Interdependence of the Yield Condition and the Stress-strain Relations for Plastic Flow.

1. The Fundamental Assumptions.-Denote by Sap the components of the deviation s of the stress tensor a. Let va be the components of the velocity vector v and efa the components of the rate of strain tensor e derived from the velocity vector. We impose the usual condition that the flow is incompressible, i.e., eaa = 0, which appears to be in agreement with experimental evidence. Hence e is identical with its deviation. ' We now make the following fundamental assumptions: I. The stress deviation s is an invariant of the tensor e under proper orthogonal coordinate transformations. In other words we have