Numerical Investigation Of Strain Localization In Geomaterials Based On Micropolar Theory

Strain localization is one of the major causes that lead to the progressive failure of the geostructures. The elastic-plastic constitutive models based on the classical Boltzmann continuum do not contain any internal length scales, which result in severe mesh dependency in the numerical results. Hence, some kinds of regularization mechanisms must be adopted. One way to provide thus regularization mechanisms is to adopt the micropolar theory. In the micropolar theory, additional rotational degrees of freedom are introduced except to the translational degree of freedoms, and the couple stress and the micro curvature are also introduced. The internal length scales related to the mesostructure of the particles are added to the constitutive equations, which provide a regularization mechanism to resolve the mesh dependency problem. Based on the micropolar theory, the following several aspects are mainly investigated in this thesis:Firstly, an isotropic elastic-plastic constitutive model is adopted in the framework of micropolar theory, and the corresponding codes are completed via the user element subroutine (UEL) in ABAQUS. The influence of the additional parameters on the shear band and the structural bearing capacity are investigated. The localization conditions in the classical continuum and the micropolar continuum are verified, and it is found that the localization condition based on the weak discontinuity bifurcation theory is no longer suitable for micropolar continuum. A conclusion is drawn that the pre-bifurcation behavior, such as localization bifurcation state and the shear band angle, can be predicted according to the localization condition in the classical continuum, and the post-bifurcation behavior, such as shear band thickness, should be determined according to the micropolar continuum. In addition, the determination of the internal length parameter and the element size are discussed through quite a number of simulations and comparisons.Secondly, the fabric anisotropy of the geomaterials is considered. The isotropic Drucker-Prager yield criterion is extended through assuming that the material strength is a function of the fabric tensor and the loading direction. And then a transversely isotropic elastic-plastic constitutive model is developed, which can describe the anisotropy of the material strength only via a scalar parameter. The influence of material principal orientation and the anisotropic degree on the localization pattern and the structural bearing capacity are investigated through several examples, such as, uniaxial compression test, slope stability problem and shallow foundation analysis. Results show that the proposed model has a good performance in the simulation of the mechanical behavior for the transversely isotropic geostructures.Thirdly, the traditional non-coaxial constitutive model based on the vertex-like structure is extended to micropolar continuum, and the modified Euler integration with error control is employed for the numerical implementation. The influence of the non-coaxiality on the stress strain response is investigated through the simple shear test, and the corresponding results are compared with those in the classical continuum. It is shown that the micropolar continuum can better reflect the non-coaxial feature than the classical continuum under the same condition. Then, the influence of the non-coaxial degree on the bifurcation state, the angle and the thickness of the shear band is investigated through the uniaxial compression test. It is found that the increase of the non-coaxial degree will lead to the delay of the bifurcation state and the increase of the shear band thickness, while little effect on the shear band angle. In addition, it is observed that the non-coaxial degree has significant influences on the micro field. The increase of the non-coaxial degree will decrease the values of the micro-rotation, the couple stress and the micro-curvature, and the distribution pattern of the above field variables also has obvious difference compared with those in the coaxial model. It indicates that the non-coaxiality can reduce the micro-rotation effect from some extent.Finally, based on the concept of strain energy limit, a hyper-elastic softening model is proposed through introducing a softening function in the non-volumetric part of the strain energy, which can be used to simulate the behaviors of strain softening and critical state in the geomaterials. Only two additional parameters are introduced in the model, and they can be easily determined via the conventional tests. Compared with the traditional elastic-plastic model, the proposed model is of clear concepts and simple forms to describe the failure of materials. It provides a new perspective to simulate the strain softening behavior for geomaterials.