Eigenstresses in a Nonlinearly Elastic Sphere with Distributed Dislocations

2019 ◽  
pp. 137-155
Author(s):  
Evgeniya V. Goloveshkina ◽  
Leonid M. Zubov
Keyword(s):  
Elastic Sphere ◽  
Nonlinearly Elastic ◽  
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.

scholarly journals The effect of distributed dislocations on bending of a rectangular beam with a preliminarily stressed layer under superposition of large strains

2019 ◽  
Vol 485 (6) ◽  
pp. 686-690
Author(s):  
V. A. Levin ◽  
L. M. Zubov ◽  
K. M. Zingerman
Keyword(s):  
Strain State ◽  
Elastic Solid ◽  
Numerical Results ◽  
Large Strains ◽  
Stress Strain ◽  
Stress Strain State ◽  
Stressed Layer ◽  
Nonlinearly Elastic ◽  
Formulation Of Problems ◽  
Distributed Dislocations

The formulation of problems on the equilibrium of a nonlinearly elastic solid with continuously distributed dislocations is proposed for the case of superposition of large strains. The numerical results showing the effect of distributed dislocations on the stress-strain state of the beam are presented.

Cavitation in Nonlinearly Elastic Solids: A Review

1995 ◽  
Vol 48 (8) ◽  
pp. 471-485 ◽  
Author(s):  
C. O. Horgan ◽  
D. A. Polignone
Keyword(s):  
Rapid Growth ◽  
Original Work ◽  
Tensile Load ◽  
Elastic Sphere ◽  
Extensive Investigation ◽  
Elastic Solids ◽  
The Subject ◽  
Bifurcation Problems ◽  
Nonlinearly Elastic ◽  
Theoretical Developments

Cavitation phenomena in nonlinearly elastic solids have been the subject of extensive investigation in recent years. The impetus for much of these theoretical developments has been supplied by pioneering work of Ball in 1982. Ball investigated a class of bifurcation problems for the equations of nonlinear elasticity which model the appearance of a cavity in the interior of an apparently solid homogensous isotropic elastic sphere or cylinder once a critical external tensile load is attained. This model may also be interpreted in terms of the sudden rapid growth of a pre-existing microvoid. In this paper, we briefly summarize some of the main results obtained to date on radially symmetric cavitation, using the bifurcation model. The paper is a review and a comprehensive list of references is given to original work where details of the analyses may be found.

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