Nonlinear Deformations of an Elastic Sphere with Couple Stresses and Distributed Dislocations

2020 ◽  
pp. 175-187
Author(s):  
Leonid M. Zubov
Keyword(s):  
Elastic Sphere ◽  
Couple Stresses ◽  
Nonlinear Deformations ◽  
Distributed Dislocations

Influence of Distributed Dislocations on Stability of Hollow Nonlinearly Elastic Sphere

2020 ◽  
pp. 17-21
Author(s):  
Evgeniya V. Goloveshkina
Keyword(s):  
Boundary Value Problem ◽  
Elasticity Theory ◽  
Elastic Body ◽  
Nonlinear Elasticity ◽  
External Pressure ◽  
Elastic Sphere ◽  
Unperturbed State ◽  
Nonlinear Elasticity Theory ◽  
Edge Dislocations ◽  
Distributed Dislocations

The phenomenon of stability loss of a hollow elastic sphere containing distributed dislocations and loaded with external hydrostatic pressure is studied. The study was carried out in the framework of the nonlinear elasticity theory and the continuum theory of continuously distributed dislocations. An exact statement and solution of the stability problem for a three-dimensional elastic body with distributed dislocations are given. The static problem of nonlinear elasticity theory for a body with distributed dislocations is reduced to a system of equations consisting of equilibrium equations, incompatibility equations with a given dislocation density tensor, and constitutive equations of the material. The unperturbed state is caused by external pressure and a spherically symmet-ric distribution of dislocations. For distributed edge dislocations in the framework of a harmonic (semi-linear) mate-rial model, the unperturbed state is defined as an exact spherically symmetric solution to a nonlinear boundary value problem. This solution is valid for any function that characterizes the density of edge dislocations. The perturbed equilibrium state is described by a boundary value problem linearized in the neighborhood of the equilibrium. The analysis of the axisymmetric buckling of the sphere was performed using the bifurcation method. It consists in determining the equilibrium positions of an elastic body, which differ little from the unperturbed state. By solving the linearized problem, the value of the external pressure at which the sphere first loses stability is found. The effect of dislocations on the buckling of thin and thick spherical shells is analyzed.

Study of couple stresses and wall permeability effects on the flow in permeable membranes

2021 ◽  
Vol 69 ◽  
pp. 271-284
Author(s):  
Muhammad Kahshan ◽  
Dianchen Lu ◽  
A. Khan ◽  
Naeem Faraz
Keyword(s):  
Couple Stresses ◽  
Wall Permeability

scholarly journals Continuum elastic sphere vibrations as a model for low lying optical modes in icosahedral quasicrystals

2005 ◽  
Vol 17 (23) ◽  
pp. 3559-3565 ◽  
Author(s):  
E Duval ◽  
L Saviot ◽  
A Mermet ◽  
D B Murray
Keyword(s):  
Elastic Sphere ◽  
Optical Modes ◽  
Icosahedral Quasicrystals

Ultrasonic Scattering by an Elastic Sphere in Matrix with Imperfect Interface

2004 ◽  
Vol 21 (10) ◽  
pp. 1979-1982 ◽  
Author(s):  
Wu Rui-Xin ◽  
Wang Yao-Jun
Keyword(s):  
Imperfect Interface ◽  
Elastic Sphere ◽  
Ultrasonic Scattering
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