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.

中文翻译：

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基于修正对称和反对称分解的三维数值流形方法

借助三维（3D）数字流形方法（NMM）进行的大旋转或变形研究相对较少。开发了一种新的改进的对称和反对称分解（MSAD）理论，并将其应用于3D NMM中，从而消除了错误的体积膨胀和错误的旋转应变/应力问题。Jaumann速率用于测量物料旋转，并推导基于Jaumann速率的几何刚度。详细并举例说明了基于MSAD的3D NMM的增量公式以及有关MSAD理论实施的实用指南。新的理论和公式可用于分析大旋转和大变形问题。基于次弹塑性理论和统一强度理论，带有关联流规则的统一产量标准被实施到基于MSAD的3D NMM中。研究了几个典型示例，这些示例展示了新MSAD理论和基于MSAD的3D NMM的优势和潜力。