Catch bond kinetics are instrumental to cohesion of fire ant rafts under load.

Dynamic networks composed of constituents that break and reform bonds reversibly are ubiquitous in nature owing to their modular architectures that enable functions like energy dissipation, self-healing, and even activity. While bond breaking depends only on the current configuration of attachment in these networks, reattachment depends also on the proximity of constituents. Therefore, dynamic networks composed of macroscale constituents (not benefited by the secondary interactions cohering analogous networks composed of molecular-scale constituents) must rely on primary bonds for cohesion and self-repair. Toward understanding how such macroscale networks might adaptively achieve this, we explore the uniaxial tensile response of 2D rafts composed of interlinked fire ants (S. invicta). Through experiments and discrete numerical modeling, we find that ant rafts adaptively stabilize their bonded ant-to-ant interactions in response to tensile strains, indicating catch bond dynamics. Consequently, low-strain rates that should theoretically induce creep mechanics of these rafts instead induce elastic-like response. Our results suggest that this force-stabilization delays dissolution of the rafts and improves toughness. Nevertheless, above 35[Formula: see text] strain low cohesion and stress localization cause nucleation and growth of voids whose coalescence patterns result from force-stabilization. These voids mitigate structural repair until initial raft densities are restored and ants can reconnect across defects. However mechanical recovery of ant rafts during cyclic loading suggests that-even upon reinstatement of initial densities-ants exhibit slower repair kinetics if they were recently loaded at faster strain rates. These results exemplify fire ants' status as active agents capable of memory-driven, stimuli-response for potential inspiration of adaptive structural materials.

Programming Motion into Materials Using Electricity-Driven Liquid Crystal Elastomer Actuators.

As thermally driven smart materials capable of large reversible deformations, liquid crystal elastomers (LCEs) have great potential for applications in bionic soft robots, artificial muscles, controllable actuators, and flexible sensors due to their ability to program controllable motion into materials. In this article, we introduce conductive LCE actuators using a liquid metal electrothermal layer and a polyethylene terephthalate substrate. Our LCE actuators can be stimulated at low currents from 2 to 4 A and produce a maximum work density of 9.4 kJ∕m3. We illustrate the potential applications of this system by designing a palm-activated artificial muscle gripper, which can be used to grasp soft objects ranging from 5 to 55 mm in size, and even ring-shaped workpieces with precise external or internal support. Furthermore, inspired by the movement of fruit fly larvae, we designed a new soft robot capable of bioinspired crawling and turning by inducing anisotropic friction with an asymmetric design. Finally, we illustrate advanced motional control by designing an autonomously rotating wheel based on the asymmetric contraction of its spokes. To assist in the production of autonomously moving robots, we provide a thorough characterization of its motion dynamics.

Material assembly from collective action of shape-changing polymers.

Some animals form transient, responsive and solid-like ensembles through dynamic structural interactions. These ensembles demonstrate emergent responses such as spontaneous self-assembly, which are difficult to achieve in synthetic soft matter. Here we use shape-morphing units comprising responsive polymers to create solids that self-assemble, modulate their volume and disassemble on demand. The ensemble is composed of a responsive hydrogel, liquid crystal elastomer or semicrystalline polymer ribbons that reversibly bend or twist. The dispersions of these ribbons mechanically interlock, inducing reversible aggregation. The aggregated liquid crystal elastomer ribbons have a 12-fold increase in the yield stress compared with cooled dispersion and contract by 34% on heating. Ribbon type, concentration and shape dictate the aggregation and govern the global mechanical properties of the solid that forms. Coating liquid crystal elastomer ribbons with a liquid metal begets photoresponsive and electrically conductive aggregates, whereas seeding cells on hydrogel ribbons enables self-assembling three-dimensional scaffolds, providing a versatile platform for the design of dynamic materials.

Micromechanics and damage in slide-ring networks.

We explore the mechanics and damage of slide-ring gels by developing a discrete model for the mechanics of chain-ring polymer systems that accounts for both crosslink motion and internal chain sliding. The proposed framework utilizes an extendable Langevin chain model to describe the constitutive behavior of polymer chains undergoing large deformation and includes a rupture criterion to innately capture damage. Similarly, crosslinked rings are described as large molecules that also store enthalpic energy during deformation and thus have their own rupture criterion. Using this formalism, we show that the realized mode of damage in a slide-ring unit is a function of the loading rate, distribution of segments, and inclusion ratio (number of rings per chain). After analyzing an ensemble of representative units under different loading conditions, we find that failure is driven by damage to crosslinked rings at slow loading rates, but polymer chain scission at fast loading rates. Our results indicate that increasing the strength of the crosslinked rings may improve the toughness of the material.

Nonlinear Viscoelasticity and Toughening Mechanisms in Nanoclay-PNIPAAm Double Network Hydrogels.

We investigate the mechanical properties of a magnetic temperature-sensitive hydrogel at varying concentrations of covalent and physical cross-linking. The hydrogel consists of covalently cross-linked poly(N-isopropylacrylamide) (PNIPAAm), physically interacting nanoclay particles, and magnetic ferric oxide nanoparticles. The physical nanoclay network exhibits strong viscoplastic behavior, and we find that increasing nanoclay content improves both strength and toughness in the double network materials. We investigate the behavior of the gels using a nonlinear viscoplasticity model with a modified rule of mixtures approach and attribute the observed trends to two factors: (a) the yield-stress behavior of the nanoclay network and (b) load-sharing interactions between the PNIPAAm and the nanoclay. Our findings indicate a strong correlation between the mass ratio of covalent cross-linker used and fractional percolation of the PNIPAAm network.

Coupled bond dynamics alters relaxation in polymers with multiple intrinsic dissociation rates.

Dynamic networks containing multiple bond types within a continuous network grant engineers another design parameter - relative bond fraction - by which to tune storage and dissipation of mechanical energy. However, the mechanisms governing emergent properties are difficult to deduce experimentally. Therefore, we here employ a network model with prescribed fractions of dynamic and stable bonds to predict relaxation characteristics of hybrid networks. We find that during stress relaxation, predominantly dynamic networks can exhibit long-term moduli through conformationally inhibited relaxation of stable bonds due to exclusion interactions with neighboring chains. Meanwhile, predominantly stable networks exhibit minor relaxation through non-affine reconfiguration of dynamic bonds. Given this, we introduce a single fitting parameter, ξ, to Transient Network Theory via a coupled rule of mixture, that characterizes the extent of stable bond relaxation. Treating ξ as a fitting parameter, the coupled rule of mixture's predicted stress response not only agrees with the network model's, but also unveils likely micromechanical traits of gels hosting multiple bond dissociation timescales.

Locomotion of an untethered, worm-inspired soft robot driven by a shape-memory alloy skeleton.

Soft, worm-like robots show promise in complex and constrained environments due to their robust, yet simple movement patterns. Although many such robots have been developed, they either rely on tethered power supplies and complex designs or cannot move external loads. To address these issues, we here introduce a novel, maggot-inspired, magnetically driven "mag-bot" that utilizes shape memory alloy-induced, thermoresponsive actuation and surface pattern-induced anisotropic friction to achieve locomotion inspired by fly larvae. This simple, untethered design can carry cargo that weighs up to three times its own weight with only a 17% reduction in speed over unloaded conditions thereby demonstrating, for the first time, how soft, untethered robots may be used to carry loads in controlled environments. Given their small scale and low cost, we expect that these mag-bots may be used in remote, confined spaces for small objects handling or as components in more complex designs.

Thermosensitive P(AAc-co-NIPAm) Hydrogels Display Enhanced Toughness and Self-Healing via Ion-Ligand Interactions.

Hydrogels containing thermosensitive polymers such as poly(N-isopropylacrylamide) (P(NIPAm)) may contract during heating and show great promise in fields ranging from soft robotics to thermosensitive biosensors. However, these gels often exhibit low stiffness, tensile strength, and mechanical toughness, limiting their applicability. Through copolymerization of P(NIPAm) with poly(Acrylic acid) (P(AAc)) and introduction of ferric ions (Fe3+ ) that coordinate with functional groups along the P(AAc) chains, here a thermoresponsive hydrogel with enhanced mechanical extensibility, strength, and toughness is introduced. Using both experimentation and constitutive modeling, it is found that increasing the ratio of m(AAc):m(NIPAm) in the prepolymer decreases strength and toughness but improves extensibility. In contrast, increasing Fe3+ concentration generally improves strength and toughness with little decrease in extensibility. Due to reversible coordination of the Fe3+ bonds, these gels display excellent recovery of mechanical strength during cyclic loading and self-healing ability. While thermosensitive contraction imbued by the underlying P(NIPAm) decreases slightly with increased Fe3+ concentration, the temperature transition range is widened and shifted upward toward that of human body temperature (between 30 and 40 °C), perhaps rendering these gels suitable as in vivo biosensors. Finally, these gels display excellent adsorptive properties with a variety of materials, rendering them possible candidates in adhesive applications.

Computational exploration of treadmilling and protrusion growth observed in fire ant rafts.

Collective living systems regularly achieve cooperative emergent functions that individual organisms could not accomplish alone. The rafts of fire ants (Solenopsis invicta) are often studied in this context for their ability to create aggregated structures comprised entirely of their own bodies, including tether-like protrusions that facilitate exploration of and escape from flooded environments. While similar protrusions are observed in cytoskeletons and cellular aggregates, they are generally dependent on morphogens or external gradients leaving the isolated role of local interactions poorly understood. Here we demonstrate through an ant-inspired, agent-based numerical model how protrusions in ant rafts may emerge spontaneously due to local interactions. The model is comprised of a condensed structural network of agents that represents the monolayer of interconnected worker ants, which floats on the water and gives ant rafts their form. Experimentally, this layer perpetually contracts, which we capture through the pairwise contraction of all neighboring structural agents at a strain rate of [Formula: see text]. On top of the structural layer, we model a dispersed, on-lattice layer of motile agents that represents free ants, which walk on top of the floating network. Experimentally, these self-propelled free ants walk with some mean persistence length and speed that we capture through an ant-inspired phenomenological model. Local interactions occur between neighboring free ants within some radius of detection, R, and the persistence length of freely active agents is tuned through a noise parameter, η as introduced by the Vicsek model. Both R and η where fixed to match the experimental trajectories of free ants. Treadmilling of the raft occurs as agents transition between the structural and free layers in accordance with experimental observations. Ultimately, we demonstrate how phases of exploratory protrusion growth may be induced by increased ant activity as characterized by a dimensionless parameter, [Formula: see text]. These results provide an example in which functional morphogenesis of a living system may emerge purely from local interactions at the constituent length scale, thereby providing a source of inspiration for the development of decentralized, autonomous active matter and swarm robotics.

A network model of transient polymers: exploring the micromechanics of nonlinear viscoelasticity.

Dynamic networks contain crosslinks that re-associate after disconnecting, imparting them with viscoelastic properties. While continuum approaches have been developed to analyze their mechanical response, these approaches can only describe their evolution in an average sense, omitting local, stochastic mechanisms that are critical to damage initiation or strain localization. To address these limitations, we introduce a discrete numerical model that mesoscopically coarse-grains the individual constituents of a dynamic network to predict its mechanical and topological evolution. Each constituent consists of a set of flexible chains that are permanently cross-linked at one end and contain reversible binding sites at their free ends. We incorporate nonlinear force-extension of individual chains via a Langevin model, slip-bond dissociation through Eyring's model, and spatiotemporally-dependent bond attachment based on scaling theory. Applying incompressible, uniaxial tension to representative volume elements at a range of constant strain rates and network connectivities, we then compare the mechanical response of these networks to that predicted by the transient network theory. Ultimately, we find that the idealized continuum approach remains suitable for networks with high chain concentrations when deformed at low strain rates, yet the mesoscale model proves necessary for the exploration of localized stochastic events, such as variability of the bond kinetics, or the nucleation of micro-cavities that likely conceive damage and fracture.

Mechanics of 3D Cell-Hydrogel Interactions: Experiments, Models, and Mechanisms.

Hydrogels are highly water-swollen molecular networks that are ideal platforms to create tissue mimetics owing to their vast and tunable properties. As such, hydrogels are promising cell-delivery vehicles for applications in tissue engineering and have also emerged as an important base for ex vivo models to study healthy and pathophysiological events in a carefully controlled three-dimensional environment. Cells are readily encapsulated in hydrogels resulting in a plethora of biochemical and mechanical communication mechanisms, which recapitulates the natural cell and extracellular matrix interaction in tissues. These interactions are complex, with multiple events that are invariably coupled and spanning multiple length and time scales. To study and identify the underlying mechanisms involved, an integrated experimental and computational approach is ideally needed. This review discusses the state of our knowledge on cell-hydrogel interactions, with a focus on mechanics and transport, and in this context, highlights recent advancements in experiments, mathematical and computational modeling. The review begins with a background on the thermodynamics and physics fundamentals that govern hydrogel mechanics and transport. The review focuses on two main classes of hydrogels, described as semiflexible polymer networks that represent physically cross-linked fibrous hydrogels and flexible polymer networks representing the chemically cross-linked synthetic and natural hydrogels. In this review, we highlight five main cell-hydrogel interactions that involve key cellular functions related to communication, mechanosensing, migration, growth, and tissue deposition and elaboration. For each of these cellular functions, recent experiments and the most up to date modeling strategies are discussed and then followed by a summary of how to tune hydrogel properties to achieve a desired functional cellular outcome. We conclude with a summary linking these advancements and make the case for the need to integrate experiments and modeling to advance our fundamental understanding of cell-matrix interactions that will ultimately help identify new therapeutic approaches and enable successful tissue engineering.

Nonsteady fracture of transient networks: The case of vitrimer.

We have discovered a peculiar form of fracture that occurs in polymer network formed by covalent adaptable bonds. Due to the dynamic feature of the bonds, fracture of this network is rate dependent, and the crack propagates in a highly nonsteady manner. These phenomena cannot be explained by the existing fracture theories, most of which are based on steady-state assumption. To explain these peculiar characteristics, we first revisit the fundamental difference between the transient network and the covalent network in which we highlighted the transient feature of the cracks. We extend the current fracture criterion for crack initiation to a time-evolution scheme that allows one to track the nonsteady propagation of a crack. Through a combined experimental modeling effort, we show that fracture in transient networks is governed by two parameters: the Weissenberg number [Formula: see text] that defines the history path of crack-driving force and an extension parameter Z that tells how far a crack can grow. We further use our understanding to explain the peculiar experimental observation. To further leverage on this understanding, we show that one can "program" a specimen's crack extension dynamics by tuning the loading history.

Force-dependent bond dissociation explains the rate-dependent fracture of vitrimers.

We investigate the rate-dependent fracture of vitrimers by conducting a tear test. Based on the relationship between the fracture energy and the thickness of vitrimer films, we, for the first time, obtain the intrinsic fracture energy and bulk dissipation of vitrimers during crack extension. The intrinsic fracture energy strongly depends on tear speed, and such dependence can be well explained by Eyring theory. In contrast, the bulk dissipation only weakly depends on tear speed, which is drastically different from observations on traditional viscoelastic polymers. We ascribe such a weak rate-dependence to the strong force-sensitivity of the exchange reaction of the dynamic covalent bond in the vitrimer.

Treadmilling and dynamic protrusions in fire ant rafts.

Fire ants (Solenopsis invicta) are exemplary for their formation of cohered, buoyant and dynamic structures composed entirely of their own bodies when exposed to flooded environments. Here, we observe tether-like protrusions that emerge from aggregated fire ant rafts when docked to stationary, vertical rods. Ant rafts comprise a floating, structural network of interconnected ants on which a layer of freely active ants walk. We show here that sustained shape evolution is permitted by the competing mechanisms of perpetual raft contraction aided by the transition of bulk structural ants to the free active layer and outward raft expansion owing to the deposition of free ants into the structural network at the edges, culminating in global treadmilling. Furthermore, we see that protrusions emerge as a result of asymmetries in the edge deposition rate of free ants. Employing both experimental characterization and a model for self-propelled particles in strong confinement, we interpret that these asymmetries are likely to occur stochastically owing to wall accumulation effects and directional motion of active ants when strongly confined by the protrusions' relatively narrow boundaries. Together, these effects may realize the cooperative, yet spontaneous formation of protrusions that fire ants sometimes use for functional exploration and to escape flooded environments.

Helical growth during the phototropic response, avoidance response, and in stiff mutants of Phycomyces blakesleeanus.

The sporangiophores of Phycomyces blakesleeanus have been used as a model system to study sensory transduction, helical growth, and to establish global biophysical equations for expansive growth of walled cells. More recently, local statistical biophysical models of the cell wall are being constructed to better understand the molecular underpinnings of helical growth and its behavior during the many growth responses of the sporangiophores to sensory stimuli. Previous experimental and theoretical findings guide the development of these local models. Future development requires an investigation of explicit and implicit assumptions made in the prior research. Here, experiments are conducted to test three assumptions made in prior research, that (a) elongation rate, (b) rotation rate, and (c) helical growth steepness, R, of the sporangiophore remain constant during the phototropic response (bending toward unilateral light) and the avoidance response (bending away from solid barriers). The experimental results reveal that all three assumptions are incorrect for the phototropic response and probably incorrect for the avoidance response but the results are less conclusive. Generally, the experimental results indicate that the elongation and rotation rates increase during these responses, as does R, indicating that the helical growth steepness become flatter. The implications of these findings on prior research, the "fibril reorientation and slippage" hypothesis, global biophysical equations, and local statistical biophysical models are discussed.

Spatiotemporal neocartilage growth in matrix-metalloproteinase-sensitive poly(ethylene glycol) hydrogels under dynamic compressive loading: an experimental and computational approach.

Enzyme-sensitive hydrogels containing encapsulated chondrocytes are a promising platform for cartilage tissue engineering. However, the growth of neotissue is closely coupled to the degradation of the hydrogel and is further complicated due to the encapsulated cells serving as the enzyme source for hydrogel degradation. To better understand these coupled processes, this study combined experimental and computational methods to analyze the transition from hydrogel to neotissue in a biomimetic MMP-sensitive poly(ethylene glycol) (PEG) hydrogel with encapsulated chondrocytes. A physics-based computational model that describes spatial heterogeneities in cell distribution was used. Experimentally, cell-laden hydrogels were cultured for six weeks under free swelling or subjected daily to one-hour of dynamic compressive loading. Extracellular matrix (ECM) synthesis rates were used as model inputs, and the model was fit to the experimentally determined construct modulus over time for the free swelling condition. Experimentally, ECM accumulation comprising collagen II and aggrecan increased over time concomitant with hydrogel degradation observed by a loss in PEG. Simulations demonstrated rapid degradation in regions of high cell density (i.e., cell clusters) reaching complete degradation by day 13, which facilitated localized ECM growth. Regions of low cell density degraded more slowly, had limited ECM, and led to the decrease in construct modulus during the first two weeks. The primary difference between the two culture environments was greater ECM accumulation in the clusters under free swelling, which facilitated a faster recovery in construct modulus. By 6 weeks the compressive modulus increased 2.5-fold to 107 kPa under free swelling, but dropped 1.6-fold to 26 kPa under loading. In summary, this biomimetic MMP-sensitive hydrogel supports neocartilage growth by facilitating rapid ECM growth within cell clusters, which was followed by slower growth in the rest of the hydrogel. Subtle temporal differences in hydrogel degradation and ECM accumulation, however, had a significant impact on the evolving mechanical properties.

Dynamic competition of inflation and delamination in the finite deformation of thin membranes.

The mechanics of blister delamination and growth plays a major role in a diversity of areas including medicine (skin pathology and mechanics of cell membranes), materials (adhesive and fracture) or soft robotics (actuation and morphing). The behavior of a blister in this context is typically difficult to grasp as it arises from the interplay of two highly nonlinear and time-dependent processes: membrane attachment and decohesion from a substrate. In the present work, we device a simplified approach, based on experimental systems, to predict the deformation path of a blister under various conditions. For this, we consider the problem of a growing blister made of a rubber-like membrane adhered on a rigid substrate, and develop a theoretical and experimental framework to study its stability and growth. We start by constructing a theoretical model of viscoelastic blister growth which we later validate with an experimental setup. We show that blister growth is controlled by the competition between two instabilities: one inherent to the rubber, and a second one pertaining to the adhesion with the substrate. Using these concepts, we show that a "targeted" stable blister shape can be achieved by controlling two parameters: the thickness of the film and the inflation rate.

On the blistering of thermo-sensitive hydrogel: the volume phase transition and mechanical instability.

This paper explores the physical mechanisms responsible for the appearance of small blisters on the surface of temperature sensitive hydrogels as they deswell rapidly during their volume phase transition. For this, we develop a numerical model that couples the processes of hydrogel deswelling and blister growth due to the existence of a thin quasi-impermeable layer on its surface. The model points out that blister inflation originates at defects point under the gel's surface, under the effect of the increasing osmotic pressure in the gel as it undergoes its phase transition. Due to their large deformation, these blisters often experience a mechanical instability that triggers a sudden increase in their growth rate at the expense of their closest neighbors. Using a simple computational model, we then show that blisters are able to communicate via internal pressure and that these interactions are mediated by two characteristic time scales related to solvent transport within and between adjacent blisters. Our study finally indicates that these mechanisms can be controlled by temperature and the gel's cross-link density to achieve diversity of blister patterns on the gel's surface. The proposed analysis provides predictions that agree well with experimental observations of NiPAm gels which deswell in various conditions.

Interplay of elastic instabilities and viscoelasticity in the finite deformation of thin membranes.

Pneumatic structures and actuators are found in a variety of natural and engineered systems such as dielectric actuators, soft robots, plants and fungi cells, or even the vocal sac of frogs. These structures are often subjected to mechanical instabilities arising from the thinning of their cross section and that may be harvested to perform mechanical work at a low energetic cost. While most of our understanding of this unstable behavior is for purely elastic membranes, real materials including lipid bilayers, elastomers, and connective tissues typically display a time-dependent viscoelastic response. This paper thus explores the role of viscous effects on the nature of this elastic instability when such membranes are dynamically inflated. For this, we first introduce an extension of the transient network theory to describe the finite strain viscoelastic response of membranes, enabling an elegant formulation while keeping a close connection with the dynamics of the underlying polymer network. We then combine experiments and simulations to analyze the viscoelastic behavior of an inflated blister made of a commercial adhesive tape (VHB 4905). Our results show that the viscous component induces a rich spectrum of behaviors bounded by two well-known elastic solutions corresponding to very high and very low inflation rates. We also show that membrane relaxation may induce unwanted buckling when it is subjected to cyclic inflations at certain frequencies. These results have clear implications for the inflation and mechanical work performed by time-dependent pneumatic structures and instability-based actuators.

Separating the contributions of zona pellucida and cytoplasm in the viscoelastic response of human oocytes.

The successful characterization of the mechanical properties of human oocytes and young embryos is of crucial relevance to reduce the risk of pregnancy arrest in in-vitro fertilization processes. Unfortunately, current study has been hindered by the lack of accuracy in describing the mechanical contributions of each structure (zona pellucida, cytoplasm) due to its high heterogeneity. In this work, we present a novel approach to model the oocyte response taking into account the effect of both zona and cytoplasm, as well as different loading conditions. The model is then applied to develop an experimental protocol capable of accurately separating the viscoelastic contribution of zona and cytoplasm by simply varying the loading condition. This new protocol has the potential to open the door to improving our understanding the mechanical properties of oocytes at different stages, and provide a quantitative predictive ability to the evaluation of oocyte quality. STATEMENT OF SIGNIFICANCE: Assisted reproductive technologies, such as in vitro fertilization, often rely on identifying high quality oocytes or female egg cells. The viscoelastic properties of these cells, such as stiffness and stress relaxation time, have been identified as potential objective indicators of cell quality. However, their characterization has proven difficult due to the structural heterogeneity of the cell and inconsistent loading conditions. This paper presents a new model that, although simple, addresses the above difficulties to provide accurate estimations of the cell's mechanical properties. Learning from this model, we then propose a novel non-invasive testing protocol to allow oocyte characterization with increased accuracy. We believe this effort would improve consistency in measurements and enhance our knowledge on the mechanics of oocytes.