Range of Yield Conditions in Ideal Plasticity

The properties of ideal rigid-plastic solids are used to define bounding yield conditions that remain valid when test results are available for only one stress state, such as simple tension or simple shear. For material in which yield is insensitive to changes in mean stress, the bounding yield conditions are shown to be the maximum shear-stress criterion of Tresca and a new criterion designated as the maximum reduced stress criterion. Use of both criteria enables the best possible bounds to be obtained for the carrying capacity of a structure in the absence of further information. Parallel results are obtained for material in which yield strength is a linear function of the mean stress, and some examples are given.