A robust algorithm for the generation of integration cells in Numerical Manifold Method

• A simple and robust algorithm for the generation of the integration cells in NMM is presented.
• With the help of pre-defined symbol functions and 3 different matrixes, the close-bounded polygons (integration cells) could be formed in a straightforward manner.
• Large amounts of computational geometries used in previous integration cell generating process could be replaced with computational algebra in this new algorithm.
• Several benchmarks demonstrate the accuracy and the robustness of the present method.

The finite cover system plays a critical role in Numerical Manifold Method (NMM) for the unified simulation of models from continuum to discontinuum. However, large amounts of computational geometries are usually involved in the traditional finite cover generation algorithm, which makes the process of finite cover generation a time consuming and error prone task and limits the wide applications of NMM. To achieve a simple and robust finite cover generation algorithm for NMM, a new method for the generation of integration cells including closed convex or concave polygons was developed in this paper as an important supplement to our recent work [Cai et al., 2013]. In the newly developed integration cells generation algorithm, with the help of pre-defined symbol functions and 3 different matrixes, nodes including vertexes and intersection points belonging to a same integration cell were first grouped together, and then listed in a anticlockwise manner to finally form the closed circuit. In this way, large amounts of computational geometries employed in the identification of integration cells were replaced with computational algebras. Several benchmarks were simulated to investigate the accuracy of the proposed integration cells generation algorithm and to demonstrate the robustness of NMM.