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The Quarterly Journal of Mechanics and Applied Mathematics 1987 40(1):89-104; doi:10.1093/qjmam/40.1.89
© 1987 by Oxford University Press
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ANALYTICAL AND NUMERICAL SOLUTION OF MATERIALS EXHIBITING STRAIN HARDENING OR TEMPERATURE-DEPENDENT VISCOSITY

NICOLAS CHARALAMBAKIS and EFTHIMIA MITSOPOULOU

( Aristotle University of Thessaloniki Thessaloniki, Greece )

We consider plastic shearing of plates or shearing flow of incompressible Newtonian fluids under steady shearing force at the boundary. The nonlinear constitutive relation for the stress induces a destabilizing mechanism on both processes. Here we are interested in whether the dependence of viscosity upon temperature in viscous liquids or the existence of strain hardening in solids, may ensure the asymptotic stability of the solution. We prove that asymptotic stability exists under certain conditions, and present numerical examples that agree with the analytical solution.


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