The rotation degree of freedom in discontinuous deformation analysis (DDA) may cause false volume expansion when a block undergoes a large rotation. We propose a block displacement function to prevent this defect. Specifically, the degrees of freedom in a block are redefined by incremental displacements at its vertices, and displacement is formulated based on the mean value coordinates. In addition, the finite element method with updated Lagrangian formulation is employed to derive the equilibrium equations, while the contact analysis and implicit time integration for dynamics is maintained from the original DDA. After each time step, the block configuration is updated by adding the new degrees of freedom to the previous coordinates of the block vertices. Results from numerical examples confirm the effectiveness of the proposed approach to prevent false volume expansion, ensure correctness of contact analysis, and provide realistic stress results when simulating large rotations.

中文翻译：

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基于平均值坐标的不连续变形分析的新型位移函数

当块经历大的旋转时，不连续变形分析（DDA）中的旋转自由度可能会导致错误的体积膨胀。我们提出了块位移函数来防止这种缺陷。具体地，通过在块的顶点处的增量位移来重新定义块中的自由度，并且基于平均值坐标来表示位移。此外，采用更新拉格朗日公式的有限元方法来导出平衡方程，而动力学分析的接触分析和隐式时间积分则保持原始DDA不变。在每个时间步骤之后，通过将新的自由度添加到块顶点的先前坐标来更新块配置。