Department of Mechanical Engineering, MIT, Cambridge, Massachusetts 02139, USA.
Phys Rev E. 2017 May;95(5-1):052901. doi: 10.1103/PhysRevE.95.052901. Epub 2017 May 10.
Inspired by dynamic similarity in fluid systems, we have derived a general dimensionless form for locomotion in granular materials, which is validated in experiments and discrete element method (DEM) simulations. The form instructs how to scale size, mass, and driving parameters in order to relate dynamic behaviors of different locomotors in the same granular media. The scaling can be derived by assuming intrusion forces arise from resistive force theory or equivalently by assuming the granular material behaves as a continuum obeying a frictional yield criterion. The scalings are experimentally confirmed using pairs of wheels of various shapes and sizes under many driving conditions in a common sand bed. We discuss why the two models provide such a robust set of scaling laws even though they neglect a number of the complexities of granular rheology. Motivated by potential extraplanetary applications, the dimensionless form also implies a way to predict wheel performance in one ambient gravity based on tests in a different ambient gravity. We confirm this using DEM simulations, which show that scaling relations are satisfied over an array of driving modes even when gravity differs between scaled tests.
受流固动力学相似性的启发，我们推导出了一种通用的颗粒物质运动无量纲形式，该形式在实验和离散元方法（DEM）模拟中得到了验证。该形式指导如何缩放尺寸、质量和驱动参数，以便在相同的颗粒介质中比较不同运动体的动力学行为。通过假设侵入力来自阻力理论，或者等效地假设颗粒材料作为遵循摩擦屈服准则的连续体，就可以推导出这种缩放。通过在常见沙床中使用各种形状和尺寸的车轮在多种驱动条件下进行实验，证实了这些缩放。我们讨论了为什么这两个模型提供了如此一组稳健的缩放定律，即使它们忽略了颗粒流变学的许多复杂性。受潜在的行星际应用的启发，该无量纲形式还暗示了一种方法，可根据在不同环境重力下的测试，预测在一个环境重力下的车轮性能。我们使用 DEM 模拟证实了这一点，该模拟表明，即使在缩放测试之间的重力不同的情况下，也可以在一系列驱动模式下满足缩放关系。
