Research On Constitutive Model Of Continuum In Geotechnical Mechanics

Geotechnical materials are a sort of engineering materials with very complicated mechanics behavior. They are taken as continuous media in macroscopic mechanical analysis. In this dissertation, within the framework of the principles of continuum mechanics, based on research results of elastic-plastic constitutive models for geotechnical materials, the method of derivation of multi-dimensional elastic-plastic increment constitutive model is proposed under general loading; the stress increment considering the rotation of principal stress axes for geotechnical materials is analyzed; an associated yield surface constitutive model is proposed; several general problems of strain softening for geotechnical materials in the strain space are researched. These works are introduced as follows:1. The elastic-plastic constitutive model under simple loading in one dimensional stress space is generalized to under general loading in multidimensional stress increment space. General formulations of elastic-plastic stress-strain relation of hardening materials and elastic-plastic flexibility matrix are derived. The method of derivation of multi-dimensional elastic-plastic increment constitutive model is proposed under general loading, by theoretical discussion, the method is valid for elastic-perfectly plastic, isotropic hardening and kinematic hardening materials.2. The stress increment considering the rotation of principal stress axes for geotechnical materials is analyzed by using tensor form and matrix form, respectively. In two-dimensional and three-dimensional principal stress space coordinate systems, the stress increment considering the rotation of principal stress axes is divided into the coaxial increment components and rotational increment components. Then, the problem of plastic deformation considering therotation of principal stress axes will be founded upon the rigorous mathematical reasoning.3. The principal stress space coordinate system oσ1σ2σ3, is transformed to p -q -θσ space coordinate system by using two linear transformations and one non-linear transformation. In p-q space, considering the values of principal stress changes and the rotation of principal stress axes, the relation between plastic strain increment and stress increment is derived. The theoretical result shows that the direction of plastic strain increment is determined by the direction of principal stress and stress increment.4. Based on the models at present and deformation behaviors under the critical state, considering shear yield and volume yield behaviors, an elastic-plastic increment constitutive model with an associated yield surface is proposed. According to various stress states, loading-unloading conditions including elastic, elastic unloading, plastic loading, neutral loading are given. By analyzing various stress paths, the proposed model can describe the plastic deformation behaviors under the various loading paths. The elastic-plastic constitutive formulations between strain increment and stress increment including two and three stress invariants are derived, respectively. Moreover, their elastic-plastic flexibility matrixes are given, which are asymmetrical because of the shear yield and volume yield surfaces with different hardening parameters.5. The method of derivation of multi-dimensional elastic-plastic increment constitutive model under general loading in the stress space is generalized into strain space. In the strain space, united loading-unloading criterions for elastic-perfectly plastic, hardening and softening materials are discussed. United forms of elastic-plastic increment constitutive relations for isotropic hardening/ softening geotechnical materials under general loading in the strain space are derived. General formulations of elastic-plastic stress-strain relations for elastic-perfectly plastic, isotropic hardening and kinematic hardening materials in stress space are transformed into strain space. By the research and discus...