Evaluation and improvement of macroscopic yield criteria of porous media having a Drucker-Prager matrix

A large number of analytical strength criteria have been developed for porous materials having a Drucker-Prager solid matrix by using different up-scaling methods. A number of representative exisitng criteria are selected and summarized. These criteria are first evaluated and compared both analytically and numerically with new FEM solutions obtained in this work. A wide variety of new numerical results are then provided from finite element simulations to enlarge the comparisons. In particular, the strength under the pure shear condition is discussed and studied in depth, either numerically and theoretically. Based on these comparisons, a new improvement of the prediction of pure shear strength is established. With this improvement, we derive a new macroscopic strength criterion for the porous materials with a Drucker-Prager type solid matrix. The new criterion is validated against those numerical solutions for a wide range of porosity and frictional coefficient. The special case of a porous material with a von Mises type solid matrix is also studied with a good validation.