Abstract This paper presents the vector-based discrete element method applied to two-dimensional elastic bodies, including details of formulation, its implementation on graphics processing units (GPUs) for accelerating simulations and validation cases. Simulation of elastic bodies has traditionally been realised through continuum-mechanics based methods such as finite elements while using discrete element methods have been restricted to small spatial and temporal scales due to the relatively high computational cost. The vector-based discrete element method, or V-model, overcomes the limitations of both traditional continuum-based mechanics and discrete element approaches to enable the possibility to model additional physics such as cracking, recombination and rupture in future studies. In this study we develop and compare CPU and GPU implementations for elastic bodies under deformation only with both static and dynamic validation studies to assess the performance of the method. Results demonstrate the ability of the method to model linear deformation within 1% of the analytical solution and provide qualitative representation of non-linear deformation. The spatial rate of convergence with decreasing particle size is demonstrated to be approximately first order with a methodology to clarify selection of time step size. This paper presents the first implementation of the V-model on GPUs to model elastic bodies demonstrating a 20x speed-up over the CPU implementation and is applied to the stochastic modelling of material properties in a deforming beam.

中文翻译：

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基于矢量的固体弹性材料离散元方法

摘要 本文介绍了应用于二维弹性体的基于向量的离散元方法，包括公式的详细信息，其在图形处理单元 (GPU) 上的实现，以加速模拟和验证案例。弹性体的模拟传统上是通过基于连续介质力学的方法（例如有限元）来实现的，而由于计算成本相对较高，使用离散元方法已被限制在较小的空间和时间尺度上。基于矢量的离散元方法或 V 模型克服了传统的基于连续介质的力学和离散元方法的局限性，从而能够在未来的研究中模拟其他物理现象，例如开裂、复合和破裂。在这项研究中，我们开发并比较了 CPU 和 GPU 对变形下弹性体的实现，仅通过静态和动态验证研究来评估方法的性能。结果证明了该方法能够模拟 1% 解析解内的线性变形，并提供非线性变形的定性表示。随着粒子尺寸减小的空间收敛速率被证明是近似一阶的，并使用一种方法来阐明时间步长的选择。本文介绍了 GPU 上 V 模型的首次实现，以模拟弹性体，展示了比 CPU 实现快 20 倍的速度，并应用于变形梁中材料属性的随机建模。