Constitutive relation for the system-spanning dynamically jammed region in response to impact of cornstarch and water suspensions

Effective viscosity and elasticity in dense suspensions under impact: Toward a modeling of walking on suspensions

The elastic response of dense suspensions under an impact is studied using coupled lattice Boltzmann method and discrete element method (LBM-DEM) and its reduced model. We succeed to extract the elastic force acting on the impactor in dense suspensions, which can exist even in the absence of percolating clusters of suspended particles. We then propose a reduced model to describe the motion of the impactor and demonstrate its relevancy through the comparison of the solution of the reduced model and that of LBM-DEM. Furthermore, we illustrate that the perturbation analysis of the reduced model captures the short-time behavior of the impactor motion quantitatively. We apply this reduced model to the impact of a foot-spring-body system on a dense suspension, which is the minimal model to realize walking on the suspension. Due to the spring force of the system and the stiffness of the suspension, the foot undergoes multiple bounces. We also study the parameter dependencies of the hopping motion and find that multiple bounces are suppressed as the spring stiffness increases.

Fabric Impregnation with Shear Thickening Fluid for Ballistic Armor Polymer Composites: An Updated Overview

As destructive power of firearms raises over the years, ballistic armors are in continuous need of enhancement. For soft armors, this improvement is invariably related to the increase of stacked layers of high-strength fiber fabrics, which potentially restrains wearer mobility. A different solution was created in the early 2000s, when a research work proposed a new treatment of the ballistic panels with non-Newtonian colloidal shear thickening fluid (STF), in view of weight decreasing with strength reinforcement and cost-effective production. Since then, databases reveal a surge in publications generally pointing to acceptable features under ballistic impact by exploring different conditions of the materials adopted. As a result, several works have not been covered in recent reviews for a wider discussion of their methodologies and results, which could be a barrier to a deeper understanding of the behavior of STF-impregnated fabrics. Therefore, the present work aims to overview the unexplored state-of-art on the effectiveness of STF addition to high-strength fabrics for ballistic applications to compile achievements regarding the ballistic strength of this novel material through different parameters. From the screened papers, SiO2, Polyethylene glycol (PEG) 200 and 400, and Aramid are extensively being incorporated into the STF/Fabric composites. Besides, parameters such as initial and residual velocity, energy absorbed, ballistic limit, and back face signature are common metrics for a comprehensive analysis of the ballistic performance of the material. The overview also points to a promising application of natural fiber fabrics and auxetic fabrics with STF fluids, as well as the demand for the adoption of new materials and more homogeneous ballistic test parameters. Finally, the work emphasizes that the ballistic application for STF-impregnated fabric based on NIJ standards is feasible for several conditions.

Relation between dilation and stress fluctuations in discontinuous shear thickening suspensions

We investigate dilation-induced surface deformations in a discontinuous shear thickening (DST) suspension to determine the relationship between dilation and stresses in DST. Video is taken at two observation points on the surface of the suspension in a rheometer while shear and normal stresses are measured. A roughened surface of the suspension is observed as particles poke through the liquid-air interface, an indication of dilation in a suspension. These surface roughening events are found to be intermittent and localized spatially. Shear and normal stresses also fluctuate between high- and low-stress states, and surface roughening is observed frequently in the high-stress state. On the other hand, a complete lack of surface roughening is observed when the stresses remain at low values for several seconds. Surface roughening is most prominent while the stresses grow from the low-stress state to the high-stress state, and the roughened surface tends to span the entire surface by the end of the stress growth period. Surface roughening is found only at stresses and shear rates in and above the shear thickening range. These observed relations between surface roughening and stresses confirm that dilation and stresses are coupled in the high-stress state of DST.

Simulation of dense non-Brownian suspensions with the lattice Boltzmann method: shear jammed and fragile states

Dense non-Brownian suspensions, including both hydrodynamic interactions and frictional contacts between particles, are numerically studied under simple and oscillatory shears in terms of the lattice Boltzmann method. We successfully reproduce the discontinuous shear thickening (DST) under a simple shear for bulk three-dimensional systems. For our simulation of an oscillatory shear in a quasi-two-dimensional system, we measure the mechanical response after the reduction of the strain amplitude from the initial oscillations. Here, we find the existence of a shear-jammed state under this protocol in which the storage modulus G' is only finite for high initial strain amplitude γI0. We also find the existence of a fragile state in which both fluid-like and solid-like responses can be detected for an identical area fraction and an initial strain amplitude γI0 depending on the initial phase Θ (or the asymmetricity of the applied strain) of the oscillatory shear. We also observe a DST-like behavior under the oscillatory shear in the fragile state. Moreover, we find that the stress anisotropy becomes large in the fragile state. Finally, we confirm that a stress formula based on the angular distribution of the contact force recovers the contact contributions to the stress tensors for both simple and oscillatory shears with large strains.

Unsteady flow, clusters, and bands in a model shear-thickening fluid

We analyze the flow curves of a two-dimensional assembly of granular particles which are interacting via frictional contact forces. For packing fractions slightly below jamming, the fluid undergoes a large scale instability, implying a range of stress and strain rates where no stationary flow can exist. Whereas small systems were shown previously to exhibit hysteretic jumps between the low and high stress branches, large systems exhibit continuous shear thickening arising from averaging unsteady, spatially heterogeneous flows. The observed large scale patterns as well as their dynamics are found to depend on strain rate: At the lower end of the unstable region, force chains merge to form giant bands that span the system in the compressional direction and propagate in the dilational direction. At the upper end, we observe large scale clusters which extend along the dilational direction and propagate along the compressional direction. Both patterns, bands and clusters, come in with infinite correlation length similar to the sudden onset of system-spanning plugs in impact experiments.

Stress Controlled Rheology of Dense Suspensions Using Transient Flows

Dense suspensions of hard particles in a Newtonian liquid can be jammed by shear when the applied stress exceeds a certain threshold. However, this jamming transition from a fluid into a solidified state cannot be probed with conventional steady-state rheology because the stress distribution inside the material cannot be controlled with sufficient precision. Here we introduce and validate a method that overcomes this obstacle. Rapidly propagating shear fronts are generated and used to establish well-controlled local stress conditions that sweep across the material. Exploiting such transient flows, we can track how a dense suspension approaches its shear-jammed state dynamically and quantitatively map out the onset stress for solidification in a state diagram.

A general constitutive model for dense, fine-particle suspensions validated in many geometries

Fine-particle suspensions (such as cornstarch mixed with water) exhibit dramatic changes in viscosity when sheared, producing fascinating behaviors that captivate children and rheologists alike. Examination of these mixtures in simple flow geometries suggests intergranular repulsion and its influence on the frictional nature of granular contacts is central to this effect-for mixtures at rest or shearing slowly, repulsion prevents frictional contacts from forming between particles, whereas when sheared more forcefully, granular stresses overcome the repulsion allowing particles to interact frictionally and form microscopic structures that resist flow. Previous constitutive studies of these mixtures have focused on particular cases, typically limited to 2D, steady, simple shearing flows. In this work, we introduce a predictive and general, 3D continuum model for this material, using mixture theory to couple the fluid and particle phases. Playing a central role in the model, we introduce a microstructural state variable, whose evolution is deduced from small-scale physical arguments and checked with existing data. Our space- and time-dependent model is implemented numerically in a variety of unsteady, nonuniform flow configurations where it is shown to accurately capture a variety of key behaviors: 1) the continuous shear-thickening (CST) and discontinuous shear-thickening (DST) behavior observed in steady flows, 2) the time-dependent propagation of "shear jamming fronts," 3) the time-dependent propagation of "impact-activated jamming fronts," and 4) the non-Newtonian, "running on oobleck" effect, wherein fast locomotors stay afloat while slow ones sink.

Testing constitutive relations by running and walking on cornstarch and water suspensions

The ability of a person to run on the surface of a suspension of cornstarch and water has fascinated scientists and the public alike. However, the constitutive relation obtained from traditional steady-state rheology of cornstarch and water suspensions has failed to explain this behavior. In another paper we presented an averaged constitutive relation for impact rheology consisting of an effective compressive modulus of a system-spanning dynamically jammed structure [R. Maharjan et al., this issue, Phys. Rev. E 97, 052602 (2018)10.1103/PhysRevE.97.052602]. Here we show that this constitutive model can be used to quantitatively predict, for example, the trajectory and penetration depth of the foot of a person walking or running on cornstarch and water. The ability of the constitutive relation to predict the material behavior in a case with different forcing conditions and flow geometry than it was obtained from suggests that the constitutive relation could be applied more generally. We also present a detailed calculation of the added mass effect to show that while it may be able to explain some cases of people running or walking on the surface of cornstarch and water for pool depths H>1.2 m and foot impact velocities V_{I}>1.7 m/s, it cannot explain observations of people walking or running on the surface of cornstarch and water for smaller H or V_{I}.

System-spanning dynamically jammed region in response to impact of cornstarch and water suspensions

We experimentally characterize the structure of concentrated suspensions of cornstarch and water in response to impact. Using surface imaging and particle tracking at the boundary opposite the impactor, we observed that a visible structure and particle flow at the boundary occur with a delay after impact. We show the delay time is about the same time as the strong stress response, confirming that the strong stress response results from deformation of the dynamically jammed structure once it spans between the impactor and a solid boundary. A characterization of this strong stress response is reported in a companion paper [Maharjan, Mukhopadhyay, Allen, Storz, and Brown, Phys. Rev. E 97, 052602 (2018)10.1103/PhysRevE.97.052602]. We observed particle flow in the outer part of the dynamically jammed region at the bottom boundary, with a net transverse displacement of up to about 5% of the impactor displacement, indicating shear at the boundary. Direct imaging of the surface of the outer part of the dynamically jammed region reveals a change in surface structure that appears the same as the result of dilation in other cornstarch suspensions. Imaging also reveals cracks, like a brittle solid. These observations suggest the dynamically jammed structure can temporarily support stress according to an effective modulus, like a soil or dense granular material, along a network of frictional contacts between the impactor and solid boundary.