Strain Stiffening Research Articles

Nonlinear elastic behaviors and deformation mechanisms of nano-structured crosslinked biopolymer networks

Cells always undergo large deformation in response to external stimulations or internal stresses in many cell functions (e.g., cell migration, cell division and cell growth). When undergoing large deformation, crosslinked actin filament networks (CAFNs) always show strong nonlinear elasticity to maintain the cell shape and integrity, known as strain stiffening, which plays a crucial role in many cell functions. To investigate the nonlinear elastic behaviors of CAFNs, a three-dimensional representative volume element model is used to perform finite element method simulations. Simulation results show that actin filament volume fraction, crosslinking density and components’ Young’s moduli show significant influences on the nonlinear elastic behaviors of CAFNs. In addition, the shear stress–strain curves of CAFNs highly depend on the bending stiffness and tensile stiffness of filamins as well as the bending stiffness of actin filaments, however, they are almost insensitive to the tensile stiffness of actin filaments. The present work not only sheds light on the nonlinear elastic behaviors of CAFNs but also provides a valuable reference for developing advanced artificial composite structures that can be used as semi-flexible biomedical scaffolds and wearable electronics.

Free and Forced Vibration Behaviors of Magnetodielectric Effect in Magnetorheological Elastomers

This paper is concerned with the free and forced vibration responses of a magneto/electroactive dielectric elastomer, emphasizing the chaotic phenomena. The dielectric elastomers under external magnetic and electrical excitations undergo large elastic deformation. The magnetodielectric elastomer is modeled based on the Gent–Gent strain energy function to incorporate the influence of the second invariant and the strain stiffening. The viscoelasticity of the active polymer is also considered in the form of Rayleigh’s dissipation function. The equation of motion is governed with the aid of the Lagrangian equation in terms of a physical quantity, namely, the stretch of the elastomer. An energy-based approach is utilized to re-evaluate the static and DC voltage instabilities of the resonator. Time-stretch response (time history behavior), phase plane diagram, Poincaré map, and fast Fourier transform are numerically obtained and presented to explore the chaotic oscillation behavior of the active polymer actuators. The results reveal that the magnetic field may tune the stability and instability regions of the active polymeric membrane. It has also been shown that the applied magnetic field may lead to chaotic vibration responses when a sinusoidal voltage is applied simultaneously to the system. The results presented in this paper can be effectively used to design magnetic and electrical soft robotic actuators and elastomer membranes under electrical and magnetic stimulants.

Resilience study of wheat protein networks with large amplitude oscillatory shear rheology

This study investigates the effect of standard laboratory production steps on the network properties of vital gluten. Gluten experiences high mechanical input during production from wheat dough and subsequent processing, which influences the network characteristics. The production of vital gluten in laboratory scale ensures full control on all processing parameters and the possibility to obtain the protein using the mildest washing, drying and milling techniques. Large Amplitude Oscillatory Shear (LAOS) tests were performed on wheat dough, intermediate materials during gluten production and the final product vital gluten at frequencies of 1–15 rad/s and strains from 0.01 to 100%. The elastic and viscous behavior of the material are described by analyzing the fundamental response and the higher harmonics, based on Lissajous-Bowditch curves. The intra-cycle behavior revealed that vital gluten only exhibits network stiffening, whereas dough shows both strain stiffening and shear thinning effects. This suggests that starch induces the shear thinning effects in dough.Comparison of rehydrated and fresh gluten obtained from the same starting material reveals minor alteration of the protein secondary structures during the production process by means of Fourier-transform infrared spectroscopy (FTIR). A pronounced difference in water uptake accounts for modified rheological network properties.

Large amplitude oscillatory shear study of a colloidal gel near the critical state.

A system undergoing sol-gel transition passes through a unique point, known as the critical gel state, where it forms the weakest space spanning percolated network. We investigate the nonlinear viscoelastic behavior of a colloidal dispersion at the critical gel state using large amplitude oscillatory shear rheology. The colloidal gel at the critical point is subjected to oscillatory shear flow with increasing strain amplitude at different frequencies. We observe that the first harmonic of the elastic and viscous moduli exhibits a monotonic decrease as the material undergoes a linear to nonlinear transition. We analyze the stress waveform across this transition and obtain the nonlinear moduli and viscosity as a function of frequency and strain amplitude. The analysis of the nonlinear moduli and viscosities suggests intracycle strain stiffening and intracycle shear thinning in the colloidal dispersion. Based on the insights obtained from the nonlinear analysis, we propose a potential scenario of the microstructural changes occurring in the nonlinear region. We also develop an integral model using the time-strain separable Kaye-Bernstein-Kearsley-Zapas constitutive equation with a power-law relaxation modulus and damping function obtained from experiments. The proposed model with a slight adjustment of the damping function inferred using a spectral method, compares well with experimental data at all frequencies.

An Experimental Study and Modeling on the Thermo‐Rheological Properties of Polyurethane‐Based Magnetorheological Gel

Magnetorheological (MR) gel is a novel type of smart material with field‐dependent rheological properties, which is mainly composited of soft magnetic particles and a gel‐like matrix. Its controllable rheological behaviors depend on many factors, in which temperature is a significant factor requiring further study. Herein, polyurethane‐based MR gel with a 60% weight fraction of carbonyl iron is developed. The influence of temperature on the rheological characteristics of the MR gel sample is systematically investigated. The steady shear test is adopted to determine the yield stress and dynamic viscosity of MR gel under different temperatures. A new stress model based on Bingham constitutive model and Arrhenius relation is proposed to incorporate the influence of the temperature and to capture the hysteresis characteristics and strain stiffening properties. The results show that yield stress shows exponential decay with temperature and at the same time, dynamic viscosity displays exponential decay both along with temperature and current. Finally, hysteresis behavior responses by sinusoidal strain excitation with the frequency of 0.1, 5, and 15 Hz at the fixed amplitude of 50% and current of 2 A have been extracted to analyze the impact of temperature on the damping and stiffness properties of the MR gel.

Bionic artificial penile Tunica albuginea

Bionic artificial penile Tunica albuginea

A Semi-Analytical Finite Element Framework for Lamb Waves in Soft Compressible Plates Considering Strain Stiffening Effect

This paper investigates the elastic wave propagation through soft materials that are being subjected to finite deformations. The nonlinear elastic and linearized incremental theories have been exploited to formulate governing wave equations and elastic moduli in Lagrangian space. Semi-analytical finite element (SAFE) method, a numerical approach has been formulated for computing dispersive relations of guided waves in compressible hyper-elastic plates. This framework requires finite element discretization of the cross section of the waveguide and harmonic exponential function assumes the motion along the wave propagation direction. Here, explicit phase velocity results have been shown for soft materials with a prominent stiffening effect by employing the Gent model, and these results are analyzed for elastic wave propagation through compressible materials. It has been noticed that Lamb waves have a strong dependence on the frequency-thickness product, prestretch, and direction of wave propagation. Moreover, with the strain stiffening effect, the dependence becomes stronger, especially for fundamental symmetric and anti-symmetric modes. The numerical results display that at certain prestretch the Gent material encounter snap-through instability resulting from geometrical and material nonlinearities. The influence of material properties like Gent constant and direction of wave propagation on snap-through instability has been discussed. The proposed SAFE framework reveals that finite deformations can affect elastic wave propagation through stiffness and compressibility.

Nonlinear rheological properties of Chinese cold skin noodle (liangpi) and wheat starch gels by large amplitude oscillatory shear (LAOS)

The recipe secret of making Chinese cuisine cold skin noodles (liangpi) with wheat flour was revealed by linear and nonlinear rheological characterization of wheat starch gel systems, which were made from different concentrations of liangpi slurry (LPS) and wheat starch slurry (WSS). The peak viscosity of LPS was suppressed at low concentrations and significantly higher than that of WSS at high concentrations. The G′ and G″ of LPS gels were higher than that of WSS gels under the same concentration, while the tanδ values were low in LPS gels and exhibited relatively greater mobility. This difference in LPS may be related to the non-starch components in it. The two starch gel systems were further characterized by the large amplitude oscillatory shear (LAOS) test. Lissajous curves showed that LPS gels follow a highly different elastic and viscous evolution than WSS gels during large deformation cycles. This was also evidenced by more pronounced strain stiffening and shear thickening trends of LPS gels and the larger I3/I1 values. The introduction of non-starch components was responsible for the significant changes in the properties of starch gels, and the LAOS method helped us to better understand these differences.

Importance of experimental evaluation of structural parameters for constitutive modelling of aorta

The study compares stresses and strains in the aortic wall derived using different constitutive models for various stress-strain conditions. Structure-based constitutive models with two fibre families with (GOH) and without (HGO) dispersion of collagen fibres are compared. The constitutive models were fitted to data from equibiaxial tension tests of two separated layers of the porcine aortic wall. The initial fit was evaluated with unrestricted parameters and subsequently, the mean angles of the fibre families and the angular dispersion were fixed to the values obtained from histology. Surprisingly, none of the tested models was capable to provide a good quality fit with histologically obtained structural parameters. Fitting the HGO model to experimental data resulted in two fibre families under angles close to ±45°, while the GOH model resulted in a nearly isotropic fibre distribution. These results indicate that both of these models suffer from the absence of isotropic strain stiffening. After having modified both models with corresponding additional members based on the Yeoh model of matrix, we obtained a perfect fit to the measured data while keeping the structural histology-based parameters. Finally, significant differences in compliance and resulting stresses and strains between different models are shown by means of simulations of uniaxial tension test, equibiaxial tension tests and inflation of the aorta.

A new micro–macro transition for hyperelastic materials

Many classic hyperelastic models fail to predict the stress responses of soft materials in complex loading conditions with parameters calibrated through one simple test. To address this fundamental issue, we propose a new micro–macro transition for the microstructural hyperelasticity modeling, which is further integrated into the full network framework. With a Gaussian chain distribution, this new mapping scheme yields an explicit one-parameter hyperelastic model in terms of principal stretches. This new linear model achieves remarkable success in capturing the stress responses in multi-axial deformation modes for soft materials with an absence of strain stiffening effect, which is beyond the capability of the widely used neo-Hookean model. A new two-parameter hyperelastic model is further developed by combining the new micro–macro transition and non-Gaussian Langevin chain distribution. Compared with other two-parameter hyperelastic models based on Langevin statistics, such as the eight-chain model, affine full network model, and equilibrated microsphere model, our new model exhibits greatly improved predictive ability for complex loading types. The new model is also implemented for finite element analysis, which shows the ability to capture the responses of soft materials with heterogeneous strain distribution. In all cases, the parameters in our models can be determined through the data of uniaxial loading tests, along with the behaviors in other loading modes being well forecast, which is a challenge for various other existing hyperelastic models. This novel micro–macro transition is shown to properly capture the inherent correlations between different deformation modes, which may advance fundamentally modeling hyperelasticity and other constitutive behaviors for soft materials.

A generalized model of lead rubber bearing considering large strain stiffening and degradation

Lead rubber bearings (LRBs) have been widely used in seismic isolation systems to mitigate earthquake damage in regions characterized by high seismic intensity. However, effective isolation is achieved at the expense of largely concentrated displacement in the isolation layer. Past experimental studies have confirmed that rubber stiffening and degradation properties are essential for LRBs at large cyclic strains. That is, accurately simulating the complex nonlinear behavior of LRBs is significant to evaluate the performance of isolated structures under strong earthquakes. Nevertheless, most LRB models in engineering practice cannot capture the strong nonlinear properties and the existing models for elaborate modeling are not widely used due to the complicated shape parameters. For this reason, the present study proposes a generalized Bouc–Wen model that can reasonably reflect the large strain stiffening and strength degradation properties of rubber. The traditional Bouc–Wen model of LRBs was introduced first. Subsequently, a generalized Bouc–Wen model of LRBs that is capable of simulating the observed large cyclic behavior with reasonable accuracy was developed. The model was further verified by the experimental results of LRBs with different design parameters under various loading conditions. Moreover, time history analyses were conducted to evaluate the earthquake responses of the single-degree-of-freedom system with the traditional Bouc–Wen and generalized Bouc–Wen model. Comparison proves that the two bearing models can closely estimate the peak deformation and shear force in minor and moderate earthquakes. By contrast, the generalized model can accurately capture the LRB properties under large cyclic strain that can restrain the bearing deformation but possibly increase the shear force significantly under strong earthquakes.

Heat-induced gelation of protein from mealworm (Tenebrio molitor): influence of pH and zinc concentration

Mealworm protein has the general potential to substitute environmentally less favourable, animal derived raw-materials as a gelling biomaterial for zinc enriched wound healing ointments. However, various factors affecting heat-induced gelation of mealworm protein have not yet been studied in detail. Therefore, we investigated the influence of pH (pH 5.5 and 7.5) and zinc concentration (0 M, 0.1 M and 0.3 M) on rheological properties and gel structure of heat-induced mealworm protein gels. Additionally, we used gel solubility experiments and rheological investigations to study the gels with regard to the involved types of interactions. Generally, all examined samples were able to form heat-induced gels. From gel solubility experiments and temperature sweeps, hydrophobic interactions and hydrogen bonds were found to be dominant in all samples. From higher storage moduli we derive the contribution of additional electrostatic and/or covalent interactions in samples with ZnSO4, while shorter linear viscoelastic regimes and more pronounced intracycle strain stiffening were related to less homogenous and more particulate gel structures. From our results strategies for the customisation of gel properties and gel composition may be deduced, that may advance the potential for future utilisation of mealworm protein in wound dressings.

Large amplitude oscillatory shear behavior of thermoresponsive hydrogels: Single versus double network

Double network (DN) hydrogels have been recognized as new tough materials for several industries due to their precise structural platforms and significant properties. However, a comprehensive understanding of microstructural changes of DN hydrogels under large deformations is required to extend their applications. In this work, we use the large amplitude oscillatory shear (LAOS) technique to study the nonlinear response of a thermoresponsive κ-carrageenan/polyacrylamide DN system and its nanocomposite containing graphene oxide (GO) in comparison to its single network components. The results show a combination of strain stiffening and shear thickening nonlinear responses. The elastic intracycle strain stiffening was mainly attributed to the shear-induced increase in the elasticity of network chains and non-Gaussian stretching of individual chains. In addition, the orientation of the κ-carrageenan double helix segments and their enhancing effect on molecular orientation could be proposed as another possible mechanism of strain stiffening. The viscous intracycle shear thickening is also interpreted by two mechanisms of shear-induced temporary structure formation and reformation of dissociated physical interactions. It is also found that the GO nanosheets could contribute to the viscoelastic response by increasing the molecular interactions and, thus, amplification of energy dissipation. Furthermore, temperature dependency of the DN hydrogel owing to the conformational changes of the κ-carrageenan network at sufficiently high temperatures is used to investigate the effect of temperature on nonlinear behaviors. Increasing the temperature is found to have a significant decreasing effect on viscous nonlinearity, while its effect on the elastic nonlinearity was strongly dependent on the strain amplitude. This study provides a better understanding of the correlation between the microstructure and viscoelastic properties for designing tough hydrogels.

Using high-pressure homogenization as a potential method to pretreat soybean protein isolate: Effect on conformation changes and rheological properties of its acid-induced gel

This study evaluated the conformational changes and rheological properties of acid-induced gels of insoluble soybean protein isolate (SPI) pretreated with high-pressure homogenization (HPH) under different pressure and cycles. Results showed that HPH pretreatment destroyed the spatial structure of the insoluble SPI, significantly decreased the particle size of the SPI dispersion, and increased the SH content. Through the characterization of its acid-induced gelation product, the best ability to withstand small strains (< 3%) of gel was found in a single HPH cycle under 100 MPa. The SPI gels with a relatively compact structure transformed from strain stiffening to strain softening with the strain increased, and it provided satisfactory stability to withstand large-amplitude oscillatory shear in three-time HPH cycles under 100 MPa. Meanwhile, SPI gels exhibited a more chaos spatial topology network after HPH pretreatment through fractal analysis, and the gels eventually exhibited “soft gel” and shear-thinning behavior with HPH pretreatment. This provides an evidence for the beneficial effect of HPH on the structural homogenization and subsequent gel formation stability of protein gels, and explores its potential applications in the food industry.

Strain stiffening of Ndc80 complexes attached to microtubule plus ends

In the mitotic spindle, microtubules attach to chromosomes via kinetochores. The microtubule-binding Ndc80 complex is an integral part of kinetochores, and is essential for kinetochores to attach to microtubules and to transmit forces from dynamic microtubule ends to the chromosomes. The Ndc80 complex has a rod-like appearance with globular domains at its ends that are separated by a long coiled coil. Its mechanical properties are considered important for the dynamic interaction between kinetochores and microtubules. Here, we present a novel method that allows us to time trace the effective stiffness of Ndc80 complexes following shortening microtubule ends against applied force in optical trap experiments. Applying this method to wild-type Ndc80 and three variants (calponin homology (CH) domains mutated or Hec1 tail unphosphorylated, phosphorylated, or truncated), we reveal that each variant exhibits strain stiffening; i.e., the effective stiffness increases under tension that is built up by a depolymerizing microtubule. The strain stiffening relation is roughly linear and independent of the state of the microtubule. We introduce structure-based models that show that the strain stiffening can be traced back to the specific architecture of the Ndc80 complex with a characteristic flexible kink, to thermal fluctuations of the microtubule, and to the bending elasticity of flaring protofilaments, which exert force to move the Ndc80 complexes. Our model accounts for changes in the amount of load-bearing attachments at various force levels and reproduces the roughly linear strain stiffening behavior, highlighting the importance of force-dependent binding affinity.

Evolution of Force Chains Explains the Onset of Strain Stiffening in Fiber Networks

Abstract Fiber networks are the primary structural components of many biological structures, including the cell cytoskeleton and the extracellular matrix. These materials exhibit global nonlinearities, such as stiffening in extension and shear, during which the fibers bend and align with the direction of applied loading. Precise details of deformations at the scale of the fibers during strain stiffening are still lacking, however, as prior work has studied fiber alignment primarily from a qualitative perspective, which leaves incomplete the understanding of how the local microstructural evolution leads to the global mechanical behavior. To fill this gap, we studied how axial forces are transmitted inside the fiber network along paths called force chains, which continuously evolve during the course of deformation. We performed numerical simulations on two-dimensional networks of random fibers under uniaxial extension and shear, modeling the fibers using beam elements in finite element software. To quantify the force chains, we identified all chains of connected fibers for which the axial force was larger than a preset threshold and computed the total length of all such chains. To study the evolution of force chains during loading, we computed the derivative of the total length of all force chains with respect to the applied engineering strain. Results showed that the highest rate of evolution of force chains coincided with the global critical strain for strain stiffening of the fiber network. Therefore, force chains are an important factor connecting understanding of the local kinematics and force transmission to the macroscale stiffness of the fiber network.

Photo-Controlled Dynamics and Transport in Entangled Wormlike Micellar Nanocomposites Studied by XPCS

Dynamics of nanoparticles (NPs) in microscopic networks, in particular, localization and transport, play a key role in designing new functional nanocomposites and drug delivery systems. To this aim, it is crucial to understand the interplay between the network structure and dynamics on the microscopic scale which determines NP diffusion. Here, we study the localization and transport of spherical NPs in photorheological wormlike micellar nanocomposites where the mobility of the NPs is controlled by the network mesh size and the micelle length, which can be tuned by UV-illumination. The macroscopic viscoelastic properties are measured by classical rheology, while X-ray photon correlation spectroscopy and nanorheology provide information on the microscopic NP dynamics on length scales on the order of the network mesh size. On long time scales, the data reveal that transport through the network is determined by the ratio between the NP size and the network mesh size, while upon UV illumination, the NP mobility is drastically enhanced. On shorter time scales, the influence of the dynamical and structural micelle properties on the NP dynamics under confinement is explored and indicates an anomalous speed-up of the dynamics, which is discussed in the context of changes in the local structure and non-linear phenomena such as strain stiffening and hopping motion.

Mechanical properties of the premature lung: From tissue deformation under load to mechanosensitivity of alveolar cells.

Many preterm infants require mechanical ventilation as life-saving therapy. However, ventilation-induced overpressure can result in lung diseases. Considering the lung as a viscoelastic material, positive pressure inside the lung results in increased hydrostatic pressure and tissue compression. To elucidate the effect of positive pressure on lung tissue mechanics and cell behavior, we mimic the effect of overpressure by employing an uniaxial load onto fetal and adult rat lungs with different deformation rates. Additionally, tissue expansion during tidal breathing due to a negative intrathoracic pressure was addressed by uniaxial tension. We found a hyperelastic deformation behavior of fetal tissues under compression and tension with a remarkable strain stiffening. In contrast, adult lungs exhibited a similar response only during compression. Young’s moduli were always larger during tension compared to compression, while only during compression a strong deformation-rate dependency was found. In fact, fetal lung tissue under compression showed clear viscoelastic features even for small strains. Thus, we propose that the fetal lung is much more vulnerable during inflation by mechanical ventilation compared to normal inspiration. Electrophysiological experiments with different hydrostatic pressure gradients acting on primary fetal distal lung epithelial cells revealed that the activity of the epithelial sodium channel (ENaC) and the sodium-potassium pump (Na,K-ATPase) dropped during pressures of 30 cmH2O. Thus, pressures used during mechanical ventilation might impair alveolar fluid clearance important for normal lung function.

The micromorphology and large amplitude oscillatory shear behaviors of hydrocarbon gel fuels filled with fumed silica and aluminium sub-microparticles

The gel network structure filled with attractive nanoparticles (NPs) significantly affects the viscoelasticity of the nanocomposites, which is poorly understood and troubles industrial processes. In this work, the nanoparticle gel matrices were prepared with hydrophilic fumed silica (FS), and filled with aluminium sub-microparticles (Al SMPs) loading in the range of 10%− 50%. The effects of particle content and composition on the large amplitude oscillatory shear (LAOS) behaviors are investigated by stress decomposition methods. Meanwhile, the higher harmonics and the Chebyshev harmonics coefficients were obtained. We found that the gels exhibit consistent progressive stiffening with particles filling, companying with plastic transformation and weak strain overshoot (WSO). With aluminum increasing, nonlinear viscoelastic responses gradually weaken in LAOS, severely decreasing the linear viscoelastic (LVE) region, and were validated by strain stiffening index S, T and high-order harmonics. In confocal microscopy (CFM) images, the aluminum particles were fluorescently labeled and found to be adhered together with FS clusters. This article could provide a perspective on understanding the flow mechanism of particulate network structure by combining morphological details and LAOS behaviors.

Heterotropic roles of divalent cations in the establishment of allostery and affinity maturation of integrin αXβ2.

SUMMARYAllosteric activation and silencing of leukocyte β2-integrins transpire through cation-dependent structural changes, which mediate integrin biosynthesis and recycling, and are essential to designing leukocyte-specific drugs. Stepwise addition of Mg2+ reveals two mutually coupled events for the αXβ2 ligand-binding domain—the αX I-domain—corresponding to allostery establishment and affinity maturation. Electrostatic alterations in the Mg2+-binding site establish long-range couplings, leading to both pH− and Mg2+-occupancy-dependent biphasic stability change in the αX I-domain fold. The ligand-binding sensorgrams show composite affinity events for the αX I-domain accounting for the multiplicity of the αX I-domain conformational states existing in the solution. On cell surfaces, increasing Mg2+ concentration enhanced adhesiveness of αXβ2. This work highlights how intrinsically flexible pH− and cation-sensitive architecture endows a unique dynamic continuum to the αI-domain structure on the intact integrin, thereby revealing the importance of allostery establishment and affinity maturation in both extracellular and intracellular integrin events.