Hysteretic Endochronic Theory for Sand

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Abstract
A new form of endochronic constitutive model is presented to describe the behavior of dry or drained sand, and its parameters are determined by extensive comparisons with published test data. Jump‐kinematic hardening is used to guarantee that the hysteresis loops always close, yield positive energy dissipation, and give an increase in tangent modulus when unloading changes to reloading. Criteria for virgin loading, unloading and reloading are formulated in terms of deviatoric work, and changes of material parameters at loading‐unloading‐reloading transition points are determined. Two endochronic units coupled in parallel are used to describe the measured response over a broad range of strain amplitude. The inelastic volume change is characterized so as to include both densification and dilatancy. Certain material properties are determined as functions of the void ratio. Calculations show that the lateral stress in a simple shear test quickly becomes almost equal to the vertical stress. A three‐dimensional finite element analysis of the simple shear test with endochronic theory reveals significant stress nonuniformity; but this is found to have little effect on the resulting hysteresis loops.

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