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Presented By: Applied Interdisciplinary Mathematics (AIM) Seminar - Department of Mathematics

AIM Seminar: Understanding the deformation of granular matter and its implications for granular locomotion

Hongyi Xiao, Mechanical Engineering, University of Michigan

Abstract: Granular matter, being an assembly of discrete particles, has complex mechanical behaviors emerging from the interactions of these particles, which often have a disordered yet non-trivial spatial arrangement. Unlike crystalline materials, the packing structure in a disordered material is often hard to describe mathematically, which prohibits us from understanding the deformation from a structure-property point of view. In this presentation, I will first present experimental results of the deformation of a layer of granular particles floating at an air-oil interface, through which I can demonstrate the elasto-plastic nature of deformation in the quasi-static regime. Based on the experimental results, a machine learning-based modeling framework was developed based on the interplay between elasticity, packing structure, and quasi-localized rearrangements of particles. The model can capture a ductile-to-brittle transition observed in the experimental system due to the change of particle properties.

In the second part of the talk, I will demonstrate the implications of the complex mechanical behaviors of granular materials for locomotion. In this problem, granular matter can be considered as a soft and yielding medium that interacts with a deforming body. I will show experimentally that a scallop-like swimmer with reciprocally flapping wings generates locomotion in granular matter, which is often not possible in Newtonian liquids at low Reynolds numbers. We use X-ray imaging and discrete element method simulations to reveal the microscopic picture of how the wings interact with surrounding particles. The locomotion is enabled by a prolonged hysteresis in the material response that originates from a combination of jamming-induced material rigidity and plastic deformation of the free surface. Cooperative effects are observed when the two wings are in close proximity, which potentially involves interaction of zones with jammed particles as well as heap building on the free surface.

Contact: Silas Alben

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