arXiv subjects

Mark D. Shattuck

Publications and source records attributed to Mark D. Shattuck.

At least 37 records · Page 2Linked to original sources

arXiv2023

Designing the pressure-dependent shear modulus using tessellated granular metamaterials

Jammed packings of granular materials display complex mechanical response. For example, the ensemble-averaged shear modulus $\left\langle G \right\rangle$ increases as a power-law in pressure $p$ for static packings of soft spherical particles that can rearrange during compression. We seek to design granular materials with shear moduli that can either increase {\it or} decrease with pressure without particle rearrangements even in the large-system limit. To do this, we construct {\it tessellated} granular metamaterials by joining multiple particle-filled cells together. We focus on cells that contain a small number of bidisperse disks in two dimensions. We first study the mechanical properties of individual disk-filled cells with three types of boundaries: periodic boundary conditions (PBC), fixed-length walls (FXW), and flexible walls (FLW). Hypostatic jammed packings are found for cells with FLW, but not in cells with PBC and FXW, and they are stabilized by quartic modes of the dynamical matrix. The shear modulus of a single cell depends linearly on $p$. We find that the slope of the shear modulus with pressure, $λ_c < 0$ for all packings in single cells with PBC where the number of particles per cell $N \ge 6$. In contrast, single cells with FXW and FLW can possess $λ_c > 0$, as well as $λ_c < 0$, for $N \le 16$. We show that we can force the mechanical properties of multi-cell granular metamaterials to possess those of single cells by constraining the endpoints of the outer walls and enforcing an affine shear response. These studies demonstrate that tessellated granular metamaterials provide a novel platform for the design of soft materials with specified mechanical properties.

cond-mat.soft↗

arXiv2023

Tessellated granular metamaterials with tunable elastic moduli

Most granular packings possess shear moduli ($G$) that increase with the applied external pressure, and bulk moduli ($B$) that increase or remain constant with pressure. This paper presents "tessellated" granular metamaterials for which both $G$ and the ratio $G/B$ decrease with increasing pressure. The granular metamaterials are made from flexible tessellations forming a ring of closed cells, each containing a small number of solid particles. For under-constrained tessellations, the dominant contributions to $G$ and $B$ are the particle-particle and particle-cell interactions. With specific particle configurations in the cells, we limit the number of possible particle rearrangements to achieve decreasing $G$ as we increase the pressure difference between the inside and outside of the tessellation, leading to $G/B \ll 1$ at large pressures. We further study tessellated granular metamaterials with cells containing a single particle and many particles to determine the variables that control the mechanical response of particle-filled tessellations as a function of pressure.

cond-mat.soft↗

arXiv2023

Characterizing the mechanical response of metallic glasses to uniaxial tension using a spring network model

Metallic glasses are frequently used as structural materials. Therefore, it is important to develop methods to predict their mechanical response as a function of the microstructure prior to loading. We develop a coarse-grained spring network model, which describes the mechanical response of metallic glasses using an equivalent series network of springs, which can break and re-form to mimic atomic rearrangements during deformation. To validate the model, we perform simulations of quasistatic, uniaxial tension of Lennard-Jones and embedded atom method (EAM) potentials for Cu$_{50}$Zr$_{50}$ metallic glasses. We consider samples prepared using a wide range of cooling rates and with different amounts of crystalline order. We show that both the Lennard-Jones and EAM models possess qualitatively similar stress $σ$ versus strain $γ$ curves. By specifying five parameters in the spring network model (ultimate strength, strain at ultimate strength, slopes of $σ(γ)$ at $γ=0$ and at large strain, and strain at fracture where $σ=0$), we can accurately describe the form of the stress-strain curves during uniaxial tension for the computational studies of Cu$_{50}$Zr$_{50}$, as well as recent experimental studies of several Zr-based metallic glasses. For the computational studies of Cu$_{50}$Zr$_{50}$, we find that the yield strain distribution is shifted to larger strains for slowly cooled glasses compared to rapidly cooled glasses. In addition, the average number of new springs and their rate of formation decreases with decreasing cooling rate. These effects offset each other at large strains, causing the stress-strain curve to become independent of the sample preparation protocol in this regime. In future studies, we will extract the parameters that define the spring network model directly from atomic rearrangements that occur during uniaxial deformation.

cond-mat.mtrl-sci↗

arXiv2022

Localized growth drives spongy mesophyll morphogenesis

The spongy mesophyll is a complex, porous tissue found in plant leaves that enables carbon capture and provides mechanical stability. Unlike many other biological tissues, which remain confluent throughout development, the spongy mesophyll must develop from an initially confluent tissue into a tortuous network of cells with a large proportion of intercellular airspace. How the airspace in the spongy mesophyll develops while the cells remain mechanically stable remains unknown. Here, we used computer simulations of deformable particles to develop a purely mechanical model for the development of the spongy mesophyll tissue. By stipulating that (1) cell perimeter grows only near voids, (2) cells both form and break adhesive bonds, and (3) the tissue pressure remains constant, the computational model was able to recapitulate the developmental trajectory of the microstructure of the spongy mesophyll observed in Arabidopsis thaliana leaves. Robust generation of pore space in the spongy mesophyll requires a balance of cell growth, adhesion, stiffness and tissue pressure to ensure cell networks remain both porous yet mechanically robust. The success of this mechanical model of tissue growth and porosity evolution suggests that simple physical principles can coordinate and drive the development of complex plant tissues like the spongy mesophyll.

physics.bio-ph↗

arXiv2022

Evolving Programmable Computational Metamaterials

Granular metamaterials are a promising choice for the realization of mechanical computing devices. As preliminary evidence of this, we demonstrate here how to embed Boolean logic gates (AND and XOR) into a granular metamaterial by evolving where particular grains are placed in the material. Our results confirm the existence of gradients of increasing "AND-ness" and "XOR-ness" within the space of possible materials that can be followed by evolutionary search. We measure the computational functionality of a material by probing how it transforms bits encoded as vibrations with zero or non-zero amplitude. We compared the evolution of materials built from mass-contrasting particles and materials built from stiffness-contrasting particles, and found that the latter were more evolvable. We believe this work may pave the way toward evolutionary design of increasingly sophisticated, programmable, and computationally dense metamaterials with certain advantages over more traditional computational substrates.

cs.ET↗

arXiv2022

Universal mechanical response of metallic glasses during strain-rate-dependent uniaxial compression

Experimental data on the compressive strength $σ_{\rm max}$ versus strain rate ${\dot \varepsilon}_{\rm eng}$ for metallic glasses undergoing uniaxial compression shows significantly different behavior for different alloys. For some metallic glasses, $σ_{\rm max}$ decreases with increasing ${\dot \varepsilon}_{\rm eng}$, for others, $σ_{\rm max}$ increases with increasing ${\dot \varepsilon}_{\rm eng}$, and for others $σ_{\rm max}$ versus ${\dot \varepsilon}_{\rm eng}$ is nonmonotonic. Using numerical simulations of metallic glasses undergoing uniaxial compression at nonzero strain rate and temperature, we show that they obey a universal relation for the compressive strength versus temperature, which determines their mechanical response. At low ${\dot \varepsilon}_{\rm eng}$, increasing strain rate leads to increases in temperature and decreases in $σ^*_{\rm max}$, whereas at high ${\dot \varepsilon}_{\rm eng}$, increasing strain rate leads to decreases in temperature and increases in $σ^*_{\rm max}$. This non-monotonic behavior of $σ^*_{\rm max}$ versus temperature causes the nonmonotonic behavior of $σ^*_{\rm max}$ versus ${\dot \varepsilon}_{\rm eng}$. Variations in the internal dissipation change the characteristic strain rate at which the nonmonotonic behavior occurs. These results are general for a wide range of metallic glasses with different atomic interactions, damping coefficients, and chemical compositions.

cond-mat.soft↗

arXiv2022

The glass-forming ability of binary Lennard-Jones systems

The glass-forming ability (GFA) of alloys, colloidal dispersions, and other particulate materials, as measured by the critical cooling rate $R_c$, can span more than ten orders of magnitude. Even after numerous previous studies, the physical features that control the GFA are still not well understood. For example, it is well-known that mixtures are better glass-formers than monodisperse systems and that particle size and cohesive energy differences among constituents improve the GFA, but it is not currently known how particle size differences couple to cohesive energy differences to determine the GFA. We perform molecular dynamics simulations to determine the GFA of equimolar, binary Lennard-Jones (LJ) mixtures versus the normalized cohesive energy difference $ε_\_$ and mixing energy $\bar ε_{AB}$ between particles A and B. We find several important results. First, the $\log_{10} R_c$ contours in the $\bar ε_{AB}$-$ε_\_$ plane are ellipsoidal for all diameter ratios, and thus $R_c$ is determined by the Mahalanobis distance $d_M$ from a given point in the $\bar ε_{AB}$-$ε_\_$ plane to the center of the ellipsoidal contours. Second, LJ systems for which the larger particles have larger cohesive energy are generally better glass formers than those for which the larger particles have smaller cohesive energy. Third, $d_M(ε_\_,\bar ε_{AB})$ is determined by the relative Voronoi volume difference between particles and local chemical order $S_{AB}$, which gives the average fraction of nearest-neighbor B particles surrounding an A particle and vice-versa. In particular, the shifted Mahalanobis distance $d_M - d^0_M$ versus the shifted chemical order $S_{AB}-S_{AB}^0$ collapses onto a hyperbolic master curve for all diameter ratios.

cond-mat.mtrl-sci↗

arXiv2021

The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions

We investigate the structural, vibrational, and mechanical properties of jammed packings of deformable particles with shape degrees of freedom in three dimensions (3D). Each 3D deformable particle is modeled as a surface-triangulated polyhedron, with spherical vertices whose positions are determined by a shape-energy function with terms that constrain the particle surface area, volume, and curvature, and prevent interparticle overlap. We show that jammed packings of deformable particles without bending energy possess low-frequency, quartic vibrational modes, whose number decreases with increasing asphericity and matches the number of missing contacts relative to the isostatic value. In contrast, jammed packings of deformable particles with non-zero bending energy are isostatic in 3D, with no quartic modes. We find that the contributions to the eigenmodes of the dynamical matrix from the shape degrees of freedom are significant over the full range of frequency and shape parameters for particles with zero bending energy. We further show that the ensemble-averaged shear modulus $\langle G \rangle$ scales with pressure $P$ as $\langle G \rangle \sim P^β$, with $β\approx 0.75$ for jammed packings of deformable particles with zero bending energy. In contrast, $β\approx 0.5$ for packings of deformable particles with non-zero bending energy, which matches the value for jammed packings of soft, spherical particles with fixed shape. These studies underscore the importance of incorporating particle deformability and shape change when modeling the properties of jammed soft materials.

cond-mat.soft↗

arXiv2021

Bridging particle deformability and collective response in soft solids

Soft, amorphous solids such as tissues, foams, and emulsions are composed of deformable particles. However, the effect of single-particle deformability on the collective behavior of soft solids is still poorly understood. We perform numerical simulations of two-dimensional jammed packings of explicitly deformable particles to study the mechanical response of model soft solids. We find that jammed packings of deformable particles with excess shape degrees of freedom possess low-frequency quartic vibrational modes that stabilize the packings even though they possess fewer interparticle contacts than the nominal isostatic value. Adding intra-particle constraints can rigidify the particles, but these particles undergo a buckling transition and gain an effective shape degree of freedom when their preferred perimeter is above a threshold value. We find that the mechanical response of jammed packings of deformable particles with shape degrees of freedom differs significantly from that of jammed packings of rigid-shape particles, which emphasizes the importance of particle deformability in modelling soft solids.

cond-mat.soft↗

arXiv2020

Shear response of granular packings compressed above jamming onset

We investigate the mechanical response of jammed packings of repulsive, frictionless spherical particles undergoing isotropic compression. Prior simulations of the soft-particle model, where the repulsive interactions scale as a power-law in the interparticle overlap with exponent $α$, have found that the ensemble-averaged shear modulus $\langle G \rangle$ increases with pressure $P$ as $\sim P^{(α-3/2)/(α-1)}$ at large pressures. However, a deep theoretical understanding of this scaling behavior is lacking. We show that the shear modulus of jammed packings of frictionless, spherical particles has two key contributions: 1) continuous variations as a function of pressure along geometrical families, for which the interparticle contact network does not change, and 2) discontinuous jumps during compression that arise from changes in the contact network. We show that the shear modulus of the first geometrical family for jammed packings can be collapsed onto a master curve: $G^{(1)}/G_0 = (P/P_0)^{(α-2)/(α-1)} - P/P_0$, where $P_0 \sim N^{-2(α-1)}$ is a characteristic pressure that separates the two power-law scaling regions and $G_0 \sim N^{-2(α-3/2)}$. Deviations from this form can occur when there is significant non-affine particle motion near changes in the contact network. We further show that $\langle G (P)\rangle$ is not simply a sum of two power-laws, but $\langle G \rangle \sim (P/P_c)^a$, where $a \approx (α-2)/(α-1)$ in the $P \rightarrow 0$ limit and $\langle G \rangle \sim (P/P_c)^b$, where $b \gtrsim (α-3/2)/(α-1)$ above a characteristic pressure $P_c$. In addition, the magnitudes of both contributions to $\langle G\rangle$ from geometrical families and changes in the contact network remain comparable in the large-system limit for $P >P_c$.

cond-mat.soft↗

arXiv2020

Homogeneous crystallization in cyclically sheared frictionless grains

Many experiments over the past half century have shown that, for a range of protocols, granular materials compact under pressure and repeated small disturbances. A recent experiment on cyclically sheared spherical grains showed significant compaction via homogeneous crystallization (Rietz et al., 2018). Here we present numerical simulations of frictionless, purely repulsive spheres undergoing cyclic simple shear with dissipative Newtonian dynamics at fixed vertical load. We show that for sufficiently small strain amplitudes, cyclic shear gives rise to homogeneous crystallization at a volume fraction $ϕ= 0.646 \pm 0.001$. This result indicates that neither friction nor gravity is essential for homogeneous crystallization in driven granular media.

cond-mat.soft↗

arXiv2020

Glass formation in binary alloys with different atomic symmetries

Prediction of the glass forming ability (GFA) of alloys remains a major challenge. We are not able to predict the composition dependence of the GFA of even binary alloys. To investigate the effect of each element's propensity to form particular crystal structures on glass formation, we focus on binary alloys composed of elements with the same size, but different atomic symmetries using the patchy-particle model. For mixtures with atomic symmetries that promote different crystal structures, the minimum critical cooling rate $R_c$ is only a factor of $5$ lower than that for the pure substances. For mixtures with different atomic symmetries that promote local crystalline and icosahedral order, the minimum $R_c$ is more than $3$ orders of magnitude lower than that for pure substances. Results for $R_c$ for the patchy-particle model are in agreement with those from embedded atom method simulations and sputtering experiments of NiCu, TiAl, and high entropy alloys.

cond-mat.mtrl-sci↗

arXiv2019

Jammed packings of 3D superellipsoids with tunable packing fraction, contact number, and ordering

We carry out numerical studies of static packings of frictionless superellipsoidal particles in three spatial dimensions. We consider more than $200$ different particle shapes by varying the three shape parameters that define superellipsoids. We characterize the structural and mechanical properties of both disordered and ordered packings using two packing-generation protocols. We perform athermal quasi-static compression simulations starting from either random, dilute configurations (Protocol 1) or thermalized, dense configurations (protocol $2$), which allows us to tune the orientational order of the packings. In general, we find that the contact numbers at jamming onset for superellipsoid packings are hypostatic, with $z_J < z_{\rm iso}$, where $z_{\rm iso} = 2d_f$ and $d_f = 5$ or $6$ depending on whether the particles are axi-symmetric or not. Over the full range of orientational order, we find that the number of quartic modes of the dynamical matrix for the packings always matches the number of missing contacts relative to the isostatic value. This result suggests that there are no mechanically redundant contacts for ordered, yet hypostatic packings of superellipsoidal particles. Additionally, we find that the packing fraction at jamming onset for disordered packings of superellipsoidal particles can be collapsed using two particle shape parameters, e.g. the asphericity $\mathcal{A}$ and reduced aspect ratio $β$ of the particles.

cond-mat.soft↗

arXiv2019

Pressure-dependent shear response of jammed packings of spherical particles

The mechanical response of packings of purely repulsive, spherical particles to athermal, quasistatic simple shear near jamming onset is highly nonlinear. Previous studies have shown that, at small pressure $p$, the ensemble-averaged static shear modulus $\langle G-G_0 \rangle$ scales with $p^α$, where $α\approx 1$, but above a characteristic pressure $p^{**}$, $\langle G-G_0 \rangle \sim p^β$, where $β\approx 0.5$. However, we find that the shear modulus $G^i$ for an individual packing typically decreases linearly with $p$ along a geometrical family where the contact network does not change. We resolve this discrepancy by showing that, while the shear modulus does decrease linearly within geometrical families, $\langle G \rangle$ also depends on a contribution from discontinuous jumps in $\langle G \rangle$ that occur at the transitions between geometrical families. For $p > p^{**}$, geometrical-family and rearrangement contributions to $\langle G \rangle$ are of opposite signs and remain comparable for all system sizes. $\langle G \rangle$ can be described by a scaling function that smoothly transitions between the two power-law exponents $α$ and $β$. We also demonstrate the phenomenon of {\it compression unjamming}, where a jammed packing can unjam via isotropic compression.

cond-mat.soft↗

arXiv2019

The role of deformability in determining the structural and mechanical properties of bubbles and emulsions

We perform computational studies of jammed particle packings in two dimensions undergoing isotropic compression using the well-characterized soft particle (SP) model and the deformable particle (DP) model that we developed for compressed bubbles and emulsions. In the SP model, circular particles are allowed to overlap, generating purely repulsive forces. In the DP model, particles minimize their perimeter, while deforming at fixed area to avoid overlap during compression. We directly compare the structural and mechanical properties of jammed particle packings generated using the SP and DP models as a function of the true packing fraction $ρ$, instead of the reduced number density $ϕ$. We show that near jamming onset the excess contact number $Δz=z-z_J$ and shear modulus ${\cal G}$ scale as $Δρ^{0.5}$ in the large system limit for both the SP and DP models, where $Δρ= ρ-ρ_J$ and $z_J \approx 4$ and $ρ_J \approx 0.842$ are the values at jamming onset. $Δz$ and ${\cal G}$ for the SP and DP models begin to differ for $ρ\gtrsim 0.88$. In this regime, $Δz \sim {\cal G}$ can be described by a sum of two power-laws in $Δρ$, i.e. $Δz \sim {\cal G} \sim C_0Δρ^{0.5} +C_1Δρ^{1.0}$ to lowest order. We show that the ratio $C_1/C_0$ is much larger for the DP model compared to to that for the SP model. We also characterize the void space in jammed packings as a function of $ρ$. We find that, unlike the SP model, the DP model is able to describe the formation of Plateau borders as the system approaches $ρ= 1$. We further show that the results for $z$ and the shape factor ${\cal A}$ versus $ρ$ for the DP model agree with recent experimental studies of compressed foams and emulsions.

physics.app-ph↗

arXiv2019

Intrinsic dissipation mechanisms in metallic glass resonators

Micro- and nano-resonators have important applications including sensing, navigation, and biochemical detection. Their performance is quantified using the quality factor $Q$, which gives the ratio of the energy stored to the energy dissipated per cycle. Metallic glasses are a promising materials class for micro- and nano-scale resonators since they are amorphous and can be fabricated precisely into complex shapes on these lengthscales. To understand the intrinsic dissipation mechanisms that ultimately limit large $Q$-values in metallic glasses, we perform molecular dynamics simulations to model metallic glass resonators subjected to bending vibrations. We calculate the vibrational density of states, redistribution of energy from the fundamental mode of vibration, and $Q$ versus the kinetic energy per atom $K$ of the excitation. In the linear and nonlinear response regimes where there are no atomic rearrangements, we find that $Q \rightarrow \infty$ (since we do not consider coupling to the environment). We identify a characteristic $K_r$ above which atomic rearrangements occur, and there is significant energy leakage from the fundamental mode to higher frequencies, causing finite $Q$. Thus, $K_r$ is a critical parameter determining resonator performance. We show that $K_r$ decreases as a power-law, $K_r\sim N^{-k},$ with increasing system size $N$, where $k \approx 1.3$. We estimate the critical strain $\langle γ_r \rangle \sim 10^{-8}$ for micron-sized resonators below which atomic rearrangements do not occur, and thus large $Q$-values can be obtained when they are operated below $γ_r$. We find that $K_r$ for amorphous resonators is comparable to that for resonators with crystalline order.

cond-mat.mtrl-sci↗

arXiv2019

Tuning the glass-forming ability of metallic glasses through energetic frustration

The design of multi-functional BMGs is limited by the lack of a quantitative understanding of the variables that control the glass-forming ability (GFA) of alloys. Both geometric frustration (e.g. differences in atomic radii) and energetic frustration (e.g. differences in the cohesive energies of the atomic species) contribute to the GFA. We perform molecular dynamics simulations of binary Lennard-Jones mixtures with only energetic frustration. We show that there is little correlation between the heat of mixing and critical cooling rate $R_c$, below which the system crystallizes, except that $ΔH_{\rm mix} < 0$. By removing the effects of geometric frustration, we show strong correlations between $R_c$ and the variables $ε_- = (ε_{BB}-ε_{AA})/(ε_{AA}+ε_{BB})$ and ${\overline ε}_{AB} = 2ε_{AB}/(ε_{AA}+ε_{BB})$, where $ε_{AA}$ and $ε_{BB}$ are the cohesive energies of atoms $A$ and $B$ and $ε_{AB}$ is the pair interaction between $A$ and $B$ atoms. We identify a particular $f_B$-dependent combination of $ε_-$ and ${\overline ε}_{AB}$ that collapses the data for $R_c$ over nearly $4$ orders of magnitude in cooling rate.

cond-mat.mtrl-sci↗

arXiv2019

Active acoustic switches using 2D granular crystals

We employ numerical simulations to study active transistor-like switches made from two-dimensional (2D) granular crystals containing two types of grains with the same size, but different masses. We tune the mass contrast and arrangement of the grains to maximize the width of the frequency band gap in the device. The input signal is applied to a single grain on one side of the device, and the output signal is measured from another grain on the other side of the device. Changing the size of one or many grains tunes the pressure, which controls the vibrational response of the device. Switching between the on and off states is achieved using two mechanisms: 1) pressure-induced switching where the interparticle contact network is the same in the on and off states, and 2) switching through contact breaking. In general, the performance of the acoustic switch, as captured by the gain ratio and switching time between the on and off states, is better for pressure-induced switching. We show that in these acoustic switches the gain ratio between the on and off states can be larger than $10^4$ and the switching time (multiplied by the driving frequency) is comparable to that obtained recently for sonic crystals and less than that for photonic transistor-like switches. Since the self-assembly of grains with different masses into 2D granular crystals is challenging, we describe simulations of circular grains with small circular knobs placed symmetrically around the perimeter mixed with circular grains without knobs. Using umbrella sampling techniques, we show that devices with grains with $3$ knobs most efficiently form the hexagonal crystals that yield the largest band gap.

cond-mat.soft↗