A simple hypoplastic constitutive model for sand

Abstract

SUMMARYThe paper presents a hypoplastic constitutive model for the three-dimensional non-linear stress-strain and dilatant volume change behaviour of sand. The model is developed without recourse to the concept in elastoplasticity theory such as yield surface, plastic potential and decomposition into elastic and plastic parts. Benefited from the non-linear tensorial functions available from the representation theorem the model possesses simple mathematical formulation and contains only four material parameters, which can be easily identified with triaxial compression tests. Comparison of the predictions with the experimental results shows that the model is capable of capturing the salient behaviour of sand under monotonic loading and is applicable to both drained and undrained conditions.

A hypoplastic constitutive model for debris materials

“…Actually, debris materials are normally simplified as solid spherical particle-viscous fluid mixture and treated as a fluid continuum with microstructural effect in the constitutive modeling [10,11]. In most conventional models, constitutive equations for the static and dynamic regimes are formulated and applied separately, such as the models for the solid-like behaviors of granular materials [8,27,41,43] and that for the fluid-like behaviors [1,6,21]. Although some models for granular-fluid flows have taken the stress state of the quasi-static stage into account, the employed theories for the static regime, such as Mohr-Coulomb criterion [34] and extended von Mises yield criterion [32], still fail to determine the changing of pore water pressure from the deformation directly.…”

“…Although some models for granular-fluid flows have taken the stress state of the quasi-static stage into account, the employed theories for the static regime, such as Mohr-Coulomb criterion [34] and extended von Mises yield criterion [32], still fail to determine the changing of pore water pressure from the deformation directly. Hypoplasticity was proposed as an alternative to plasticity for the description of solid-like behavior of granular materials [41,43]. The distinctive features of hypoplasticity are its simple formulation and capacity to capture some salient features of granular materials, such as non-linearity, dilatancy and yielding [42].…”

“…The hypoplastic model with critical state is an improvement of a basic hypoplastic model for sand developed by Wu and Bauer [43] as…”

“…The hypoplastic model (16) possesses simple mathematical formulation and contains only four material parameters, c 1 $ c 4 . The specific determination process of c 1 $ c 4 can be obtained in the literatures [5,41,43]. Two stress states, the initial hydrostatic and the state at failure, are chosen for the identification of c 1 $ c 4 based on a triaxial test with constant confining pressure, i. e. _ T h ð2; 2Þ ¼ _ T h ð3; 3Þ ¼ 0.…”

“…Two stress states, the initial hydrostatic and the state at failure, are chosen for the identification of c 1 $ c 4 based on a triaxial test with constant confining pressure, i. e. _ T h ð2; 2Þ ¼ _ T h ð3; 3Þ ¼ 0. And then, the following parameters are introduced: the stress ratio, R ¼ T h ð1; 1Þ=T h ð3; 3Þ; the initial tangent modulus, The failure stress ratio R f and the failure Poisson ratio t f are related to the friction angle / 0 and the dilatancy angle w, respectively, through the following relations [43]:…”