边坡大变形损伤破坏的高效无网格模拟

Numerical simulation of slope failure at finite deformation by using an accelerated meshfree method

首先讨论了Lagrangian和Eulerian无网格近似的联系和区别,然后基于稳定节点积分和增量本构理论,建立了分析边坡静动力破坏的高效大变形无网格法,并给出了详细的计算流程。该方法采用弹塑性损伤耦合本构关系来模拟岩土类材料的破坏演化过程,其中屈服函数采用Drucker-Prager准则,损伤准则为基于应变的各项同性损伤函数。由于无网格近似和稳定节点积分具有非局部近似的特性,在保证空间离散稳定性和提高计算效率的同时,也可准确有效地模拟应变集中所形成的剪切带的发生与扩展,通过数值算例验证了方法的有效性。

A comparison between the Lagrangian and Eulerian kernels used in meshfree approximation is illustrated. Then with the Lagrangian approximation an accelerated meshfree formulation for dynamic as well as static analysis of slope failure at finite deformation range is presented. The present formulation employs the stabilized conforming nodal integration(SCNI) to ensure the spatial stability and improve computational efficiency. The degradation of slope materials is characterized by the coupled elasto-plastic damage model via the rate form,where the Druker-Prager yield function and isotropic strain-based damage criterion are used. The non-local nature of meshfree approximation and SCNI scheme enables the current approach to effectively simulate the shear band arising from strain localization during slope failure process. Finally a numerical example is given to demonstrate the proposed method.