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Sedimentation in active fluids has come into focus due to the ubiquity of swimming micro-organisms in natural and industrial processes. Here, we investigate sedimentation dynamics of passive particles in a fluid as a function of bacteria E. coli concentration. Results show that the presence of swimming bacteria significantly reduces the speed of the sedimentation front even in the dilute regime, in which the sedimentation speed is expected to be independent of particle concentration. Furthermore, bacteria increase the dispersion of the passive particles, which determines the width of the sedimentation front. For short times, particle sedimentation speed has a linear dependence on bacterial concentration. Mean square displacement data shows, however, that bacterial activity decays over long experimental (sedimentation) times. An advection-diffusion equation coupled to bacteria population dynamics seems to capture concentration profiles relatively well. A single parameter, the ratio of single particle speed to the bacteria flow speed can be used to predict front sedimentation speed., Comment: Soft Matter, (2021). arXiv admin note: substantial text overlap with arXiv:1710.04068

Advances in three-dimensional nanofabrication techniques have enabled the development of lightweight solids, such as hollow nanolattices, having record values of specific stiffness and strength, albeit at low production throughput. At the length scales of the structural elements of these solids-which are often tens of nanometers or smaller-forces required for elastic deformation can be comparable to adhesive forces, rendering the possibility to tailor bulk mechanical properties based on the relative balance of these forces. Herein, we study this interplay via the mechanics of ultralight ceramic-coated carbon nanotube (CNT) structures. We show that ceramic-CNT foams surpass other architected nanomaterials in density-normalized strength and that, when the structures are designed to minimize internal adhesive interactions between CNTs, more than 97% of the strain after compression beyond densification is recovered.

Blood clots form at the site of vascular injury to seal the wound and prevent bleeding. Clots are in tension as they perform their biological functions and withstand hydrodynamic forces of blood flow, vessel wall fluctuations, extravascular muscle contraction and other forces. There are several mechanisms that generate tension in a blood clot, of which the most well-known is the contraction/retraction caused by activated platelets. Here we show through experiments and modeling that clot tension is generated by the polymerization of fibrin. Our mathematical model is built on the hypothesis that the shape of fibrin monomers having two-fold symmetry and off-axis binding sites is ultimately the source of inherent tension in individual fibers and the clot. As the diameter of a fiber grows during polymerization the fibrin monomers must suffer axial twisting deformation so that they remain in register to form the half-staggered arrangement characteristic of fibrin protofibrils. This deformation results in a pre-strain that causes fiber and network tension. Our results for the pre-strain in single fibrin fibers is in agreement with experiments that measured it by cutting fibers and measuring their relaxed length. We connect the mechanics of a fiber to that of the network using the 8-chain model of polymer elasticity. By combining this with a continuum model of swellable elastomers we can compute the evolution of tension in a constrained fibrin gel. The temporal evolution and tensile stresses predicted by this model are in qualitative agreement with experimental measurements of the inherent tension of fibrin clots polymerized between two fixed rheometer plates. These experiments also revealed that increasing thrombin concentration leads to increasing internal tension in the fibrin network. Our model may be extended to account for other mechanisms that generate pre-strains in individual fibers and cause tension in three-dimensional proteinaceous polymeric networks.

Constitutive modeling of dielectric elastomers has been of long standing interest in mechanics. Over the last two decades rigorous constitutive models have been developed that couple the electrical response of these polymers with large deformations characteristic of soft solids. A drawback of these models is that unlike classic models of rubber elasticity they do not consider the coupled electromechanical response of single polymer chains which must be treated using statistical mechanics. The objective of this paper is to compute the stretch and polarization of single polymer chains subject to a fixed force and fixed electric field using statistical mechanics. We assume that the dipoles induced by the applied electric field at each link do not interact with each other and compute the partition function using standard techniques. We then calculate the stretch and polarization by taking appropriate derivatives of the partition function and obtain analytical results in various limits. We also perform Markov chain Monte Carlo simulations using the Metropolis and umbrella sampling methods, as well as develop a new sampling method which improves convergence by exploiting a symmetry inherent in dielectric polymer chains. The analytical expressions are shown to agree with the Monte Carlo results over a range of forces and electric fields. Our results complement recent work on the statistical mechanics of electro-responsive chains which obtains analytical expressions in a different ensemble.

We study the isometric conical deformation of an inextensible elastic sheet in response to a distributed external loading that is normal to the deformed sheet. The sheet is planar in the reference configuration and it deforms into a cone with a flower-shaped cross-section under load. These deformed configurations are distinguished by the number of lobes. We focus on the geometry and energetics of various lobed-cones in the deformed configuration and discuss their relative stability. First, we assume that the displacements are small which leads to linear governing equations for the curvature that we solve analytically to yield sinusoidal solutions. Then, we relax this restriction on the magnitude of the displacement which leads to nonlinear governing equations, which we again solve analytically using Jacobi elliptic functions which are periodic but not sinusoidal. We show that the sinusoidal solution can be recovered in the limit that the external loads are small.

We systematically study linear and nonlinear wave propagation in a chain composed of piecewise-linear bistable springs. Such bistable systems are ideal test beds for supporting nonlinear wave dynamical features including transition and (supersonic) solitary waves. We show that bistable chains can support the propagation of subsonic wave packets which in turn can be trapped by a low-energy phase to induce energy localization. The spatial distribution of these energy foci strongly affects the propagation of linear waves, typically causing scattering, but, in special cases, leading to a reflectionless mode analogous to the Ramsauer-Townsend effect. Furthermore, we show that the propagation of nonlinear waves can spontaneously generate or remove additional foci, which act as effective ``impurities.'' This behavior serves as a new mechanism for reversibly programming the dynamic response of bistable chains.

A number of biological tissues and synthetic gels consist of a fibrous network infused with liquid. There have been a few experimental studies of the rheological properties of such gels under applied compressive strain. Their results suggest that a plot of rheological moduli as a function of applied compressive strain has a long plateau flanked by a steeply increasing curve for large compressive strains and a slowly decreasing curve for small strains. In this paper we explain these trends in rheological properties using a chemo-elastic model characterized by a double-well strain energy function for the underlying fibrous network. The wells correspond to rarefied and densified phases of the fibrous network at low and high strains, respectively. These phases can co-exist across a movable transition front in the gel in order to accommodate overall applied compression. We find that the rheological properties of fibrous gels share similarities with a Kelvin–Voigt visco-elastic solid. The storage modulus has its origins in the elasticity of the fibrous network, while the loss modulus is determined by the dissipation caused by liquid flow through pores. The rheological properties can depend on the number of phase transition fronts present in a compressed sample. Our analysis may explain the dependence of storage and loss moduli of fibrin gels on the loading history. We also point to the need for combining rheological measurements on gels with a microstructural analysis that could shed light on various dissipation mechanisms.

The Jarzynski relation, as an equality form of the second law of thermodynamics, represents an exact thermodynamic statement that is valid arbitrarily far away from equilibrium. This remarkable relation directly links the equilibrium free energy difference between two states and the probability distribution of the work done along a process that drives the system from one state to the other. Here, we leverage the Jarzynski equality and a local equilibrium assumption, to go beyond the calculation of free energy differences and also extract the dissipation potential from additional measurements of kinematic field variables (strain and velocity fields). The proposed strategy is exemplified over pulling experiments of mass–spring models obeying overdamped Langevin dynamics, which is a prototype for nanorods, fibrous macro-molecules and the Rouse model of polymers. Different interaction potentials, fluid viscosities and bath temperatures are studied, so as to intrinsically control how close or far away the system is from equilibrium. The data-inferred continuum models are then validated against processes governed by different pulling protocols, thereby demonstrating their predictive capability. The methods presented here represent a first step toward full material characterization from non-equilibrium data of macroscopic observables, which could potentially be obtained from experimental observations.

This paper aims to relate the energy dissipated at a shock wave in a nonlinearly elastic bar to the energy in the oscillations in two related dissipationless, dispersive systems. Three, one-dimensional, dynamic impact problems are studied: Problem 1 concerns a nonlinearly elastic bar, Problem 2 a discrete chain of particles, and Problem 3 a continuum with a strain gradient term in the constitutive relation. In the impact problem considered, the free boundary of each initially quiescent body is subjected to a sudden velocity, that is then held constant for all subsequent time. There is energy dissipation at the shock in Problem 1, but Problems 2 and 3 are conservative. Problem 1 is solved analytically, Problem 2 numerically, and an approximate solution to Problem 3 is constructed analytically. The rate of increase of the oscillatory energy in Problems 2 and 3 are calculated and compared with the dissipation rate at the shock in Problem 1. The results indicate that the former is a good qualitative measure of the latter. The quantitative agreement is satisfactory at larger impact speeds but less so at smaller speeds, some possible reasons for which are discussed.

Intracellular elastic filaments such as microtubules are subject to thermal Brownian noise and active noise generated by molecular motors that convert chemical energy into mechanical work. Similarly, polymers in living fluids such as bacterial suspensions and swarms suffer bending deformations as they interact with single bacteria or with cell clusters. Often these filaments perform mechanical functions and interact with their networked environment through cross-links, or have other similar constraints placed on them. Here we examine the mechanical properties - under tension - of such constrained active filaments under canonical boundary conditions motivated by experiments. Fluctuations in the filament shape are a consequence of two types of random forces - thermal Brownian forces, and activity derived forces with specified time and space correlation functions. We derive force-extension relationships and expressions for the mean square deflections for tethered filaments under various boundary conditions including hinged and clamped constraints. The expressions for hinged-hinged boundary conditions are reminiscent of the worm-like-chain model and feature effective bending moduli and mode-dependent non-thermodynamic effective temperatures controlled by the imposed force and by the activity. Our results provide methods to estimate the activity by measurements of the force-extension relation of the filaments or their mean-square deflections which can be routinely performed using optical traps, tethered particle experiments, or other single molecule techniques.

Self-assembly of proteins on lipid membranes underlies many important processes in cell biology, such as, exo- and endo-cytosis, assembly of viruses, etc. An attractive force that can cause self-assembly is mediated by membrane thickness interactions between proteins. The free energy profile associated with this attractive force is a result of the overlap of thickness deformation fields around the proteins. The thickness deformation field around proteins of various shapes can be calculated from the solution of a boundary value problem and is relatively well understood. Yet, the time scales over which self-assembly occurs has not been explored. In this paper we compute this time scale as a function of the initial distance between two inclusions by viewing their coalescence as a first passage time problem. The first passage time is computed using both Langevin dynamics and a partial differential equation, and both methods are found to be in excellent agreement. Inclusions of three different shapes are studied and it is found that for two inclusions separated by about hundred nanometers the time to coalescence is hundreds of milliseconds irrespective of shape. Our Langevin dynamics simulation of self-assembly required an efficient computation of the interaction energy of inclusions which was accomplished using a finite difference technique. The interaction energy profiles obtained using this numerical technique were in excellent agreement with those from a previously proposed semi-analytical method based on Fourier-Bessel series. The computational strategies described in this paper could potentially lead to efficient methods to explore the kinetics of self-assembly of proteins on lipid membranes.Author summarySelf-assembly of proteins on lipid membranes occurs during exo- and endo-cytosis and also when viruses exit an infected cell. The forces mediating self-assembly of inclusions on membranes have therefore been of long standing interest. However, the kinetics of self-assembly has received much less attention. As a first step in discerning the kinetics, we examine the time to coalescence of two inclusions on a membrane as a function of the distance separating them. We use both Langevin dynamics simulations and a partial differential equation to compute this time scale. We predict that the time to coalescence is on the scale of hundreds of milliseconds for two inclusions separated by about hundred nanometers. The deformation moduli of the lipid membrane and the membrane tension can affect this time scale.

The double-helical topology of DNA molecules observed at room temperature in the absence of any external loads can be disrupted by increasing the bath temperature or by applying tensile forces, leading to spontaneous strand separation known as DNA melting. Here, continuum mechanics of a 2D birod is combined with statistical mechanics to formulate a unified framework for studying both thermal melting and tensile force induced melting of double-stranded molecules: it predicts the variation of melting temperature with tensile load, provides a mechanics-based understanding of the cooperativity observed in melting transitions, and reveals an interplay between solution electrostatics and micromechanical deformations of DNA which manifests itself as an increase in the melting temperature with increasing ion concentration. This novel predictive framework sheds light on the micromechanical aspects of DNA melting and predicts trends that were observed experimentally or extracted phenomenologically using the Clayperon equation.

Structural transitions in some rod-like biological macromolecules under tension are known to proceed by the propagation through the length of the molecule of an interface separating two phases. A continuum mechanical description of the motion of this interface, or phase boundary, takes the form of a kinetic law which relates the thermodynamic driving force across it with its velocity in the reference configuration. For biological macromolecules immersed in a heat bath, thermally activated kinetics described by the Arrhenius law is often a good choice. Here we show that ‘stick-slip’ kinetics, characteristic of friction, can also arise in an overdamped bistable bar immersed in a heat bath. To mimic a rod-like biomolecule we model the bar as a chain of masses and bistable springs moving in a viscous fluid. We conduct Langevin dynamics calculations on the chain and extract a temperature dependent kinetic relation by observing that the dissipation at a phase boundary can be estimated by performing an energy balance. Using this kinetic relation we solve boundary value problems for a bistable bar immersed in a constant temperature bath and show that the resultant force-extension relation matches very well with the Langevin dynamics results. We estimate the force fluctuations at the pulled end of the bar due to thermal kicks from the bath by using a partition function. We also show rate dependence of hysteresis in cyclic loading of the bar arising from the stick-slip kinetics. Our kinetic relation could be applied to rod-like biomolecules, such as, DNA and coiled-coil proteins which exhibit structural transitions that depend on both temperature and loading rate.

Several biological materials are fibre networks infused with fluid, often referred to as fibrous gels. An important feature of these gels is that the fibres buckle under compression, causing a densification of the network that is accompanied by a reduction in volume and release of fluid. Displacement-controlled compression of fibrous gels has shown that the network can exist in a rarefied and a densified state over a range of stresses. Continuum chemo-elastic theories can be used to model the mechanical behaviour of these gels, but they suffer from the drawback that the stored energy function of the underlying network is based on neo-Hookean elasticity, which cannot account for the existence of multiple phases. Here we use a double-well stored energy function in a chemo-elastic model of gels to capture the existence of two phases of the network. We model cyclic compression/decompression experiments on fibrous gels and show that they exhibit propagating interfaces and hysteretic stress–strain curves that have been observed in experiments. We can capture features in the rate-dependent response of these fibrous gels without recourse to finite-element calculations. We also perform experiments to show that certain features in the stress–strain curves of fibrous gels predicted by our model can be found in the compression response of blood clots. Our methods may be extended to other tissues and synthetic gels that have a fibrous structure.

Polymerization of dendritic actin networks underlies important mechanical processes in cell biology such as the protrusion of lamellipodia, propulsion of growth cones in dendrites of neurons, intracellular transport of organelles and pathogens, among others. The forces required for these mechanical functions have been deduced from mechano-chemical models of actin polymerization; most models are focused on single growing filaments, and only a few address polymerization of filament networks through simulations. Here, we propose a continuum model of surface growth and filament nucleation to describe polymerization of dendritic actin networks. The model describes growth and elasticity in terms of macroscopic stresses, strains and filament density rather than focusing on individual filaments. The microscopic processes underlying polymerization are subsumed into kinetic laws characterizing the change of filament density and the propagation of growing surfaces. This continuum model can predict the evolution of actin networks in disparate experiments. A key conclusion of the analysis is that existing laws relating force to polymerization speed of single filaments cannot predict the response of growing networks. Therefore, a new kinetic law, consistent with the dissipation inequality, is proposed to capture the evolution of dendritic actin networks under different loading conditions. This model may be extended to other settings involving a more complex interplay between mechanical stresses and polymerization kinetics, such as the growth of networks of microtubules, collagen filaments, intermediate filaments and carbon nanotubes.

The S-shaped curvature of the spine has been hypothesized as the underlying mechanical cause of adolescent idiopathic scoliosis. In earlier work we proposed a reduced order model in which the spine was viewed as an S-shaped elastic rod under torsion and bending. Here, we simulate the deformation of S-shaped rods of a wide range of curvatures and inflection points under a fixed mechanical loading. Our analysis determines three distinct axial projection patterns of these S-shaped rods: two loop (in opposite directions) patterns and one lemniscate pattern. We further identify the curve characteristics associated with each deformation pattern showing that for rods deforming in a loop 1 shape the position of the inflection point is the highest and the curvature of the rod is smaller compared to the other two types. For rods deforming in the loop 2 shape the position of the inflection point is the lowest (closer to the fixed base) and the curvatures are higher than the other two types. These patterns matched the common clinically observed scoliotic curves - Lenke 1 and Lenke 5. Our elastic rod model predicts deformations that are similar to those of a pediatric spine and it can differentiate between the clinically observed deformation patterns. This provides validation to the hypothesis that changes in the sagittal profile of the spine can be a mechanical factor in parthenogenesis of pediatric idiopathic scoliosis.

The mechanism of the scoliotic curve development in healthy adolescents remains unknown in the field of orthopedic surgery. Variations in the sagittal curvature of the spine are believed to be a leading cause of scoliosis in this patient population. Here, we formulate the mechanics of S-shaped slender elastic rods as a model for pediatric spine under physiological loading. Second, applying inverse mechanics to clinical data of the subtypes of scoliotic spines, with characteristic 3D deformity, we determine the undeformed geometry of the spine before the induction of scoliosis. Our result successfully reproduces the clinical data of the deformed spine under varying loads, confirming that the prescoliotic sagittal curvature of the spine impacts the 3D loading that leads to scoliosis.

We investigate the biomechanical and structural origins of blood clot rupture with implications for thrombotic embolization., Fibrin is the three-dimensional mechanical scaffold of protective blood clots that stop bleeding and pathological thrombi that obstruct blood vessels. Fibrin must be mechanically tough to withstand rupture, after which life-threatening pieces (thrombotic emboli) are carried downstream by blood flow. Despite multiple studies on fibrin viscoelasticity, mechanisms of fibrin rupture remain unknown. Here, we examined mechanically and structurally the strain-driven rupture of human blood plasma–derived fibrin clots where clotting was triggered with tissue factor. Toughness, i.e., resistance to rupture, quantified by the critical energy release rate (a measure of the propensity for clot embolization) of physiologically relevant fibrin gels was determined to be 7.6 ± 0.45 J/m2. Finite element (FE) simulations using fibrin material models that account for forced protein unfolding independently supported this measured toughness and showed that breaking of fibers ahead the crack at a critical stretch is the mechanism of rupture of blood clots, including thrombotic embolization.

Cellulose-based materials are increasingly finding applications in technology due to their sustainability and biodegradability. The sensitivity of cellulose fiber networks to environmental conditions such as temperature and humidity is well known. Yet, there is an incomplete understanding of the dependence of the fracture toughness of cellulose networks on environmental conditions. In the current study, we assess the effect of moisture content on the out-of-plane (i.e., z-dir.) fracture toughness of a particular cellulose network, specifically Whatman cellulose filter paper. Experimental measurements are performed at 16% RH along the desorption isotherm and 23, 37, 50, 75% RH along the adsorption isotherm using out-of-plane tensile tests and double cantilever beam (DCB) tests. Cohesive zone modeling and finite element simulations are used to extract quantitative properties that describe the crack growth behavior. Overall, the fracture toughness of filter paper decreased with increasing humidity. Additionally, a novel model is developed to capture the high peak and sudden drop in the experimental force measurement caused by the existence of an initiation region. This model is found to be in good agreement with experimental data. The relative effect of each independent cohesive parameter is explored to better understand the cohesive zone-based humidity dependence model. The methods described here may be applied to study rupture of other fiber networks with weak bonds.

Ordered synthesis of one-dimensional nanostructures, such as carbon nanotubes (CNTs), involves competition between the growth kinetics of individual structures, their physical entanglement, and intermolecular forces that cause coupling of structures in close proximity. Specifically, CNT synthesis by chemical vapor deposition can directly produce films and fibers by providing CNT growth sites in close proximity such that the CNTs self-align into macroscopic assemblies. Because CNTs are mechanically coupled during these processes, the question arises as to whether or not mechanical forces intrinsic to the formation of CNT ensembles influence the growth kinetics and quality of CNTs, as can be expected from fundamental theories of mechanochemistry. Here, we study how mechanical forces influence CNT growth by applying controlled compression to CNT forests in situ; and relate the outcomes quantitatively to the CNT morphology and lengthening rate. We find that applied forces inhibit the self-organization of CNTs...

Allosteric interactions in DNA are crucial for various biological processes. These interactions are quantified by measuring the change in free energy as a function of the distance between the binding sites for two ligands. Here we show that trends in the interaction energy of ligands binding to DNA can be explained within an elastic birod model. The birod model accounts for the deformation of each strand as well as the change in stacking energy due to perturbations in position and orientation of the bases caused by the binding of ligands. The strain fields produced by the ligands decay with distance from the binding site. The interaction energy of two ligands decays exponentially with the distance between them and oscillates with the periodicity of the double helix in quantitative agreement with experimental measurements. The trend in the computed interaction energy is similar to that in the perturbation of groove width produced by the binding of a single ligand which is consistent with molecular simulations. Our analysis provides a new framework to understand allosteric interactions in DNA and can be extended to other rod-like macromolecules whose elasticity plays a role in biological functions.

“Viscosity is the most ubiquitous dissipative mechanical behavior” ( Maugin, 1999 ). Despite its ubiquity, even for those systems where the mechanisms causing viscous and other forms of dissipation are known there are only a few quantitative models that extract the macroscopic rheological response from these microscopic mechanisms. One such mechanism is the stochastic breaking and forming of bonds which is present in polymer networks with transient cross-links, strong inter-layer bonding between graphene sheets, and sliding dry friction. In this paper we utilize a simple yet flexible model to show analytically how stochastic bonds can induce an array of rheological behaviors at the macroscale. We find that varying the bond interactions induces a Maxwell-type macroscopic material behavior with Newtonian viscosity, shear thinning, shear thickening, or solid like friction when subjected to shear at constant rates. When bond rupture is independent of the force applied, Newtonian viscosity is the predominant behavior. When bond breaking is accelerated by the applied force, a shear thinning response becomes most prevalent. Further connections of the macroscopic response to the interaction potential and rates of bonding and unbonding are illustrated through phase diagrams and analysis of limiting cases. Finally, we apply this model to polymer networks and to experimental data on “solid bridges” in polydisperse granular media. We imagine possible applications to material design through engineering bonds with specific interactions to bring about a desired macroscopic behavior.

Measuring vital physiological pressures is important for monitoring health status, preventing the buildup of dangerous internal forces in impaired organs, and enabling novel approaches of using mechanical stimulation for tissue regeneration. Pressure sensors are often required to be implanted and directly integrated with native soft biological systems. Therefore, the devices should be flexible and at the same time biodegradable to avoid invasive removal surgery that can damage directly interfaced tissues. Despite recent achievements in degradable electronic devices, there is still a tremendous need to develop a force sensor which only relies on safe medical materials and requires no complex fabrication process to provide accurate information on important biophysiological forces. Here, we present a strategy for material processing, electromechanical analysis, device fabrication, and assessment of a piezoelectric Poly-l-lactide (PLLA) polymer to create a biodegradable, biocompatible piezoelectric force sensor, which only employs medical materials used commonly in Food and Drug Administration-approved implants, for the monitoring of biological forces. We show the sensor can precisely measure pressures in a wide range of 0-18 kPa and sustain a reliable performance for a period of 4 d in an aqueous environment. We also demonstrate this PLLA piezoelectric sensor can be implanted inside the abdominal cavity of a mouse to monitor the pressure of diaphragmatic contraction. This piezoelectric sensor offers an appealing alternative to present biodegradable electronic devices for the monitoring of intraorgan pressures. The sensor can be integrated with tissues and organs, forming self-sensing bionic systems to enable many exciting applications in regenerative medicine, drug delivery, and medical devices.

Curvature mediated elastic interactions between inclusions in lipid membranes have been analyzed using both theoretical and computational methods. Entropic corrections to these interactions have also been studied. Here we show that elastic and entropic forces between inclusions in membranes can compete under certain conditions to a yield a maximum in the free energy at a critical separation. If the distance between the inclusions is less than this critical separation then entropic interactions dominate and there is an attractive force between them, while if the distance is more than the critical separation then elastic interactions dominate and there is a repulsive force between them. We assume the inclusions to be rigid and use a previously developed semi-analytic method based on Gaussian integrals to compute the free energy of a membrane with inclusions. We show that the critical separation between inclusions decreases with increasing bending modulus and with increasing tension. We also compute the projected area of a membrane with rigid inclusions under tension and find that the trend of the effective bending modulus as a function of area fraction occupied by inclusions is in agreement with earlier results. Our technique can be extended to account for entropic effects in other methods which rely on quadratic energies to study the interactions of inclusions in membranes.

Architected metastructures offer unprecedented mechanical characteristics due to particular design and assembly of engineered local structures. Here, we study the out-of-plane deflection of plate-like metastructures designed with hexagonal corrugation. Due to the out-of-plane asymmetry of the corrugation, our metaplates develop out-of-plane deflection when put under tension. A theoretical model is developed to analyze the tensile response of the corrugated metaplates, and experiments are conducted on the metaplates made of silicone rubber. The tensile modulus of the silicone rubber is calibrated and the rubber metaplates are then measured under tension. Numerical simulations validate the theoretical and experimental results, and satisfactory agreements are obtained for the force–displacement relations (i.e., effective tensile modulus) and out-of-plane deflection. Parametric studies are carried out to investigate the influences of the geometry (e.g., height h and thickness t ) and the corrugation pattern (e.g., hexagonal diameter D h e x and rib width W r i b ) on the tensile response of the metaplates. The presented corrugated metaplates are envisioned as a promising path to optimize structures for multifunctional applications (e.g., wings in flying robots or light sails for interstellar space travel).

We carried out dynamic force manipulations in silico on a variety of coiled-coil protein fragments from myosin, chemotaxis receptor, vimentin, fibrin, and phenylalanine zippers that vary in size and topology of their α-helical packing. When stretched along the superhelical axis, all superhelices show elastic, plastic, and inelastic elongation regimes and undergo a dynamic transition from the α-helices to the β-sheets, which marks the onset of plastic deformation. Using the Abeyaratne-Knowles formulation of phase transitions, we developed a new theoretical methodology to model mechanical and kinetic properties of protein coiled-coils under mechanical nonequilibrium conditions and to map out their energy landscapes. The theory was successfully validated by comparing the simulated and theoretical force-strain spectra. We derived the scaling laws for the elastic force and the force for α-to-β transition, which can be used to understand natural proteins' properties as well as to rationally design novel biomaterials of required mechanical strength with desired balance between stiffness and plasticity.

In this paper we describe experiments and a continuum phase transition model for the compression of carbon nanotube (CNT) forests. Our model is inspired by the observation of one or more moving interfaces across which densified and rarefied phases of the CNT forests co-exist. We use a quasi-static version of the Abeyaratne-Knowles theory of phase transitions for continua with a stick-slip type kinetic law and a nucleation criterion based on the critical stress for buckling of CNT forests to describe the formation and motion of these interfaces in uniaxial compression experiments. We investigate micropillars made from bare CNTs, as well as those coated with different thicknesses of alumina using atomic layer deposition (ALD). The coating thickness affects the moduli of individual CNTs as well as the adhesion energy per contact between CNTs. In order to test the applicability of our model to more complex stress states, we carry out nanoindentation experiments on the CNT pillars and interpret the load-indentation data by incorporating a constitutive law allowing for phase transitions into solutions for the indentation of a linearly elastic half-space. Even though the state of stress in a nanoindentation experiment is more complex than that in a uniaxial compression test, we find that the parameters extracted from the nanoindentation experiments are close to those from uniaxial compression. Our models could therefore aid the design of CNT forests to have engineered mechanical properties, and guide further understanding of their behavior under large deformations.

Blood clots are required to stem bleeding and are subject to a variety of stresses, but they can also block blood vessels and cause heart attacks and ischemic strokes. We measured the compressive response of human platelet-poor plasma (PPP) clots, platelet-rich plasma (PRP) clots and whole blood clots and correlated these measurements with confocal and scanning electron microscopy to track changes in clot structure. Stress-strain curves revealed four characteristic regions, for compression-decompression: (1) linear elastic region; (2) upper plateau or softening region; (3) non-linear elastic region or re-stretching of the network; (4) lower plateau in which dissociation of some newly made connections occurs. Our experiments revealed that compression proceeds by the passage of a phase boundary through the clot separating rarefied and densified phases. This observation motivates a model of fibrin mechanics based on the continuum theory of phase transitions, which accounts for the pre-stress caused by platelets, the adhesion of fibrin fibers in the densified phase, the compression of red blood cells (RBCs), and the pumping of liquids through the clot during compression/decompression. Our experiments and theory provide insights into the mechanical behavior of blood clots that could have implications clinically and in the design of fibrin-based biomaterials. Statement of Significance The objective of this paper is to measure and mathematically model the compression behavior of various human blood clots. We show by a combination of confocal and scanning electron microscopy that compression proceeds by the passage of a front through the sample that separates a densified region of the clot from a rarefied region, and that the compression/decompression response is reversible with hysteresis. These observations form the basis of a model for the compression response of clots based on the continuum theory of phase transitions. Our studies may reveal how clot rheology under large compression in vivo due to muscle contraction, platelet retraction and hydrodynamic flow varies under various pathophysiological conditions and could inform the design of fibrin based biomaterials.

Advances in fabrication techniques have led to a proliferation of studies on new mechanical metamaterials, particularly on elastic and linear phenomena (for example, their phonon spectrum and acoustic band gaps). More recently, there has been a growing interest in nonlinear wave phenomena in these systems, and particularly how geometric parameters affect the propagation of high-amplitude nonlinear waves. In this paper, we analytically, numerically, and experimentally demonstrate the propagation of cnoidal waves in an elastic architected material. This class of traveling waves constitutes a general family of nonlinear waves, which reduce to phonons and solitons under suitable limits. Although cnoidal waves were first discovered as solutions to the conservation laws for shallow water, they have subsequently appeared in contexts as diverse as ion plasmas and nonlinear optics, but have rarely been explored in elastic solids. We show that geometrically nonlinear deformations in architected soft elastic solids can result in cnoidal waves. Insights from our analysis will be critical to controlling the propagation of stress waves in advanced materials.

Coiled-coils are filamentous proteins that form the basic building block of important force-bearing cellular elements, such as intermediate filaments and myosin motors. In addition to their biological importance, coiled-coil proteins are increasingly used in new biomaterials including fibers, nanotubes, or hydrogels. Coiled-coils undergo a structural transition from an a-helical coil to an unfolded state upon extension, which allows them to sustain large strains and is critical for their biological function. By performing equilibrium and out-of-equilibrium all-atom molecular dynamics (MD) simulations of coiledcoils in explicit solvent, we show that two-state models based on Kramers’ or Bell’s theories fail to predict the rate of unfolding at high pulling rates. We further show that an atomistically informed continuum rod model accounting for phase transformations and for the hydrodynamic interactions with the solvent can reconcile two-state models with our MD results. Our results show that frictional forces, usually neglected in theories of fibrous protein unfolding, reduce the thermodynamic force acting on the interface, and thus control the dynamics of unfolding at different pulling rates. Our results may help interpret MD simulations at high pulling rates, and could be pertinent to cytoskeletal networks or protein-based artificial materials subjected to shocks or blasts.

In the first phase of axon growth, axons sprout from neuron bodies and are extended by the pull of the migrating growth cones towards their targets. Thereafter, once the target is reached, a lesser known second phase of axon growth ensues as the mechanical forces from the growth of the animal induce extension of the integrated axons in the process of forming tracts and nerves. Although there are several microscopic physics based models of the first phase of axon growth, to date, there are no models of the very different second phase. Here we propose a mathematical model for stretch growth of axon tracts in which the rate of production of proteins required for growth is dependent on the membrane tension. We assume that growth occurs all along the axon, and are able to predict the increase in axon cross-sectional area after they are rapidly stretched and held at a constant length for several hours. We show that there is a length dependent maximum stretching rate that an axon can sustain without disconnection in steady state when the axon length is primarily increased near the cell body. Our results could inform better design of stretch growth protocols to create transplantable axon tracts to repair the nervous system.

Mass–spring chains with only extensional degrees of freedom have provided insights into the behavior of crystalline solids, including those capable of phase transitions. Here we add rotational degrees of freedom to the masses in a chain and study the dynamics of phase boundaries across which both the twist and stretch can jump. We solve impact and Riemann problems in the chain by numerical integration of the equations of motion and show that the solutions are analogous to those in a phase transforming rod whose stored energy function depends on both twist and stretch. From the dynamics of phase boundaries in the chain we extract a kinetic relation whose form is familiar from earlier studies involving chains with only extensional degrees of freedom. However, for some combinations of parameters characterizing the energy landscape of our springs we find propagating phase boundaries for which the rate of dissipation, as calculated using isothermal expressions for the driving force, is negative. This suggests that we cannot neglect the energy stored in the oscillations of the masses in the interpretation of the dynamics of mass–spring chains. Keeping this in mind we define a local temperature of our chain and show that it jumps across phase boundaries, but not across sonic waves. Hence, impact problems in our mass–spring chains are analogous to those on continuum thermoelastic bars with Mie–Gruneisen type constitutive laws. At the end of the paper we use our chain to shed some light on experiments involving yarns that couple twist and stretch to perform useful work in response to various stimuli.

The thermal fluctuations of lipid bi-layer membranes are key to their interaction with cellular components as well as the measurement of their mechanical properties. Typically, membrane fluctuations are analyzed by decomposing into normal modes or by molecular simulations. Here we propose two new approaches to calculate the partition function of a membrane. In the first approach we view the membrane as a fluctuating von Karman plate and discretize it into triangular elements. We express its energy as a function of nodal displacements, and then compute the partition function and co-variance matrix using Gaussian integrals. We recover well-known results for the dependence of the projected area of the membrane on the applied tension and recent simulation results on the dependence of membrane free energy on geometry, spontaneous curvature and tension. As new applications we compute the fluctuations of the membrane of a malaria infected cell and analyze the effects of boundary conditions on fluctuations. Our second approach is based on the cell model of Lennard-Jones and Devonshire. This model, which was developed for liquids, assumes that each molecule fluctuates within a cell on which a potential is imposed by all the surrounding molecules. We adapt the cell model to a lipid membrane by recognizing that it is a 2D liquid with the ability to deform out of plane whose energetic penalty must be factored into the partition function of a cell. We show, once again, that some results on membrane fluctuations can be recovered using this new cell model. However, unlike some well established results, our cell model gives an entropy that scales with the number of molecules in a membrane. Our model makes predictions about the heat capacity of the membrane that can be tested in experiments.

Flexible mechanical metamaterials have been recently shown to support a rich nonlinear dynamic response. In particular, it has been demonstrated that the behavior of rotating-square architected systems in the continuum limit can be described by nonlinear Klein–Gordon equations. Here, we report on a general class of solutions of these nonlinear Klein–Gordon equations, namely cnoidal waves based on the Jacobi elliptic functions sn, cn and dn. By analyzing theoretically and numerically their validity and stability in the design- and wave-parameter space, we show that these cnoidal wave solutions extend from linear waves (or phonons) to solitons, while covering also a wide family of nonlinear periodic waves. The presented results thus reunite under the same framework different concepts of linear and non-linear waves and offer a fertile ground for extending the range of possible control strategies for nonlinear elastic waves and vibrations.

Pulmonary embolism occurs when blood flow to a part of the lungs is blocked by a venous thrombus that has traveled from the lower limbs. Little is known about the mechanical behavior of emboli under compressive forces from the surrounding musculature and blood pressure. We measured the stress-strain responses of human pulmonary emboli under cyclic compression, and showed that emboli exhibit a hysteretic stress-strain curve. The fibrin fibers and red blood cells (RBCs) are damaged during the compression process, causing irreversible changes in the structure of the emboli. We showed using electron and confocal microscopy that bundling of fibrin fibers occurs due to compression, and damage is accumulated as more cycles are applied. The stress-strain curves depend on embolus structure, such that variations in composition give quantitatively different responses. Emboli with a high fibrin component demonstrate higher normal stress compared to emboli that have a high RBC component. We compared the compression response of emboli to that of whole blood clots containing various volume fractions of RBCs, and found that RBCs rupture at a certain critical stress. We describe the hysteretic response characteristic of foams, using a model of phase transitions in which the compressed foam is segregated into coexisting rarefied and densified phases whose fractions change during compression. Our model takes account of the rupture of RBCs in the compressed emboli and stresses due to fluid flow through their small pores. Our results can help in classifying emboli as rich in fibrin or rich in red blood cells, and can help in understanding what responses to expect when stresses are applied to thrombi in vivo.

Irradiation-induced oxidation of lipid membranes is implicated in diseases and has been harnessed in medical treatments. Irradiation induces the formation of oxidative free radicals, which attack double bonds in the hydrocarbon chains of lipids. Studies of the kinetics of this reaction suggest that the result of the first stage of oxidation is a structural change in the lipid that causes an increase in the area per molecule in a vesicle. Since area changes are directly connected to membrane tension, irradiation-induced oxidation affects the mechanical behavior of a vesicle. Here, we analyze shape changes of axisymmetric vesicles that are under simultaneous influence of adhesion, micropipette aspiration, and irradiation. We study both the equilibrium and kinetics of shape changes and compare our results with experiments. The tension–area relation of a membrane, which is derived by accounting for thermal fluctuations, and the time variation of the mechanical properties due to oxidation play important roles in our analysis. Our model is an example of the coupling of mechanics and chemistry, which is ubiquitous in biology.

We develop a model to explain discontinuities in the increase of the length of a DNA plectoneme when the DNA filament is continuously twisted under tension. We account for DNA elasticity, electrostatic interactions and entropic effects due to thermal fluctuation. We postulate that a corrugated energy landscape that contains energy barriers is the cause of jumps in the length of the plectoneme as the number of turns is increased. Thus, our model is similar to the Prandtl–Tomlinson model of atomic scale friction. The existence of a corrugated energy landscape can be justified due to the close proximity of the neighboring pieces of DNA in a plectoneme. We assume the corrugated energy landscape to be sinusoidal since the plectoneme has a periodic helical structure and rotation of the bead is a form of periodic motion. We perform calculations with different tensile forces and ionic concentrations, and show that rotation–extension curves manifest stair-step shapes under relatively high ionic concentrations and high forces. We show that the jump in the plectonemic growth is caused by the flattening of the energy barrier in the corrugated landscape.

A solid is said to be flexoelectric when it polarizes in proportion to strain gradients. Since strain gradients are large near defects, we expect the flexoelectric effect to be prominent there and decay away at distances much larger than a flexoelectric length scale. Here, we quantify this expectation by computing displacement, stress and polarization fields near defects in flexoelectric solids. For point defects we recover some well known results from strain gradient elasticity and non-local piezoelectric theories, but with different length scales in the final expressions. For edge dislocations we show that the electric potential is a maximum in the vicinity of the dislocation core. We also estimate the polarized line charge density of an edge dislocation in an isotropic flexoelectric solid which is in agreement with some measurements in ice. We perform an asymptotic analysis of the crack tip fields in flexoelectric solids and show that our results share some features from solutions in strain gradient elasticity and piezoelectricity. We also compute the energy release rate for cracks using simple crack face boundary conditions and use them in classical criteria for crack growth to make predictions. Our analysis can serve as a starting point for more sophisticated analytic and computational treatments of defects in flexoelectric solids which are gaining increasing prominence in the field of nanoscience and nanotechnology.

Summary Background Ultrasound accelerates tissue-type plasminogen activator (t-PA)–induced fibrinolysis of clots in vitro and in vivo. Objective To identify mechanisms for the enhancement of t-PA–induced fibrinolysis of clots. Methods Turbidity is an accurate and convenient method, not previously used, to follow the effects of ultrasound. Deconvolution microscopy was used to determine changes in structure, while fluorescence recovery after photobleaching was used to characterize the kinetics of binding/unbinding and transport. Results The ultrasound pulse repetition frequency affected clot lysis times, but there were no thermal effects. Ultrasound in the absence of t-PA produced a slight but consistent decrease in turbidity, suggesting a decrease in fibrin diameter due solely to the action of the ultrasound, likely caused by an increase in protofibril tension because of vibration from ultrasound. Changes in fibrin network structure during lysis with ultrasound were visualized in real time by deconvolution microscopy, revealing that the network becomes unstable when 30–40% of the protein in the network was digested, whereas without ultrasound, the fibrin network was digested gradually and retained structural integrity. Fluorescence recovery after photobleaching during lysis revealed that the off-rate of oligomers from digesting fibers was little affected, but the number of binding/unbinding sites was increased. Conclusions Ultrasound causes a decrease in the diameter of the fibers due to tension as a result of vibration, leading to increased binding sites for plasmin(ogen)/t-PA. The positive feedback of this structural change together with increased mixing/transport of t-PA/plasmin(ogen) is likely to account for the observed enhancement of fibrinolysis by ultrasound.

Recent advances in materials, manufacturing, biotechnology, and microelectromechanical systems (MEMS) have fostered many exciting biosensors and bioactuators that are based on biocompatible piezoelectric materials. These biodevices can be safely integrated with biological systems for applications such as sensing biological forces, stimulating tissue growth and healing, as well as diagnosing medical problems. Herein, the principles, applications, future opportunities, and challenges of piezoelectric biomaterials for medical uses are reviewed thoroughly. Modern piezoelectric biosensors/bioactuators are developed with new materials and advanced methods in microfabrication/encapsulation to avoid the toxicity of conventional lead-based piezoelectric materials. Intriguingly, some piezoelectric materials are biodegradable in nature, which eliminates the need for invasive implant extraction. Together, these advancements in the field of piezoelectric materials and microsystems can spark a new age in the field of medicine.