Vector-based discrete element method for solid elastic materials
Vector-based discrete element method for solid elastic materials
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DOI：
10.1016/j.cpc.2020.107353
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发表时间：
2020-05
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影响因子：
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通讯作者：
B. Owen;Abouzied M. A. Nasar;A. Harwood;Sam Hewitt;N. Bojdo;B. Keavney;B. Rogers;A. Revell
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文献类型：
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作者：
B. Owen;Abouzied M. A. Nasar;A. Harwood;Sam Hewitt;N. Bojdo;B. Keavney;B. Rogers;A. Revell
本文介绍了应用于二维弹性体的基于矢量的离散元方法，包括公式细节、其在图形处理单元（GPU）上用于加速模拟的实现和验证案例。传统上，弹性体的模拟是通过基于连续介质力学的方法（例如有限元）来实现的，而使用离散元方法由于计算成本相对较高而仅限于较小的空间和时间尺度。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，使在未来的研究中模拟额外的物理现象（例如裂纹、重组和破裂）成为可能。在本研究中，我们仅通过静态和动态验证研究来开发和比较变形下弹性体的 CPU 和 GPU 实现，以评估该方法的性能。结果证明该方法能够对解析解 1% 以内的线性变形进行建模，并提供非线性变形的定性表示。通过阐明时间步长大小选择的方法，证明了随着粒径减小而收敛的空间速率近似为一阶。本文首次在 GPU 上实现了 V 模型来对弹性体进行建模，其速度比 CPU 实现提高了 20 倍，并应用于变形梁中材料属性的随机建模。
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.