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为很好地描述岩石的剪切变形局部化现象,给出一个非连续平面应变弹塑性模型。这个模型以经典滑移线理论为框架,采用光滑函数组合描述位移场在滑移线上的间断;其控制方程是在局部正交曲线坐标系下由物理定律推导得出。材料的变形被划分为3个阶段:弹性、塑性及峰后局部剪切阶段。材料在滑移线上服从库仑强度准则。峰后在滑移线上出现断裂,材料初始黏聚力线性减小并最终消失。对模型进行有限元离散,并用Newmark法求解。采用Fortran语言编写代码并做一个简单算例。与传统连续介质模型比较,该模型中材料的应变、应力均不对称,材料的塑性行为、能量耗散与间断界面的变形运动密切相关。非连续模型能够深刻地描述深部围岩峰后剪切变形局部化现象。
In order to describe the localization of shear deformation in rock well, a discontinuous plane strain elastoplastic model is given. The model uses the classical slip-line theory as the framework, and uses the smooth function combination to describe the discontinuity of the displacement field on the slip line. The governing equation is derived from the laws of physics in the local orthogonal curvilinear coordinate system. The deformation of the material is divided into three stages: elastic, plastic and post-peak shear stage. The material obeys Coulomb’s strength criterion on the slip line. After the peak in the slip line fracture occurs, the initial linear cohesion of the material decreases and eventually disappears. Finite element discretization of the model and solving with Newmark method. Write code in Fortran and make a simple example. Compared with the traditional continuum model, the strain and stress of the material in this model are not symmetrical. The plastic behavior and energy dissipation of the material are closely related to the deformation of the discontinuous interface. The discontinuous model can profoundly describe the localization of shear deformation after the deep surrounding rock peak.