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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N. Charalambakis, Adiabatic shearing flow caused by time dependent inertial force, Quart. Appl. Math. 42, 275–280 (1984)
N. Charalambakis, Adiabatic shearing of an incompressible gas caused by “oscillatory” inertial force, Bull. Greek Math. Soc. (to appear)
N. Charalambakis, Adiabatic shearing of an incompressible fluid under periodic or steady boundary conditions, J. Thermal Stresses (to appear)
R. J. Clifton, J. Duffy, K. A. Hartley and T. G. Shawki, On critical conditions for shear band formation at high strain rates, Scripta Met. 18, 443–448 (1984).
C. M. Dafermos, Global smooth solutions to the initial boundary value problem for the equations of one-dimensional nonlinear thermoviscoelasticity. SIAM J. Math. Analysis 13, 297–408 (1982)
C. M. Dafermos and L. Hsiao, Global smooth thermomechanical processes in one-dimensional nonlinear thermoviscoelasticity, J. Nonlinear Analysis 6, 435–454 (1982)
C. M. Dafermos and L. Hsiao, Adiabatic shearing of incompressible fluids with temperature dependent viscosity. Quart. Appl. Math. 41, 45–58 (1983)
C. M. Dafermos, Stabilizing effects of dissipation. Proceedings EQUADIFF 82, Springer Lecture Notes in Math. No 1017, 140–147 (1983)
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© Copyright 1986
American Mathematical Society