The simulation of shear band evolution path is of vital importance in prevention of geotechnical disaster. During shear band evolution, the strain localization condition at all the shear band tips as well as the force equilibrium should be obeyed, which is proposed to be treated as the nonlinear complementarity problem (NCP). Since the partial derivative of this NCP is hard to solve, instead of the Newton method, the projection contraction algorithm (PCA) is invoked to solve the NCP to yield the shear band evolution step length. To reduce the computational expense, the meshes of improved numerical manifold (INMM) are used to discretize the domain of the soil-rock mixture (SRM). Based on the displacement-controlled method (DCM), the plasticity and contact nonlinearities are solved in a unified way. The proposed procedure could naturally simulate the growth of shear band, allowing the shear band tip to stop anywhere, alleviating the mesh dependence. Some types of slope examples are solved to test the performance of the proposed approach.

中文翻译：

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基于互补法和改进数值流形法的剪切带静态演化


剪切带演化路径模拟对于岩土灾害防治具有重要意义。在剪切带演化过程中，应遵守所有剪切带尖端的应变局部化条件以及力平衡，建议将其视为非线性互补问题（NCP）。由于该NCP的偏导数很难求解，因此不使用牛顿法，而是调用投影收缩算法（PCA）来求解NCP，以产生剪切带演化步长。为了减少计算费用，使用改进的数值流形（INMM）网格来离散土石混合物（SRM）的域。基于位移控制方法（DCM），统一求解塑性和接触非线性。所提出的程序可以自然地模拟剪切带的生长，允许剪切带尖端在任何地方停止，从而减轻网格依赖性。解决了某些类型的坡度示例以测试所提出方法的性能。