Abstract
The purpose of this paper is to present a study of elastoplastic deformation in an isotropic material disk with shaft subjected to variable density and load using Seth’s transition theory. This theory includes classical macroscopic solving problems in plasticity, creep and relaxation and assumes semi-empirical yield conditions. It has been observed that the values of angular speed decreased with increases in the values of the density parameter for an incompressible material. Radial stress has the maximum value at the internal surface of the rotating disk made of incompressible material (i.e., rubber) as compared to the compressible materials (i.e., saturated clay and copper).
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Abbreviations
- \( \hat{\varepsilon }_{ij} \) :
-
Principal finite strain components
- \( K_{1} \), \( K_{2} \) :
-
Constants of integration
- E :
-
Young’s modulus
- \( r_{i} ,r_{0} \) :
-
Inner and outer radii of the disk, respectively
- \( c \) :
-
Compressibility factor
- \( \rho \) :
-
Density of material
- \( u,v,w \) :
-
Displacement components
- \( r,\theta ,z \) :
-
Radial, circumferential and axial directions
- \( \omega \) :
-
Angular velocity of rotation
- \( \delta_{ij} \) :
-
Kronecker’s delta
- Y :
-
Yield stress
- v :
-
Poisson’s ratio
- l 0 :
-
Mechanical load
- \( \lambda ,\mu \) :
-
Lame’s constants
- \( \tau_{ij} ,\varepsilon_{ij} \) :
-
Stress and strain components
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Sethi, M., Thakur, P. Elastoplastic deformation in an isotropic material disk with shaft subjected to load and variable density. J Rubber Res 23, 69–78 (2020). https://doi.org/10.1007/s42464-020-00038-8
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DOI: https://doi.org/10.1007/s42464-020-00038-8