Application of the maximum rate of dissipation criterion to dilatant, pressure dependent plasticity models

摘要

The purpose of this paper is to demonstrate the efficacy of the maximum rate of dissipation criterion to derive constitutive relations for dilatant pressure dependent elastoplastic materials (including certain soil and rock mechanics models as well as models for crushable foams). Hitherto, it has been assumed in the literature that such materials do not satisfy the maximum rate of dissipation criterion without additional constraints. This paper elucidates how the approach using the maximum rate of dissipation can be applied to derive the constitutive equations for rate independent plasticity for both associative and non-associative materials in a consistent manner by using the tools of convex analysis (especially gauge functions) and rate of dissipation functions that are not "normlike" (a notion that will be discussed in the paper). The results obtained in the paper show that a wide class of models for which the "plastic potential" is not the same as the yield function (i.e., the flow rule is "non-associative") can be derived from this assumption in a relatively straightforward manner and without the need for any additional constraints. Specifically, both the yield function and the flow potential can be derived from the rate of dissipation function through the maximization process. As examples of the application of the general approach, the evolution equations for the Drucker-Prager and crushable foam models (where plastic volume change occurs and the plastic strain rate is not directed along the normal to the yield surface) are derived.