多种流形覆盖方式耦合的数值流形法及其应用

A numerical manifold method coupling multiple types of manifold covers and its applications

为了更好地利用数值流形法(NMM)模拟连续和非连续问题,根据NMM数学覆盖选择的灵活性,将有限元网格作为一种数学覆盖方式生成流形覆盖系统以避免细小流形单元的出现,并提出了将单个材料体描述为一个流形单元的独立覆盖方法。运用多种覆盖方式相耦合的方法模拟了混凝土的细观拉压模型,以及一个复杂结构岩质边坡模型,模拟结果较好地再现了相应的力学变形破坏过程。多种覆盖方式的耦合使得构建的NMM模拟模型更加合理;独立覆盖方式的使用降低了构建离散体系NMM模型的复杂程度,并减少了模型中的单元数量以及不连续面上的接触数量,提高了模拟计算效率。

To better use the numerical manifold method（NMM）to simulate complex continuous and discontinuous deformation problems,for the flexibility of the choice of mathematical covers in the NMM,we adopt the finite element mesh to generate NMM mathematical covers so as to avoid the appearance of too-small manifold elements,and put forward an independent cover method,in which a single material domain is described as one manifold element.Different cover types are coupled in the simulations of the tensile and compressive concrete meso-scale models,as well as a rock slope model with complex structures.The corresponding mechanical deformation and failure processes are well reproduced by NMM simulations.The coupling use of different cover types makes the generated NMM simulation models more reasonable.The independent cover method decreases the complexity to construct NMM simulation modelsfor discrete systems,and reduces the numbers of manifold elements and the contact numbers along discontinuity surfaces,which helps to improve the NMM computational efficiency.