A study on the false volume expansion problem under rigid large rotation based on the modified symmetric and anti-symmetric decomposition method

Abstract

During the simulation of large rotation deformation by the discontinuous deformation analysis method or numerical manifold method, a false volume expansion problem appears. A theoretical and experimental study on the false volume expansion problem based on the modified symmetric and anti-symmetric decomposition (MSAD) is given, reveals the intrinsic cause, and gives an insight into the false volume expansion problem. It is theoretically proven that MSAD will never lead to the false volume expansion problem, and it is also verified by two numerical experiments of large rotation deformation in both static and dynamic situations. The MSAD method can accurately distinguish rotation and strain from the incremental deformation gradient tensor and realize the objective update of rotational stress. Using the MSAD method, larger rotational deformation is allowed for each incremental step; thus, fewer calculating steps and higher computational precision can be achieved, indicating that large rotational deformation problems can be solved in a more accurate and efficient manner. The combination of the MSAD method and the Bathe implicit time integration scheme provides good numerical stability and high computational precision and satisfies the conservation of kinetic energy and momentum for conservative systems.