A Modified Symmetric and Antisymmetric Decomposition-Based Three-Dimensional Numerical Manifold Method for Finite Elastic-Plastic Deformations

There are relatively few studies on large rotation or deformation by means of the three-dimensional (3D) numerical manifold method (NMM). A new modified symmetric and antisymmetric decomposition (MSAD) theory is developed and implemented into the 3D NMM, eliminating the false-volume expansion and false-rotation strain/stress problems. The Jaumann rate is used to measure the material rotation, and the geometric stiffness built on the Jaumann rate is deduced. The incremental formulas of the MSAD-based 3D NMM and a practical guide on the implementation of the MSAD theory are given in detail and exemplified. The new theory and formulas can be applied to analyze both large rotation and large deformation problems. Based on the hypoelasto-plasticity theory and the unified strength theory, the unified yield criterion with associated flow rule is implemented into the MSAD-based 3D NMM. Several typical examples are studied, showing the advantage and potential of the new MSAD theory and the MSAD-based 3D NMM.