Adiabatic heating effect in elastic-plastic contraction / expansion of spherical cavity in isotropic incompressible material

2021 ◽  
Vol 87 ◽  
pp. 104223
Author(s):  
Georgiy M. Sevastyanov
Keyword(s):  
Spherical Cavity ◽  
Incompressible Material ◽  
Adiabatic Heating ◽  
Heating Effect ◽  
Elastic Plastic

scholarly journals Thermo elastic-plastic transition in a thin rotating disc with inclusion

2007 ◽  
Vol 11 (1) ◽  
pp. 103-118 ◽  
Author(s):  
Kumar Gupta ◽  
P Pankaj
Keyword(s):  
Thermal Effect ◽  
Internal Surface ◽  
Angular Speed ◽  
Incompressible Material ◽  
Plastic State ◽  
Percentage Increase ◽  
Compressible Material ◽  
Rotating Disc ◽  
Elastic Plastic ◽  
Different Temperatures

Stresses for the elastic-plastic transition and fully plastic state have been derived for a thin rotating disc with shaft at different temperatures and results have been discussed and depicted graphically. It has been observed that the rotating disc with inclusion and made of compressible material requires lesser angular speed to yield at the internal surface and higher percentage increase in angular speed to become fully plastic as compare to disc made of incompressible material. With the introduction of thermal effect the rotating disc with inclusion required lesser angular speed to yield at the internal surface. Rotating disc made of compressible material with inclusion requires higher percentage increase in angular speed to become fully-plastic as compare to disc made of incompressible material. Thermal effect also increases the values of radial and circumferential stresses at the internal surface for fully-plastic state. .

Dynamic Expansion of a Spherical Cavity in an Elastic, Perfectly Plastic Material

1968 ◽  
Vol 35 (2) ◽  
pp. 372-378 ◽  
Author(s):  
Chi-Hung Mok
Keyword(s):  
Spherical Cavity ◽  
High Speed ◽  
Numerical Solutions ◽  
Plastic Material ◽  
Numerical Technique ◽  
Nonlinear Dependence ◽  
Static Approximation ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

It is shown that initial and boundary-value problems involving high-speed elastic-plastic deformation with spherical symmetry can be solved using a finite-difference numerical technique. Numerical solutions for the dynamic expansion of a spherical cavity under a constant pressure are presented to demonstrate the nature and capability of the numerical scheme. While the solution for an elastic material agrees closely with the exact one, the solution for an elastic, perfectly plastic material also receives support from Green’s analytic predictions concerning the motion of the elastic-plastic boundary. At large times, the asymptotic solution of the dynamic elastic-plastic problem is different from the quasi-static solution. This result indicates that the concept of quasi-static approximation may not hold in dynamic plasticity. A nonlinear dependence of the plastic solution on the boundary condition is also observed.

Dynamic Spherical Cavity-Expansion in a Compressible Elastic-Plastic Solid

1988 ◽  
Vol 55 (2) ◽  
pp. 275-279 ◽  
Author(s):  
M. J. Forrestal ◽  
V. K. Luk
Keyword(s):  
Analytical Model ◽  
Spherical Cavity ◽  
Cavity Expansion ◽  
Spherically Symmetric ◽  
Compressible Material ◽  
Plastic Response ◽  
Elastic Plastic ◽  
Symmetric Cavity ◽  
Uniform Expansion ◽  
Spherical Cavity Expansion

We developed an analytical model for the elastic-plastic response of a compressible material from the uniform expansion of a spherically symmetric cavity. Previous models consider the material as incompressible. Numerical results from both models showed the effect of compressibility.

Dynamic Spherical Cavity Expansion of Strain-Hardening Materials

1991 ◽  
Vol 58 (1) ◽  
pp. 1-6 ◽  
Author(s):  
V. K. Luk ◽  
M. J. Forrestal ◽  
D. E. Amos
Keyword(s):  
Numerical Solution ◽  
Closed Form ◽  
Strain Hardening ◽  
Power Law ◽  
Spherical Cavity ◽  
Incompressible Material ◽  
Cavity Expansion ◽  
Closed Form Solutions ◽  
Spherical Cavities ◽  
Spherical Cavity Expansion

We developed models for the dynamic expansion of spherical cavities from zero initial radii for elastic-plastic, rate-independent materials with power-law strain hardening. The models considered the material as incompressible and compressible. For an incompressible material, we obtained closed-form solutions, whereas the compressible results required the numerical solution of differential equations. A comparison of the numerical results from both models showed the effect of compressibility.

scholarly journals Elastic-plastic transition stresses in a thin rotating disc with rigid inclusion by infinitesimal deformation under steady-state temperature

2010 ◽  
Vol 14 (1) ◽  
pp. 209-219 ◽  
Author(s):  
Thakur Pankaj
Keyword(s):  
Outer Surface ◽  
Room Temperature ◽  
Circumferential Stress ◽  
Internal Surface ◽  
Angular Speed ◽  
Incompressible Material ◽  
Plastic State ◽  
Rotating Disc ◽  
Elastic Plastic ◽  
Different Temperatures

Stresses for the elastic-plastic transition and fully plastic state have been derived for a thin rotating disc with rigid shaft at different temperatures and results have been discussed and depicted graphically. It has been observed that at room temperature rotating disc made of compressible material and of smaller radii ratio yields at the internal surface at a higher angular speed as compared to rotating disc made of incompressible material. With the introduction of thermal effect rotating disc yields at the outer surface at a lesser angular speed as compared to rotating disc at room temperature. The circumferential stress is maximum at the outer surface of the rotating disc with further increases with the increase in temperature. It means that angular speed of the rotating disc is less than that of the temperature-loaded disc in the fully plastic case.

Elastic-Plastic State of Inhomogeneous Soil Array with a Spherical Cavity

2013 ◽  
Vol 842 ◽  
pp. 462-465 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Anatoliy S. Avershyev ◽  
Stanislaw Jemiolo
Keyword(s):  
Plastic Deformation ◽  
Outer Surface ◽  
Spherical Cavity ◽  
Plastic Material ◽  
Plastic State ◽  
Cavity Model ◽  
Limit Loads ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The article deals with the elastic-plastic state of inhomogeneous array with a spherical cavity. Model is used thick-walled ball of an elastic-perfectly plastic material (Prandtl diagram). It is shown that in the inhomogeneous material, depending on the inhomogeneity functions describing the change of the modulus of elasticity and yield stress of soil plastic deformation may appear on both the inner and outer surface of the ball and inside it. Are found values of the limit loads, displacement diagrams are constructed in an array.

Displacements in a Wide Curved Bar Subjected to Pure Elastic-Plastic Bending

1957 ◽  
Vol 24 (3) ◽  
pp. 447-452
Author(s):  
Bernard W. Shaffer ◽  
Raymond N. House
Keyword(s):  
Applied Load ◽  
Bending Moment ◽  
Incompressible Material ◽  
Pure Bending ◽  
Plastic Bending ◽  
Elastic Case ◽  
Elastic Plastic ◽  
Material Thickness ◽  
Perfectly Plastic ◽  
Order Of Magnitude

Abstract Equations have been obtained for the displacements and strains within a wide curved bar made of a perfectly plastic, incompressible material subjected to a pure bending moment which is sufficiently large to cause elastic-plastic stresses. It is found that whenever the applied load is within 95 per cent of the fully plastic bending moment, displacements and strains in the elastic-plastic problem are of the order of magnitude of the corresponding elastic case. It is also found that when the bending moment reaches approximately 65 per cent of the fully plastic bending moment, the change in material thickness reaches a maximum. It decreases to zero when the bar becomes completely plastic.

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