in Plane Strain of Porous Elastic Solids

Meccanica ◽  
2004 ◽  
Vol 39 (2) ◽  
pp. 125-138 ◽  
Author(s):  
D. Ieşan ◽  
L. Nappa
Keyword(s):  
Plane Strain ◽  
Thermal Stresses ◽  
Elastic Solids

Magnetic Fields Generated by a Mechanical Singularity in a Magnetized Elastic Half Plane

1989 ◽  
Vol 56 (1) ◽  
pp. 89-95 ◽  
Author(s):  
Chau-Shioung Yeh
Keyword(s):  
Fourier Transform ◽  
Magnetic Fields ◽  
Exact Solutions ◽  
Closed Form ◽  
Plane Strain ◽  
Half Plane ◽  
Elastic Solids ◽  
Soft Ferromagnetic ◽  
Single Force ◽  
The Fourier Transform

The induced magnetic fields generated by a line mechanical singularity in a magnetized elastic half plane are investigated in this paper. One version of linear theory for soft ferromagnetic elastic solids which has been developed by Pao and Yeh (1973) is adopted to analyze the plane strain problem undertaken. By applying the Fourier transform technique, the exact solutions for the generated magnetic inductions due to various mechanical singularities such as a single force, a dipole, and single couple are obtained in a closed form. The distributions of the generated inductions on the surface are shown with figures.

Linearized plane strain of a mixture of two elastic solids. II

1968 ◽  
Vol 64 (3) ◽  
pp. 915-930 ◽  
Author(s):  
T. R. Steel
Keyword(s):  
Plane Strain ◽  
Complex Potential ◽  
Potential Functions ◽  
Equilibrium Equations ◽  
Elastic Solids

AbstractIn a recent paper (1), we derived the solutions to the equilibrium equations for linearized plane strain of an isotropic mixture of two elastic solids. The solutions were given in terms of four complex potential functions. Here we examine the properties of these solutions and evaluate the forces and couples across an arc in the mixture.

scholarly journals Dislocations and inclusions in prestressed metals

2013 ◽  
Vol 469 (2154) ◽  
pp. 20120752 ◽  
Author(s):  
Luca Argani ◽  
Davide Bigoni ◽  
Gennady Mishuris
Keyword(s):  
Shear Band ◽  
Constitutive Model ◽  
Plane Strain ◽  
Deformation Theory ◽  
Shear Band Formation ◽  
Dislocation Dipole ◽  
Elastic Solids ◽  
Band Formation ◽  
Ductile Metals ◽  
Nonlinear Elastic

The effect of prestress on dislocation (and inclusion) fields in nonlinear elastic solids is analysed by extending previous solutions by Eshelby and Willis. Using a plane-strain constitutive model (for incompressible incremental nonlinear elasticity) to describe the behaviour of ductile metals ( J 2 -deformation theory of plasticity), we show that when the level of prestress is high enough that shear band formation is approached, strongly localized strain patterns emerge, when a dislocation dipole is emitted by a source. These may explain cascade activation of dislocation clustering along slip band directions.

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