The Influence of Distributed Dislocations on Large Deformations of an Elastic Sphere

2016 ◽  
pp. 61-76 ◽  
Author(s):  
Evgeniya V. Zhbanova ◽  
Leonid M. Zubov
Keyword(s):  
Large Deformations ◽  
Elastic Sphere ◽  
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.

On Compression of Rubber Elastic Sphere Over a Large Range of Displacements—Part 2: Comparison of Theory and Experiment

1991 ◽  
Vol 113 (3) ◽  
pp. 292-295 ◽  
Author(s):  
Y. Tatara ◽  
S. Shima ◽  
J. C. Lucero
Keyword(s):  
Experimental Data ◽  
Personal Computer ◽  
Contact Surface ◽  
Large Deformations ◽  
Large Range ◽  
Elastic Sphere ◽  
Lateral Expansion ◽  
Simple Compression ◽  
Theory And Experiment ◽  
Soft Rubber

This paper presents experimental results of simple compression of a soft rubber sphere in a very large range of forces attaining at 5000 N, presenting calculational results by a set of five equations presented in Part 1. The calculational values of approach, the radius of contact surface, and lateral expansion agree well with the experimental data in the large range of deformations. It is thus verified experimentally that the set of the equations (12), (13), (31), (40), and (43) in Part 1 is approximately valid in large deformations for rubber sphere. Program using a personal computer in calculating five quantities from the five nonlinear equations associated with the five quantities is noted.

On the Mechanical Behavior of the Orthotropic Cord-Rubber Composite

1976 ◽  
Vol 4 (4) ◽  
pp. 219-232 ◽  
Author(s):  
Ö. Pósfalvi
Keyword(s):  
Mechanical Behavior ◽  
Uniaxial Tension ◽  
Elastic Properties ◽  
Large Deformations ◽  
Virtual Work ◽  
Poisson's Ratio ◽  
Principle Of Virtual Work ◽  
Effective Elastic Properties ◽  
Rubber Composite ◽  
Mooney Equation

Abstract The effective elastic properties of the cord-rubber composite are deduced from the principle of virtual work. Such a composite must be compliant in the noncord directions and therefore undergo large deformations. The Rivlin-Mooney equation is used to derive the effective Poisson's ratio and Young's modulus of the composite and as a basis for their measurement in uniaxial tension.

The dynamics of an orthotropic torus undergoing large deformations

1994 ◽  
Author(s):  
Raouf Raouf ◽  
Anthony Palazotto
Keyword(s):  
Large Deformations
Sign in / Sign up

Export Citation Format

Share Document