Existence and uniqueness of spherically-symmetric elastic-plastic interface motions

Abstract

T he spherically-symmetric motion of interfaces between regions deforming elastically and those deforming plastically is considered. It has been shown elsewhere (for example, in work by L.W. M orland and A.D. C ox (1969) and M.J. K enning (1974)) that, during both spherically-symmetric and uniaxial motions in rate-independent materials, six essentially different types of motion can occur. In the case of uniaxial motions, these six types have been shown to be unique. In the present paper, the response coefficients in the governing constitutive, stress-rate/strain-rate equations are held constant, but the existence of two classical elastic moduli is not assumed, nor is the usual simplifying assumption of plastic incompressibility made. By means of a local expansion procedure, together with matching across the curves of discontinuity which may exist in the space-time plane, explicit relations for the lowest possible order of non-vanishing rate-of-change of the yield function in terms of the given initial distributions of stress, strain and velocity are obtained for a complete set of interface speeds. The validity conditions for each of the six possible types of motion are then used to give restrictions on the initial distributions. It is shown that the sets of restrictions for each motion are exclusive, and hence that each motion is unique.