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Abstract

The condition of incompressibility, which is acceptable in the theory of large homothermal, elastic deformation of materials such as rubbers, is questionably so when the deformation gradient tensor is distortional, i.e., not spherical, and accompanied by large temperature variations. A form of the two-parameter Mooney-Rivlin model, modified by Chadwick to take account of compressibility and successfully matched by him to experiment by suitable choice of the material constants, is described as an example of a more general theory of rubberlike materials. This specific model is used to analyze by numerical methods the boundary value problem of azimuthal shear of cylindrical tubes, which are subject to a temperature gradient in the radial direction. It is found that the physical component B _<12> of the left Cauchy-Green strain tensor, which corresponds to a constant S_<12> component of the distortional stress tensor additional to the pressure, differs markedly from the value obtained from the incompressible theory when the temperature gradient is high and the inner radius of the tube is large in comparison to its thickness. The difference is even more marked if the tube of compressible material is allowed to expand in thickness by a small percentage.

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Thermoelastic Shear of Rubberlike Solid Cylindrical Tubes

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