Anisotropic yield functions in a co-rotating reference frame

In metal forming simulations large deformations are often treated based on objective formulations. Large rotations are accounted for by rotating the stress tensor or approximating the rotation by some integration rule for the rate of rotation. For isotropic material behavior, this is easily done. For anisotropic material behavior however, not only the stresses, but also the relation between stress rate and strain rate must be updated. In this case it is easier to take a co-rotating reference frame and apply the constitutive relations on a strain measure that is neutralized for rigid body translations and rotations. This paper presents an algorithm that is based on the latter idea. The algorithm directly uses the increments in the deformation gradient, avoiding as much as possible to take time derivatives that should then be integrated subsequently. The algorithm is applied to a constitutive model including an initial anisotropic yield function and isotropic and kinematic hardening. The kinematic hardening makes use of a maximal back stress surface [1] to account for behavior observed in cyclic loading

A constitutive model for unsaturated cemented soils under cyclic loading

On the basis of plastic bounding surface model, the damage theory for structured soils and unsaturated soil mechanics, an elastoplastic model for unsaturated loessic soils under cyclic loading has been elaborated. Firstly, the description of bond degradation in a damage framework is given, linking the damage of soil's structure to the accumulated strain. The Barcelona Basic Model (BBM) was considered for the suction effects. The elastoplastic model is then integrated into a bounding surface plasticity framework in order to model strain accumulation along cyclic loading, even under small stress levels. The validation of the proposed model is conducted by comparing its predictions with the experimental results from multi-level cyclic triaxial tests performed on a natural loess sampled beside the Northern French railway for high speed train and about 140 km far from Paris. The comparisons show the capabilities of the model to describe the behaviour of unsaturated cemented soils under cyclic loading

Dilatancy relation for overconsolidated clay

A distinct feature of overconsolidated (OC) clays is that their dilatancy behavior is dependent on the degree of overconsolidation. Typically, a heavily OC clay shows volume expansion, whereas a lightly OC clay exhibits volume contraction when subjected to shear. Proper characterization of the stress-dilatancy behavior proves to be important for constitutive modeling of OC clays. This paper presents a dilatancy relation in conjunction with a bounding surface or subloading surface model to simulate the behavior of OC clays. At the same stress ratio, the proposed relation can reasonably capture the relatively more dilative response for clay with a higher overconsolidation ratio (OCR). It may recover to the dilatancy relation of a modified Cam-clay (MCC) model when the soil becomes normally consolidated (NC). A demonstrative example is shown by integrating the dilatancy relation into a bounding surface model. With only three extra parameters in addition to those in the MCC model, the new model and the proposed dilatancy relation provide good predictions on the behavior of OC clay compared with experimental data

Numerical integration of the incrementally non-linear, zero elastic range, bounding surface plasticity model for sand

SANISAND-Z is a recently developed plasticity model for sands with zero purely elastic range in stress space within the framework of Bounding Surface (BS) plasticity. 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 and intrinsically implicit. An iterative algorithm based on the Backward Euler method is presented to solve the non-linear system of ordinary differential equations. A non-traditional consistency condition based on the plastic multiplier is introduced as a core element of the system. A thorough analysis of the stability and accuracy of the algorithm is presented based on error estimation. The proposed integration scheme allows the use of SANISAND-Z framework in Finite Element Analysis

Cyclic Loading and Fabric Evolution in Sand: A Constitutive Investigation

An anisotropic plasticity model is proposed to describe the effect of fabric and fabric evolution on the cyclic behaviour of sand within the framework of anisotropic critical state theory. The model employs a cone-shaped bounding surface in the deviatoric stress space and a yield cap perpendicular to the mean stress axis to describe sand behaviour in constant-mean-stress shear and constant-stress-ratio compression, respectively. The model considers a fabric tensor characterizing the internal structure of sand associated with the void space system which evolves with plastic deformation. The fabric evolution law is assumed to render the fabric tensor to become co-directional with the loading direction tensor and to reach a constant magnitude of unit at the critical state. In constant-stress-ratio compres-sion, the final degree of anisotropy is proportional to a normalized stress ratio. An anisotropic variable defined by a joint invariant of the fabric tensor and the loading direction tensor is employed to describe the fabric effect on sand behaviour in constant-mean-stress monotonic and cyclic shear. Good comparison is found between the model simulations and test results on Toyoura sand in both monotonic and cyclic loadings with a single set of parameters

Macroelement modeling of shallow foundations

The paper presents a new macroelement model for shallow foundations. The model is defined through a non-linear constitutive law written in terms of some generalized force and displacement parameters. The linear part of this constitutive law comes from the dynamic impedances of the foundation. The non-linear part comprises two mechanisms. One is due to the irreversible elastoplastic soil behavior: it is described with a bounding surface hypoplastic model, adapted for the description of the cyclic soil response. An original feature of the formulation is that the bounding surface is considered independently of the surface of ultimate loads of the system. The second mechanism is the detachment that can take place at the soil-footing interface (foundation uplift). It is totally reversible and non-dissipative and can thus be described by a phenomenological non-linear elastic model. The macroelement is qualitatively validated by application to soil-structure interaction analyses of simple real structures

Discussion of "Simplified Model of Low Cycle Fatigue for RC Frames"

To model strength degradation due to low cycle fatigue, at least three different approaches can be considered. One possibility is based on the formulation of a new free energy function and damage energy release rate, as was proposed by Ju(1989). The second approach uses the notion of bounding surface introduced in cyclic plasticity by Dafalias and Popov (1975). From this concept, some models have been proposed to quantify damage in concrete or RC (Suaris et al. 1990). The model proposed by the author to include fatigue effects is based essentially in Marigo (1985) and can be included in this approach