Assessment of Cap Model: Consistent Return Algorithms and Rate-Dependent Extension

In this paper, the standard version of the inviscid two-invariant cap model is considered and a viscoplastic rate-dependent generalization is proposed. For the inviscid case, a new algorithm is proposed based on the notion of closest-point projection. Exact satisfaction of the consistency condition is shown to reduce to a single scalar equation that may be solved by iterative methods. Special attention is given to the singular corner region at the intersection of the cap and failure surfaces. Iso-error maps are developed to demonstrate the good accuracy of the proposed closest-point projection procedure. A viscoplastic extension of the cap model of the Perzyna type is also presented, and the appropriate extension of the closest-point algorithm developed for the inviscid case is considered. This algorithm is considerably simpler than viscoplastic algorithms initially proposed by Hughes and Taylor and subsequently employed by Katona for the cap model. The predictive capabilities of the cap model are assessed through extensive simulation based on well-documented "Colorado" experimental data. To fit the model to experimental data systematically, an optimization procedure based on the Marquardt-Levenberg algorithm is developed.