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.