SANISAND: Simple anisotropic sand plasticity model

SANISAND is the name used for a family of simple anisotropic sand constitutive models developed over the past few years within the framework of critical state soil mechanics and bounding surface plasticity. The existing SANISAND models use a narrow open cone-type yield surface with apex at the origin obeying rotational hardening, which implies that only changes of the stress ratio can cause plastic deformations, while constant stress-ratio loading induces only elastic response. In order to circumvent this limitation, the present member of the SANISAND family introduces a modified eight-curve equation as the analytical description of a narrow but closed cone-type yield surface that obeys rotational and isotropic hardening. This modification enables the prediction of plastic strains during any type of constant stress-ratio loading, a feature lacking from the previous SANISAND models, without losing their well-established predictive capability for all other loading conditions including the cyclic. In the process the plausible assumption is made that the plastic strain rate decomposes in two parts, one due to the change of stress ratio and a second due to loading under constant stress ratio, with isotropic hardening depending on the volumetric component of the latter part only. The model formulation is presented firstly in the triaxial stress space and subsequently its multiaxial generalization is developed following systematically the steps of the triaxial one. A detailed calibration procedure for the model constants is presented, while successful simulation of both drained and undrained behavior of sands under constant and variable stress-ratio loadings at various densities and confining pressures is obtained by the model

Fabric evolution within shear bands of granular materials and its relation to critical state theory

In an effort to study the relation of fabrics to the critical states of granular aggregates, the discrete element method (DEM) is used to investigate the evolution of fabrics of virtual granular materials consisting of 2D elongated particles. Specimens with a great variety of initial fabrics in terms of void ratios, preferred particle orientations, and intensities of fabric anisotropy were fabricated and tested with direct shear and biaxial compression tests. During loading of a typical specimen, deformation naturally localizes within shear bands while the remaining of the sample stops deforming. Thus, studying the evolution of fabric requires performing continuous local fabric measurements inside these bands, a suitable task for the proposed DEM methodology. It is found that a common ultimate/critical state is eventually reached by all specimens regardless of their initial states. The ultimate/critical state is characterized by a critical void ratio e which depends on the mean stress p, while the other critical state fabric variables related to particle orientations are largely independent of p. These findings confirm the uniqueness of the critical state line in the e- p space, and show that the critical state itself is necessarily anisotropic. Additional findings include the following: (1) shear bands are highly heterogeneous and critical states exist only in a statistical sense; (2) critical states can only be reached at very large local shear deformations, which are not always obtained by biaxial compression tests (both physical and numerical); (3) the fabric evolution processes are very complex and highly dependent on the initial fabrics. Copyright (C) 2010 John Wiley & Sons, Ltd

Implicit integration of incrementally non-linear, zero- elastic range, bounding surface plasticity

The zero elastic range, bounding surface plasticity framework is a suitable choice for modeling materials which exhibit zero purely elastic response during shearing. As a consequence of zero elastic range the plastic strain increment direction, and consequently the elastic-plastic moduli fourth order tensor depends on the direction of the stress increment, rendering the model incrementally non-linear. The system of ordinary differential equations of the elastic-plastic formulation is intrinsically implicit. Thus, an iterative algorithm based on the Backward Euler numerical integration method and the damped Newton-Raphson method with an adaptive trial step is proposed in this work. The proposed methodology is applied to the zero elastic range SANISAND-Z model for sands and a thorough verification is done for various applied strain histories. The proposed integration scheme allows the use of SANISAND-Z or any other bounding surface zero elastic range model in displacement driven finite element analysis

Directional distortional hardening at large plastic deformations

AbstractThis paper extents the directional distortional hardening model of Feigenbaum and Dafalias (2007) into the range of large plastic deformations. This model allows the yield surface to deform such that a region of high curvature develops approximately in the direction of loading and a region of flattening develops on the opposite side. To extend this model into large deformations and in order to ensure positive dissipation and objectivity, hardening rules are derived from thermodynamic conditions in terms of corotational rates. Since this model includes a fourth order tensor-valued hardening internal variable, the corotational rates for fourth order tensors are examined in this work employing the concept of plastic spin. Several choices for plastic spins are presented and used for the simulation of the response under simple shear loading up to 1000% strain

Relating elastic and plastic fabric anisotropy of clays

A relationship between elastic anisotropy, as typically observed in clayey soils subjected to shear wave propagation tests, and plastic anisotropy, detected at yielding and leading to rotated yield loci, is proposed. Such a relationship is expected because both elastic and plastic anisotropies can be ascribed to the same directional ingredients that characterise the fabric of the soil at the microscale. The relationship takes the form of an analytical relation between an elastic and a plastic fabric tensor, the former entering a hyperelasticity theory while the latter is the rotational hardening variable of a clay plasticity theory. The elastic anisotropy can be measured experimentally by wave propagation along orthogonal planes, identifying the ratio of the corresponding elastic shear moduli while a sample is compressed at fixed stress ratio, and paired with plastic anisotropy obtained by the integration of its plastic fabric tensor evolution equation during the foregoing compression. Such experiments were available and used to calibrate and validate the proposed elastic–plastic anisotropy relationship. The findings have a two-way beneficial effect for the solution of a geotechnical boundary value problem, where one can easily measure initial elastic clay anisotropy in the field, which can be used to initialise the plastic anisotropy for the subsequent analysis of the problem, while the evolving plastic anisotropy can be used to update the elastic fabric tensor during deformation