Mechanical response of free-standing elastogranular structures
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Abstract
A novel, composite material is formed through the simple combination of grains and elastic fibers. This \emph{elastogranular} composite allows for the construction of free-standing, load bearing structures and the mechanical properties of these forms may have applications to a wide range of fields including soft robotics, architecture, and geomorphology. These elastogranular systems are discontinuous and heterogeneous, resulting in a decoupling of the shear and Young’s moduli, and in complex mechanical behavior in response to external loads. While we lack a constitutive model for the behavior of these systems, we may still develop an empirical understanding of the mechanical response through the investigation of two particular canonical structures: columns and beams.
Elastogranular columns are constructed using external and internal fibers, with internal fibers included through layer-by-layer addition, and external fibers providing the outer encasing for the columnar structure. Elastogranular beams are constructed with the addition of an applied pre-compressional load, such that these structures are capable of supporting their self-weight when cantilevered in a gravitational field, and additional external forces that cause the beam to deflect. Through experimental analysis, we observe a reproducible response to mechanical loading between specimens having general shared parameters, even when the exact location of grains and fibers appears to be variable. Simulations confirm these systems have a reduced dependence on the exact location of grains and fibers, thus allowing for the measurement of effective material properties as if they were elastic, continuous, and homogeneous structures. We apply classical mechanical theory to these structural forms to extract the effective material properties that characterize the response of the elastogranular composite to deformation through compression and bending.
Elastogranular columns consistently show three distinct regimes in their mechanical behavior: (1) at low loads, they have a similar displacement response to a pile of grains, where much of the displacement is due to rearrangement; (2) at an initial critical load, the grains jam and exhibit a mechanical response consistent with Hertzian contact mechanics; and (3) at a second, increased critical load, the columns stiffen, deviating from the Hertzian response. Initial investigations of the second critical point lead to qualitative trends in the granular response to load. Within the simulated columns we observe the development of force chains, whereby load is transmitted from one grain to the next via continuous in-series contact between multiple grains. The coupled mechanical response of the granular network and elastic fiber within these systems provides an additional degree of freedom by which we may investigate the force chain development. We propose a simple, reduced-order model for these systems in the absence of internal fiber, and apply this model to both provide a cause for the deviation from Hertzian response, as well as accurately predict the initial Hertzian stiffness of these structures.
In addition to varying the shape and general mechanical properties of the grains, we parameterize and investigate the role of fiber location. We find a general dependence on the location of fibers as well as total fiber amount within the elastogranular systems. Experimentally, we find that internal fibers seem to primarily allow the system to store elastic energy, while external fibers provide the initial spatial constraint for the jamming transition as well as subsequent formation of force chains within the elastogranular structures.
Finally, we investigate pre-compressed elastogranular beams, employing classical beam theory and the behavior of continuous material beams to guide our initial understanding of their mechanical response. We find that shear plays a significant role in the behavior of these elastogranular beams, and by accounting for this deformation in the application of theory, we may extract the effective shear modulus as a function of the pre-compression on the system. These findings may bring some new light to the mechanics of elastogranular robotic grippers and attachments, the stabilization of soils, and short-term, free-standing architectural structures utilizing the elastogranular medium.
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Attribution 4.0 International