We present a dimensional-reduction framework based on proper orthogonal decomposition (POD) for the nondissipative explicit dynamic discrete element method (DEM) simulations. Through Galerkin projection, we introduce a finite dimensional space with lower number of degree of freedoms such that the discrete element simulations are not only faster but also free of high-frequency noises. Since this method requires no injection of artificial or numerical damping, there is no need to tune damping parameters. The suppression of high-frequency responses allows a larger time step for faster explicit integration. To capture the highly nonlinear behaviors due to particle rearrangement, an automatic mode-update scheme is formulated such that the most efficient basis can be used to predict mechanical responses. Numerical examples including the wave propagation simulations and uniaxial extension and compression tests are used to demonstrate the capacity of the reduced-order model.

中文翻译：

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高频噪声颗粒材料动态响应的自适应降维离散元模型

我们提出了一个基于适当正交分解 (POD) 的降维框架，用于非耗散显式动态离散元方法 (DEM) 模拟。通过伽辽金投影，我们引入了一个具有较低自由度的有限维空间，这样离散元模拟不仅更快，而且没有高频噪声。由于此方法不需要注入人工或数值阻尼，因此无需调整阻尼参数。高频响应的抑制允许更大的时间步长进行更快的显式积分。为了捕捉由于粒子重排引起的高度非线性行为，制定了自动模式更新方案，以便最有效的基础可用于预测机械响应。