Expansion of NMM and DDA programs and their application

Numerical manifold method (NMM) and discontinuous deformation analysis (DDA) which are newly developed in the recent years have a widely application in simulation study of many problems relevant to safety such as crack propagation and engineering blasting. While the current programs are based on the first-order displacement function, it is very necessary to be expanded. The simplex integration is the basic tool which can make the two numerical analysis methods put into practice. Basing on the simplex theory and combining the two-dimensional simplex integration result of the first-order displacement function, the paper deduces the simplex integration expression of the second-order displacement functions. In the end, the expansion programs are used to simulate the crack propagation and the formulation of blasting funnel under the column charge, which demonstrate the foreground of the two numerical analysis methods in safety problems.