A Lode-Dependent Failure and Yield Criterion for Cohesive and Noncohesive Materials

Experimental studies on different materials demonstrate a wide variety of strength behavior. Although the classical failure/yield criteria might be suitable for special cases, they cannot accurately cover the whole range. Thus, the need to employ a unifying model, capable of comprising various criteria seems inevitable. This paper develops a flexible Lode-dependent failure and yield criterion that allows the generation of various shapes in both deviatoric and meridian planes. The model, thus, can cover all the classical criteria including von Mises, Drucker-Prager, Tresca, Mohr-Coulomb, Matsuoka-Nakai, Lade-Duncan, and other recently developed failure/yield criteria. Moreover, the model can consider tensile strength that makes it appropriate for cohesive materials as well. After defining the model, the condition for its convexity and differentiability is discussed. Then, the results derived from the developed model are compared with some of the well-known criteria and different sets of experimental data to attest to its accuracy and applicability in predicting the strength and yield of different materials.