The mathematical foundation of the general bounding surface constitutive formulation in plasticity is presented. Along these lines the concept of hypoplasticity is formally introduced, and it is shown that a particular class of hypoplastic formulations arises naturally from certain bounding surface models, with the distinguishing feature being the dependence of the elastoplastic moduli and/or the plastic strain rate direction on the stress rate direction. The general analytical perspective allows the better understanding and improvement of existing bounding surface plasticity and hypoplasticity models, which are briefly discussed, and suggests the proper way to construct new ones for future applications.

Bounding surface plasticity, i: mathematical foundation and hypoplasticity

Subloading surface model in unconventional plasticity

Three dimensional combined fracture-plastic material model for concrete

A rate-independent constitutive model for natural clays is presented, formulated within the framework of kinematic hardening with elements of bounding surface plasticity. The modelling framework is intended to include effects of damage to structure caused by irrecoverable plastic strains caused by sampling, laboratory testing, or geotechnical loading. The incorporation of a structure measure allows the size of the bounding surface to decay with plastic deformations. This model can be seen as a logical extension from the Cam-clay model. The steady fall of stiffness with strain towards the Cam-clay value is controlled by a particular interpolation function. This ensures a smooth degree of approach between a kinematically hardening bubble (which is the boundary of the elastic region) and the bounding surface during their relative translation with stress history. The model describes the essential phenomena of pre-failure behaviour of natural clays: stiffness variation with strain, volumetric change accompanyi...

A kinematic hardening constitutive model for natural clays with loss of structure

Based on the relationship between the current yield surface and the reference yield surface, a new model, called the three-dimensional unified hardening model for overconsolidated clays (the UH model), is proposed in this paper. A current yield surface is used to describe overconsolidated behaviour, and a reference yield surface to describe the yield characteristics corresponding to normally consolidated clays. The UH model can model many characteristics of overconsolidated clays well, including stress-strain relationships, shear dilatancy, strain-hardening and softening, and stress path dependence behaviour. The key feature of the model is the adoption of a unified hardening parameter that is independent of stress paths. Based on the SMP criterion and the corresponding transformed stress method, the proposed model can be applied conveniently to three-dimensional stress states. Compared with the Cam-clay model, the UH model requires only one additional clay parameter, the slope of the Hvorslev envelope. The validity of this new model is confirmed by data from triaxial drained and undrained compression and extension tests for clays with different overconsolidation ratios, true triaxial tests with different Lode's angles, and cyclic loading tests.

UH model: three-dimensional unified hardening model for overconsolidated clays

The subloading surface model fulfills the mechanical requirements for constitutive equations, i.e. the continuity condition, the smoothness condition and the work rate stiffness relaxation and describes pertinently the Masing effect. The constitutive equation of soils is formulated by introducing the subloading surface model and formulating the evolutional rule of rotational hardening for the description of anisotropy. The applicability of the constitutive equation to the prediction of real soil deformation behaviour is verified by predicting monotonic and cyclic loading behaviour of sands under drained and undrained conditions and comparing them with test data. © 1998 John Wiley & Sons, Ltd.

Elastoplastic constitutive equation of soils with the subloading surface and the rotational hardening

The well-known linear relation between the specific volume and the logarithm of the pressure for the isotropic consolidation has been widely incorporated into elastoplastic constitutive equations of soils. It is, however, indicated in this article that this relation has several physically unaccepted properties. Instead of this relation it is recommended to incorporate the linear relation between both logarithms of the volume and the pressure into constitutive equations, which does not have any of the unrealistic properties.

Koichi Hashiguchi

Papers

Elastoplastic constitutive equation of soils with the subloading surface and the rotational hardening

On the linear relations of V–ln p and ln v–ln p for isotropic consolidation of soils

General non-proportional loading behavior of soils

Elastoplastic constitutive equation with tangential stress rate effect

Shear band formation analysis in soils by the subloading surface model with tangential stress rate effect