Characteristic state plasticity for granular materials: Part I: Basic theory

A non-associated plasticity theory is developed for granular materials based on the concept of a characteristic stress state of vanishing incremental dilation. The theory makes use of a common format for yield surface and ¯ow potential, representing the surfaces in terms of stress invariants and a single shape function for each. The ¯ow potential surface is determined by an approximate friction hypothesis. Plastic work hardening is introduced in a linear invariant form, that permits dilation before the ultimate state, by including the work associated with shape change in addition to the traditional contribution from volume change. The model is fully three-dimensional and is de®ned by only six parameters: two for elastic sti€ness, one for plastic sti€ness, two for the shape of yield and plastic potential surfaces, and one for the dilation at failure. Typical material response is illustrated, while model calibration and its ability to represent experimental data are discussed in Part I