Physical interpretations for cap parameters of the modified Drucker-Prager cap model in relation to the deviator stress curve of a particulate compact in conventional triaxial testing

The physical meanings of the cap aspect ratio (. R) and transition surface parameter (. α) of the modified Drucker-Prager cap (MDPC) model have been uncovered in relation to the deviator stress curves of a particulate material in conventional triaxial testing by simulating the curves using varying R and α based on finite element analysis. R controls the rate of the stress rise with the increase of the strain; the smaller the R, the faster the rise of the deviator stress. This phenomenon occurs because, in the p-q plane (. p is the mean stress and q is the Mises equivalent stress), the cap with a smaller R needs to move a shorter distance on the p axis to maintain the current stress state: a smaller volumetric plastic strain is required according to the hardening law. R does not influence the maximum value of the deviator stress curve. As for the influence of α, it artificially lowers the true failure surface by an amount that is proportional to α so that a fictitious ultimate failure state is achieved. Therefore, it is desirable to set α as small as possible unless the numerical analysis using the MDPC model does not produce a converged solution. An analytical expression to calculate the maximum deviator stress that can be predicted by the MDPC model is provided in terms of α.