Session N31: Non-Equilibrium and Transient Mechanics of Granular and Soft Materials I

Adaptive Data-Driven Modeling of Complex Systems

In this talk, we present a multiscale adaptive data-driven framework to simulate the behavior of complex systems. Such complex systems typically display non-linear, non-local, micro-morphic features that have challenged continuum and discrete models for over a century. We use granular materials as canonical examples of complex systems to contextualize our proposed data-driven framework, highlighting its ability to bridge the continuum scale with experimental data or grain-scale physics-based simulations. In contrast to continuum phenomenological models and standard multiscale techniques, our approach is parameter-free, physics-based, and true to the entire data set. Additionally, we show that the adaptive nature of the data-driven approach gives rise to a new generation of models that admit goal-oriented data assimilation as a standard feature. This feature is not readily available in phenomenological models that rely on a posteriori metrics of error, resulting in increased complexity, obscurity, and inaccuracy. Conversely, the adaptive data-driven models can incorporate data seamlessly and thereby increase their accuracy to a priori user-specified levels. We argue that this approach to modeling is fundamentally different from current modeling philosophies.   

Dispersion and attenuation of acoustic waves in granular packings

Propagation of acoustic waves through granular and fluid-granular systems has many important geophysical and technology applications. A complete description should connect grain-scale loss mechanisms to functional forms for the frequency dependence of wave speed and attenuation coefficient, presumably via a wave equation derived from grain-scale forces. Dissipation at the grain scale may arise from lossy grain-grain contacts, frictional slips, or viscous damping from the interstitial fluid. Previous work for the acoustic properties of marine sediments has postulated partial differential equations (PDEs) based on different types of grain scale forces. However, these previous theoretical approaches neglect the nonlinear mechanical response of the packing itself, which is known to lead to an array of complex behavior. Here we use discrete element method (DEM) simulations to demonstrate that simple, pairwise granular forces in disordered granular packings lead to emergent scaling laws, particularly for the attenuation coefficient, that do not agree with PDE-based approaches. Our results demonstrate the necessity of considering the granular packing structure in formulating theories for acoustics of marine sediments and other granular systems.   

Plastic deformations and strain hardening in fully dense granular crystals

Granular crystals are intriguing constructs at the intersection between granular matter and architectured materials, offering new combinations of tunable mechanical properties, healing and recyclability. We have recently fabricated and tested fully dense granular FCC crystals based on millimeter size rhombic dodecahedral grains fabricated using 3D printing. Compressive experiments on these granular crystals show that they are more than ten times stronger than traditional granular materials, and that they display a rich set of mechanisms: Nonlinear deformations, crystal plasticity reminiscent of atomistic mechanisms, shear-induced dilatancy, micro-buckling. An intriguing feature of these granular crystals is strain hardening and delocalization, which contrast with typical granular materials which are governed by shear bands and strain softening. To explore these mechanisms, we used discrete elements simulations of FCC granular crystals to duplicate the triaxial compression experiments, and to capture strength and micromechanics of deformation. The models also show that compressive jamming of the grains at the intersection between slip planes is the source of strain hardening in the granular crystal. The implications in terms of size effects, confinement, free boundaries and "polycrystalline" granular crystals are also discussed.   

Packing characteristics of jammed spheres with broad, power-law dispersity

Jammed packings of power-law size disperse spheres show markedly different behavior depending on whether most of the particle volume is concentrated in large or in small particles. Using results of discrete element method simulations jammed under small applied pressure, we quantify the dependence of the salient properties of these packings on power-law exponent and the distribution width for systems with largest-to-smallest particle size ratios of up 200 in 3D. We investigate the per-particle coordination and show the increasing reliance of the mechanically stable backbone on small particles as the distribution exponent becomes more negative, and we explore the role of particle size mismatch on the distribution of contact forces. Finally, we show that packing fractal dimensions extracted from static structure factors are weakly dependent on distribution exponent in 2D and largely independent of exponent in 3D.   

Intermediate range structure in packing of frictional particles

Including friction between particles can have profound effects on particle packing compared to frictionless packings. Friction leads to looser granular sphere packings than frictionless packings: the more friction present the lower the packing fraction attainable. Using discrete element simulations, we show that the inclusion of various modes of friction – which is concomitant with decreasing packing fraction – is characterized by the development of intermediate range order as identified by the emergence of a pre-peak at lower values of the wavenumber q than that of the nearest-neighbor primary peak as seen in the static structure factor S(q).   For mono and weakly dispersed particle packings with sliding friction, the position of the pre-peak increases with the coefficient of friction and occurs at a distance scale d ~ 30 particle diameters.  Including rolling and twisting friction, to account for dissipation on these degrees of freedom, leads to lower density packings with fewer contacts, with a  stronger pre-peak, which shifts to lower q.  The length scale of this intermediate range structure is correlated with spatial fluctuations in the excess number of neighbors a particle has within a distance d compared to the global average.

    

Free-void-volume-based kinetic theory of frictional cohesive powder settling

Frictional cohesive powder (FCP) samples that are prepared by (i) starting with a dilute initial state, and then (ii) ramping the applied pressure from zero to a finite value over a time τ_ramp, have terminal packing fractions (φ_settled) that decrease logarithmically with increasing τ_ramp.  This behavior is the opposite of that exhibited by their frictionless and/or noncohesive counterparts (NCPs), and indeed the opposite of that expected from the usual glass-jamming paradigm wherein slower compression or cooling produces denser final states.  The difference arises from the fact that (in contrast to NCP settling, where the rate-limiting factor is the slow dynamics of densification), FCP powder settling is dominated by the even slower dynamics of structural void stabilization.  We present a free-void-volume-based kinetic theory of FCP settling [K. Nan and R. S. Hoy, Phys. Rev. Lett. 130, 166102 (2023)] that is similar in spirit to but different in several crucial details from late-1990s-vintage free-volume-based kinetic theories of NCP settling, and then show that it quantitatively predicts the dramatic decrease in model FCPs’ φ_settled that occurs as  τ_ramp is increased by several orders of magnitude.   

Clogging of cohesive oil droplets in a 2D hopper

We present an experiment studying the flow of microscopic monodisperse cohesive oil droplets through a two-dimensional hopper. We vary the size of the hopper opening, the size of the droplets, the effective buoyant force which drives the droplets to flow, and the cohesion between droplets. In our experiments, we find that the cohesive strength is positively correlated to the probability of clogging. We compare a range of cohesion strengths and define a parameter balancing the relevant forces of buoyancy and cohesion, which can be used to describe the process of clogging.   

Collapse of a granular raft: particle-scale features on a continuum model

Particles floating on a fluid-fluid interface can self-assemble and form a raft due to capillary interactions. In recent work, we experimentally observed that granular rafts under a bi-axial compression fail in two distinct modes: individual particle expulsion from the interface and collective folding or creasing. A preliminary continuum model related the failure modes with particle sizes and density difference between the upper and lower fluid. But it failed to capture the effect of interfacial tension or particle wettability, both of which were observed to affect raft failure as well as raft formation. To rationalize these observations, we construct a revised continuum model including the effect of particle position for the shape of the granular raft along the fluid-fluid interface. In this talk, we will present how the effect of single particle position changes the failure mode.   

Non-Affine Dynamics and Local Shear Rate in a Sheared Granular System

Granular media are large collections of disordered macroscopic particles interacting via dissipative forces. We focus on the effect of fixed pins on the dynamics of an athermal sheared system in two dimensions. The system consists of a binary 50:50 mixture of radii 1.0:1.4 and additional fixed pins of radius 0.004. A shear is applied by moving the top and bottom walls, made of frozen particles. We study the non-affine dynamics by determining the D2min profile. Despite vertical symmetry in our shearing geometry, when pins are absent the long-lasting fluctuations in stress yield an asymmetric D2min profile. This occurs even when the system is sheared over an extremely large range (a dimensionless strain of around 1.) However, as pin density increases, the D2min profile is increasingly symmetric, with higher D2min values found closer to the walls. Via the velocity profile we determine the local shear rate, and find qualitatively the same profile shapes for D2min and the local shear rate.   

Influence of Pins on the dynamics of a sheared granular system

We use molecular dynamics simulations to study a two dimensional 50:50 binary mixture of purely repulsive harmonic disks of radii 1:1.4. Via top and bottom walls of frozen particles we shear the system at constant shear rate.  We simulate at zero temperature and apply dissipative interactions depending on relative velocities.  We investigate how the dynamics is influenced by the addition of fixed miniscule disks of radius 0.004 placed on a square lattice. We find that at the absence of pins the velocity profile shows long time fluctuations about the linear velocity field. In the presence of pins, and similarly at higher shear rate, the velocity profile  does not have the long time fluctuations and can approximated with a model of B. Tighe. We will show also the long time shear stress as functions of packing fraction, shear rate and pressure for the quasistatic case as well as for fast shear rate. Furthermore, we will show preliminary results for the case of applying constant pressure on the top wall. We find that the local pressure profile is increasingly non-uniform with increasing number of pins. To study dynamical heterogeneities we determine D2min. We find that the probability of larger D2min is larger near a pin and decreases with distance from the pin. For distances approximately smaller than 10 this decrease is independent of the number of pins.   

Hygroelastic Transition: Unusual Non-Equilibrium Behavior Found in Hygroscopic Biological Materials with Rich Characteristics

Recent experiments on the hygroscopic spores of a common soil bacterium have unveiled unusual equilibrium and nonequilibrium properties that do not have counterparts in other types of solid matter (1). Among these is a marked nonequilibrium transition in mechanical properties at short timescales called the hygroelastic transition, which was predicted to originate from jamming of water molecules confined between biomolecules. Several predictions about this transition remain to be tested. Specifically, the hygroelastic theory predicts that (i) the observed transition in elastic modulus should be accompanied by a transition from a strong nonlinear elastic behavior to a linear elastic behavior, (ii) the transition timescale should depend strongly on equilibrium mechanical strain, and (iii) the transition should be observable in other types of hygroscopic biological materials. Here we present evidence for these three predictions with atomic force microscopy measurements on bacterial spores and regenerated cellulose films. Our experiments are based on frequency-dependent contact stiffness measurements. Findings suggest that the hygroelastic transition is an unusual nonequilibrium phenomenon with a rich set of features.

1. Harrellson, S.G. et al. Hydration solids. Nature 619, 500–505 (2023).

This work was supported by National Institute of General Medical Sciences of the National Institutes of Health, award no R35GM145382 and by the Office of Naval Research, award no. N00014-21-1-4004.