Element‐Free Numerical Manifold Method (E‐ <scp>NMM</scp> ) Without Generating Manifold Elements: A Solution for <scp>3D</scp> Continuous‐Discontinuous Problems

ABSTRACT Aiming at the core bottleneck of the traditional numerical manifold method (NMM)—difficulty in 3D extension caused by its reliance on complex geometric Boolean operations when solving 3D continuous‐discontinuous problems—this paper proposes an element‐free numerical manifold method (E‐NMM) that does not generate manifold element (ME). The method replaces the ME generation process with voxel discretization technology, and uses numerical manifold point (NMP) to undertake integral representation and post‐processing functions, completely avoiding 3D Boolean operations; it achieves accurate reconstruction of physical cover (PC) by combining enhanced connected component analysis. The effectiveness of E‐NMM and its applicability to complex engineering problems are verified through multiple sets of numerical examples. E‐NMM retains the core feature of NMM, that is, the unified solution for continuous and discontinuous problems, and provides an efficient and reliable numerical solution tool for 3D complex continuous‐discontinuous problems in fields such as rock mechanics and tunnel engineering.