Kinematic Equations Along Characteristics in Compressible Flows on the Facets of an Arbitrary Piecewise Linear Yield Criterion

Abstract—

The article deals with flows of the perfectly plastic compressible media for stress states corresponding to the facets of a piecewise linear yield criterion. Similar flows are observed, in particular, in loosely bonded Coulomb–Mohr media for plane strain states. It is assumed that the intermediate principle stress has no effect on the yielding or transition to the limit state. Under these conditions the system of kinematic differential equations belongs to the hyperbolic analytical type, the elements of the characteristic lines are instantly not elongating, the orthogonal projections of the displacement increment vector on characteristics are related by differential equations with the differentiations along the characteristic lines.