Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Shearing of materials exhibiting thermal softening or temperature dependent viscosity


Author: A. E. Tzavaras
Journal: Quart. Appl. Math. 44 (1986), 1-12
MSC: Primary 76A05; Secondary 73E99
DOI: https://doi.org/10.1090/qam/840438
MathSciNet review: 840438
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Abstract: We consider the adiabatic shearing of an incompressible non-Newtonian liquid with temperature dependent viscosity, subjected to steady shearing of the boundary. Identical equations govern the plastic shearing of a solid exhibiting thermal softening and strain rate sensitivity with constitutive relation obeying a certain power law. We establish that every classical solution approaches a uniform shearing solution as $ t \to + \infty $ at specific rates of convergence. Therefore, no shear bands formation is predicted for materials of this type.


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DOI: https://doi.org/10.1090/qam/840438
Article copyright: © Copyright 1986 American Mathematical Society


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