Finite Element Analysis Of Shear Band Localization Based On A Nonlocal Plasticity Theory

The shear band localization can be observed in a variety of engineering materials such as concrete, rocks, sand, and soils.. Concurrent with emergence of this phenomenon is the gradual loss of the load carrying capacity of the material and its final failure. Numerical simulation of the shear band localization is important for studying the failure mechanisms, and predicting the post-peak behavior, of concrete and other geotechnical materials. Also it is essential for estimating the load carrying capacity of the foundations of bridges and other building structures.In this thesis, the drawbacks of the classical continuum mechanics in numerical simulation of shear band localization are analyzed. One-and two-dimensional numerical examples are given to illustrate the mesh dependence of the simulation results based on the classical elasto-plastic strain softening model. The fundamental reason is the loss of strong ellipticity of the governing differential equations, which in turn results in the ill-posedness of the boundary value problems. Because of this, the finite element results become not unique. From the standpoint of physics, the basic reason for the mesh dependence lies in the constitutive equations in which no internal length scale is introduced.Various theories and models for regularizing mesh dependence are reviewed and summarized in this thesis. A nonlocal plasticity model is proposed to address this problem. The model is based on the integral-type nonlocal theory and the representative volumetric element (RVE), with internal length scale introduced in the constitutive descriptions. A link between the integral-type nonlocal plasticity model and its equivalent differential equation is established by the truncated Taylor expansion of the integrand. Variational formulae and Galerkin’s equations for the coupled incremental consistency equation and equations of balance of momentum are developed to apply the proposed model in the FE analysis of the shear band localization. A nonlocal element and a moving boundary technique are also proposed to integrate the constitutive equations to find the solutions of the two coupled fields.Numerical examples for the one-and two-dimensional problems are conducted to verify the proposed nonlocal model. It is shown that the proposed nonlocal plasticity model can results in objective numerical results. The thickness of the shear band is irrelevant to the mesh sizes, and instead it depends on the internal length scale of the material. As the internal length scale approaches to zero, the numerical results from the nonlocal theory will approach to those from the classical local theory.