Rudnicki and Rice’s Analysis of Strain Localization Revisited

Abstract

In a celebrated paper published in 1975, Rudnicki and Rice (RR) analyzed the conditions for strain localization in pressure-sensitive dilatant materials. This paper corrects certain results in their work that are relevant in exceptional cases. RR found that the normal to the plane of localization was generally orthogonal to the direction of the intermediate principal stress; however, when a certain inequality was satisfied, it was orthogonal to the direction of the minimum principal stress. In contrast, it is shown here that the normal to the plane of localization is always orthogonal to the direction of the intermediate principal stress; but there is a special case where it is parallel to the direction of either the maximum or the minimum principal stress, and in this case the expression of the critical hardening modulus at localization differs from that given by RR.