General Forms of Limit Surface: Application for Isotropic Materials

Limit surfaces are a tool used in theory of plasticity and failure analysis for dividing the safe from the unsafe regions. Their mathematical formulations are given by yield and strength criteria. The number of suggested criteria is unmanageable. By lack of the sufficient conditions only plausibility assumptions can limit this variety. Typically, the Tresca, von Mises, and Schmidt-Ishlinsky criteria are employed for the modeling of yielding. The effect of pressure-sensitivity is accounted for with the criteria of Rankine and Burzyński-Yagn. Generalizations are obtained with linear combinations of these and further criteria. However, methods for the selection of efficient criteria for a particular application are still missing. In this work, a nomenclature for isotropic yield criteria is introduced. Proposed systematization restricts the number of appropriate yield criteria. Global convexity limits for the yield criteria of trigonal and hexagonal symmetry are defined. The basic idea is to find a general form of isotropic yield surface that satisfies the plausibility assumptions. This surface should contain possible yield surfaces lying between the lower and the upper bounds of the convexity restrictions. Any known or new criteria can then be considered as a special cases of the general criterion. The discussed yield criteria are extended for pressure-sensitive materials. The selection of the effective criterion for a particular application is simplified.