Non-uniqueness in dynamic rate-independent non-associated plasticity. Technical report, 15 June 1989-31 March 1992

Ground shock calculations often use rate-independent plasticity models with non-associated flow. By means of a 'constructive' mathematical proof, it is demonstrated here that this approach leads to multiple (and therefore spurious) solutions for dynamic initial/boundary value problems; in other words, uniqueness is lost. Although a simple class of multiple solutions is presented, the results are shown to be generally valid, implying that normality of flow is a necessary (as well as a sufficient) condition for uniqueness in dynamic applications of rate-independent plasticity. This finding implies an inherent lack of robustness in numerical analyses utilizing models based on non-associated flow. Because the use of such models is widespread in ground shock (and structural) calculations, the fact that uniqueness breaks down is significant; it casts serious doubt on any (and every) calculation based on these constitutive representations. It is strongly recommended that all ground shock calculators promptly abandon their reliance on such models. To describe the situation most bluntly, these models do not provide a rational basis for the computations needed for prediction, design and/or analysis applications. In all cases for which an associated flow rule is deemed inadequate to fit observed material behavior, an approach other than rate-independent plasticity must bemore » sought in order to represent such behavior in a reliable, self-consistent and rational manner.... Plasticity, Flow Rule, Wave Propagation, Uniqueness.« less