A hypoplastic relation for granular materials with a predefined limit state surface

Abstract

A hypoplastic theory for granular materials developed by Gudehus and Bauer is discussed. The description of asymptotic states is of particular interest. Three forms of asymptotic states are defined. Useful criteria to describe the tensorial part of the constitutive relation is developed for one of them, namely for the critical states. The terms proposed by Wu are correlated to the well-known formulations of elastic plastic theory: the Drucker/Prager model and the yield condition by Matsuoka/Nakai. The suitability of the Matsuoka/Nakai criterion for critical states is discussed. Specification of tensorial functions follows in two steps. First the hypoplastic Drucker/Prager model is developed, and then the limit condition by Matsuoka/Nakai is implemented. The resulting tensorial functions require the critical friction angle as the only material constant. The limit condition in critical states obtained from the hypoplastic law coincide with the one by Matsuoka/Nakai. A more comprehensive hypoplastic constitutive relation based on these new tensorial functions is discussed and applied to simulations of element tests. These numerical results are compared with experimental results for sand.