An Analysis of Power Law Viscous Materials Under a Plane-Strain Condition Using Complex Stream and Stress Functions

Abstract

The equilibrium and compatibility equations for nonlinear viscous materials described by the power law are solved by introducing the complex stream and stress function. The stresses, strain rates, and velocities derived from the summation form of the stream function and the product form of the stress function are identical to the results obtained from the axially symmetric field equation. The stream function solution is used in the deformation analysis of a viscous hollow cylindrical inclusion buried in an infinitely large viscous medium assuming an equal biaxial boundary stress. The stream function approach is used in determining the stress-concentration factor for a cavity in a viscous material subject to the identical boundary biaxial stress. The results agree with the results of Nadai. The effect of the strain-rate-hardening exponent, the geometry of the inclusion, and the material constants on the hoop stress-concentration factor in the interface between the inclusion and the matrix are discussed.