A basic hypoplastic constitutive model for sand

Abstract

Hypoplastic constitutive models are based on nonlinear tensor functions and are characterized by simple formulation and few parameters. In its early stage, mainly basic hypoplastic constitutive equations were concerned, where the stress tensor is assumed as the only state variable. There followed some enhanced models based on the basic constitutive equation by including void ratio as an additional state variable. In this paper, we first show that the widely used hypoplastic model by Wolffersdorff is seriously flawed because the underlying basic equation does not perform properly. We proceed to develop a basic hypoplastic constitutive equation by introducing a new tensorial term, which preserves the critical state at large strain. The model performance is demonstrated by parameter study for some element tests. This simple and robust basic equation is well suited to build more sophisticated models.

A hypoplastic model for granular soils incorporating anisotropic critical state theory

“…It is noteworthy that Equation (6) implies that the two parameters in Equation are equal but with opposite signs, ie, C 3 = − C 4 , which has been shown as a necessary requirement to reaching the critical state under general stress paths . However, such requirement may reduce the parameters from four in Equation (2) to three, implying that the initial Poisson's ratio and the critical friction angle are interrelated and cannot be determined independently from the tests . In fact, such drawback can be overcome by adding a new tensorial term to the basic hypoplastic model, as detailed by Wu et al…”

Numerical integration and FE implementation of a hypoplastic constitutive model

“…Within the above framework, a simple critical state hypoplastic constitutive equation for granular materials is proposed by Wu [42], which is an improvement of an early version by Wu and Bauer [37]. This model consists of three linear terms and one nonlinear term in the stretching tensor _ e.…”

“…(4) was developed mainly for cohesionless soils, in practice, most soils show cohesion to some extent. However, the constitutive model is able to take cohesion into consideration by simply replacing the stress tensor r with the following translated stress tensor [33,42]:…”

“…Hypoplasticity represents a class of incrementally nonlinear constitutive models [9,11,16,17,28,42]. Unlike elastic-plastic models, there is no need to decompose the deformation into elastic and plastic deformations.…”

Mohr–Coulomb plasticity for sands incorporating density effects without parameter calibration

“…Second, the model is unable to capture plastic deformations under cyclic loading conditions. These limitations are the primary motivations for advanced sand plasticity models that build on critical state soil mechanics, bounding surface plasticity, and/or generalized plasticity, and/or others . Oftentimes, however, these limitations are not so problematic for routine geotechnical problems, such as the design and stability analyses of foundations, retaining walls, and slopes.…”