Existence and uniqueness of elastic-plastic interfaces

Abstract

A systematic discussion of the existence and uniqueness of spherically symmetric (Part I), and cylindrically symmetric (Part II), elastic-plastic interfaces is presented using non-linear constitutive laws. The work generalises results obtained by various authors, using both linear and non linear constitutive laws. An established local expansion procedure, together with matching across the curves of discontinuity which may exist in an appropriate space-time plane, provide explicit relations for the rate of change of the yield function in terms of given initial distributions, for a complete set of interface speeds. The validity conditions for each of the possible types of motion are used to give sets of inequalities satisfied by the initial distributions. It is shown that the inequalities constituting the set of validity conditions for each particular motion are consistent and exclusive, and hence that each motion exists and is unique.