Abstract: A detailed introduction to a modified symmetric and anti-symmetric decomposition (MSAD) based three-dimensional numerical manifold method (3D NMM) is given, and a formula to select the penalty factor of penalty method in 3D NMM is proposed. In the MSAD-based 3D NMM, a Bathe implicit time integration scheme is introduced, an ideal plastic constitutive model with the unified strength theory and non-associated flow rule is developed, and a simulation of a 3D elastic-plastic excavation problem is conducted. The MSAD-based 3D NMM is used to study nonlinear dynamics. The results show that: The Bathe implicit time integration scheme and the MSAD-based 3D NMM are able to ensure the stability of the simulation results for nonlinear dynamics problems with large rotation and long-time duration, and to maintain the conservation of kinetic energy and angular momentum for the conservative system. The MSAD theory is double-verified, in the simulation of large rotation problems, showing that it has good stability and high computational precision, and it is able to reasonably separate the rotation and strain apart from the incremental deformation gradient, and accurately update the rotational stress without causing the problem of false volume expansion.

Key words: modified symmetric and anti-symmetric decomposition(MSAD), three-dimensional numerical manifold method (3D NMM), nonlinear dynamics, Bathe implicit time integration, formula to select the penalty factor, three-dimensional elastic-plastic excavation