Yield surfaces and flow rules for deformation of granular materials with a volume constraint

This paper presents a procedure for developing yield functions with consistent flow rules for granular materials from a family of two parameter dissipation functions in combination with appropriate kinematic constraints. Through a mathematical procedure described in the paper, a general formulation is developed that can, by adjusting the values of the two parameters, reproduce a wide range of yield surfaces, including the Drucker–Prager, Matsuoka–Nakai, and Lade–Duncan. Specifically, an analytical expression for the yield function is obtained in terms of a parameter that is a selected solution to a high order polynomial. The roots of this polynomial can always be found using the eigenvalues of the companion matrix and instructions on how to select the appropriate root are given in the paper. Two ways of incorporating anisotropy into the procedure are explored and the role within it of the recent history of deformation is examined.