Nonlinear Deformation Regime Research Articles

When the Poisson Ratio of Polymer Networks and Gels Is Larger Than 0.5?

We use coarse-grained molecular dynamics simulations to study deformation of networks and gels of linear and brush strands in both linear and nonlinear deformation regimes under constant pressure conditions. The simulations show that the Poisson ratio of networks and gels could exceed 0.5 in the nonlinear deformation regime. This behavior is due to the ability of the network and gel strands to sustain large reversible deformation, which, in combination with the finite strand extensibility results in strand alignment and monomer density, increases with increasing strand elongation. We developed a nonlinear network and gel deformation model which defines conditions for the Poisson ratio to exceed 0.5. The model predictions are in good agreement with the simulation results.

Chirality in topologically interlocked material systems

The present study focuses on the mechanical chirality in plate-type topologically interlocked material systems. Topologically interlocked material (TIM) systems are a class of dense architectured materials for which the mechanical response emerges from the elastic behavior of the building blocks and the contact-frictions interactions between the blocks. The resulting mechanical behavior is strongly non-linear due to the stability-instability characteristics of the internal load transfer pattern. Two tessellations are considered (square and hexagonal) and patches from each are used as templates. While individual building blocks are achiral, chirality emerges from the assembly pattern. The measure of microstructure circulation is introduced to identify the geometric chirality of TIM systems. TIM systems identified as geometrically chiral are demonstrated to possess mechanical chiral response with a force-torque coupling under transverse mechanical loading of the TIM plate. The chiral length is found to be constant during the elastic response, yet size-dependent. During nonlinear deformation, the chiral length scale increases significantly and again exhibits a strong size dependence. The principle of dissection is introduced to transform non-chiral TIM systems into chiral ones. In the linear deformation regime, the framework of chiral elasticity is shown to be applicable. In the non-linear deformation regime, chirality is found to strongly affect the mechanical behavior more significantly than in the linear regime. Experiments on selected TIM systems validate key findings of the main computational study with the finite element method.

Shear-Triggered Release of Lipid Nanoparticles from Tissue-Mimetic Hydrogels.

Shear forces are involved in many cellular processes and increase remarkably in the case of cardiovascular diseases in the human body. While various stimuli, such as temperature, pH, light, and electromagnetic fields, have been considered for on-demand release, developing drug delivery systems that are responsive to physiological-level shear stresses remains as a challenge. For this purpose, liposomes embedded in hydrogel matrices are promising as they can dynamically engage with their environment due to their soft and deformable structure. However, for optimal drug delivery systems, the interaction between liposomes and the surrounding hydrogel matrix, and their response to the shear should be unraveled. Here, we used unilamellar DMPG liposomes as drug nanocarriers and polyethylene (glycol) diacrylate (PEGDA) hydrogels having different elasticities, from 1Pa to 180Pa, as extracellular matrix (ECM)-mimetic matrices to understand shear-triggered liposome discharge from hydrogels. The presence of liposomes provides hydrogels with temperature-controlled water uptake which is sensitive to membrane microviscosity. By systematically applying shear deformation from linear to nonlinear deformation regimes, we modulate the liposome release under transient and cyclic stimuli. Considering that shear force is commonly encountered in biofluid flow, these results will provide fundamental basis for rational design of shear-controlled liposomal drug delivery systems. This article is protected by copyright. All rights reserved.

Deformation Driven Deswelling of Brush Gels

We studied equilibrium swelling in brush gels undergoing large uniaxial deformations in contact with solvent by using a combination of the Flory–Rehner and scaling models of gels and coarse-grained molecular dynamics simulations of swollen brush networks. Our analysis showed that the swelling ratio of the brush gels Qeq(λ), describing the volume change upon swelling, is a nonmonotonic function of the gel uniaxial deformation ratio λ characterizing the gel shape. It first increases with increasing strand elongation from its value for the free-standing gel then begins to decrease. This behavior is a result of the optimization of polymer/solvent interactions and conformational entropy of brush strands in the nonlinear deformation regime. The location of the maximum in the Qeq(λ) function is directly related to the value of the strain-stiffening parameter β. This parameter depends on the degree of polymerization of the brush backbone and the backbone Kuhn length defined by both the grafting density and degree of polymerization of the side chains. Analysis of the nonlinear gel modulus confirmed that the strain-stiffening parameter β is identical in both dry networks and gels. However, the structural modulus of the gels, Gs, is smaller than that of the dry networks, Gdr, by a factor equal to the ratio of the Kuhn length of brush strands in the dry state, bK, and in the gel, bK,s, such that Gs = GdrbK/bK,s.

Surface stress decomposition in large amplitude oscillatory interfacial dilatation of complex interfaces

HypothesisMultiphase materials are often subjected to large deformations during processing, but the rheological responses of complex interfaces (e.g. stabilized by proteins) in this nonlinear deformation regime are still poorly understood. We expect nonlinearities in the response to be introduce by changes of the interfacial network and surface density of the emulsifier. ExperimentsLarge amplitude oscillatory dilatation (LAOD) experiments were performed on WPI-, pea albumin-, pea globulin- and rapeseed lecithin-stabilized interfaces and analyzed with a general stress decomposition (GSD). With GSD, the stress response was decomposed into the four stress terms (τ1-τ4). Here, τ1 and τ2 represent, the elastic and viscous contribution of the odd Fourier harmonics, and τ3 and τ4 represent the dissipative and recoverable contribution of the even harmonics. FindingsAnalysis of WPI-, pea albumin-, pea globulin- and rapeseed lecithin-stabilized interfaces revealed that higher odd harmonics (k≥3) describe in-plane network responses and that even harmonics describe surface density changes. Analysis of these complex interfaces showed that GSD is a valuable tool for (quantitative) description of interfacial responses in LAOD, providing new insights into the origin of asymmetric nonlinear stress responses.

Effect of constitutive law on the erythrocyte membrane response to large strains.

Three constitutive laws, that is the Skalak, neo-Hookean and Yeoh laws, commonly employed for describing the erythrocyte membrane mechanics are theoretically analyzed and numerically investigated to assess their accuracy for capturing erythrocyte deformation characteristics and morphology. Particular emphasis is given to the nonlinear deformation regime, where it is known that the discrepancies between constitutive laws are most prominent. Hence, the experiments of optical tweezers and micropipette aspiration are considered here, for which relationships between the individual shear elastic moduli of the constitutive laws can also be established through analysis of the tension-deformation relationship. All constitutive laws were found to adequately predict the axial and transverse deformations of a red blood cell subjected to stretching with optical tweezers for a constant shear elastic modulus value. As opposed to Skalak law, the neo-Hookean and Yeoh laws replicated the erythrocyte membrane folding, that has been experimentally observed, with the trade-off of sustaining significant area variations. For the micropipette aspiration, the suction pressure-aspiration length relationship could be excellently predicted for a fixed shear elastic modulus value only when Yeoh law was considered. Importantly, the neo-Hookean and Yeoh laws reproduced the membrane wrinkling at suction pressures close to those experimentally measured. None of the constitutive laws suffered from membrane area compressibility in the micropipette aspiration case.

Isogeometric shape optimization of missing rib auxetics with prescribed negative Poisson’s ratio over large strains using genetic algorithm

This paper presents an isogeometric shape optimization framework using genetic algorithm to design 2D auxetic structures with prescribed Poisson’s ratio over large tensile or compressive strains in the nonlinear deformation regime. The design domain is parametrized using NURBS to allow smoother shape variation of the structure and enable accurate fabrication of the optimized structures. The versatility of the framework is illustrated through the optimization of a missing rib structure with four ligaments under different loading conditions. The manufacturability of specimens using the NURBS and PolyJet 3D printing technology is also shown. The first example focuses on achieving constant negative Poisson’s ratio up to -0.7 within the applied tensile strain of 50% under plane stress condition. As auxetics experiments under large compressive strain are rarely performed and published, the second example demonstrates the optimization for compressive loading. The Poisson’s ratio determined from experiments matches well with the numerical results. The experiments highlight that for very flexible materials, deformation under self-weight and contacts between adjacent unit cells are significant factors in compression, and further investigations are needed.

Surfactant Driven Liquid to Soft Solid Transition of Cellulose Nanocrystal Suspensions

Cellulose nanocrystals (CNCs) have recently attracted wide interest due to their abundance, biocompatibility, and extraordinary physical properties. In particular, easy manipulation of their surface properties, hydrophilicity and high-aspect ratio make them ideal rheology modifiers, yet, the gelation mechanisms and microscopic origin of the complex rheological behavior in presence of secondary components, such as polymers and surfactants, are far from well-understood. In this work, we used light scattering, small-angle neutron scattering and bulk rheology to study the phase behavior and mechanical behavior of aqueous CNC solutions in presence of cationic 1-decyl trimethyl imidazolium chloride and 1-decyl trimethyl imidazolium ferric tetrachloride. The micelles of these surfactants form at similar cmc's (about 50 mM), adopt identical hydrodynamic sizes (on the order of a few nm's) and prolate-shaped ellipsoids, but vary in their inter-micelle interactions (charged vs neutral), thus allowing us to clarify the unprecedented effect of the surfactant micelle charge on the gel behavior of the aqueous CNC-surfactant complexes. Our results show that the positively charged micelles greatly strengthen the gel network while excessive free micelles weaken the gels due to repulsive micelle-micelle interaction. In the meantime, the analysis of the transition from linear to non-linear deformation regimes suggests that the gels gradually become more fragile with surfactant concentrations due to electrostatic repulsion of the charged micelles. Such a surfactant concentration dependent gel fragility was not observed in presence of the neutral micelles. These results provide a great step further in our understanding phase behavior and rheology of complex CNC-surfactant mixtures and obtaining biocompatible hydrogels with tunable mechanical properties.

Nonlinear rheological behavior of gelatin gels: In situ gels and individual layers

The gelation procedure and the gelation time of gelatin gels may lead to apparently similar materials, however, with different rheological fingerprints under small and large oscillatory shear deformations. Here, in the first paper of this series, gelation of 3 and 5% w/w gelatin solutions at 5 °C was performed in situ on the rheometer plate and in custom-made casting modules to obtain individual gel layers. Large amplitude oscillatory shear (LAOS) tests were performed. The nonlinear deformation regime was qualitatively analyzed using normalized Lissajous-Bowditch curves. The MITlaos software was employed to decompose the total intracycle stress response and to calculate the Chebyshev coefficients ratios. The dynamic moduli of the fresh gels were measured directly after the in situ preparation and within a time frame until 1.5 h. In the strain sweeps, we observed intense stiffening followed by yielding above 200% strain. However, the individual gel layers aged for 24 and 48 h show different LAOS fingerprints. The extensive loops in the viscous Lissajous-Bowditch curves indicate an elastoplastic material response. Based on the overall nonlinear rheological response, we propose a structural formation that describes the behavior of the gels for the conditions studied here. In the second paper of this series, we give the impact of hard micro-fillers (glass beads) and we describe the nonlinear characteristics of the filled gels.

Modulation of acoustomechanical instability and bifurcation behavior of soft materials

We demonstrate acoustically triggered giant deformation of soft materials, and reveal the snap-through instability and bifurcation behavior of soft materials in nonlinear deformation regime in response to combined loading of mechanical and acoustic radiation forces. Our theoretical results suggest that acoustomechanical instability and bifurcation can be readily modulated by varying either the mechanical or acoustic force. This modulation functionality arises from the sensitivity of acoustic wave propagation to nonlinear deformation of soft material, particularly to ratio of initial geometrical size of soft material to acoustic wavelength in the material. The tunable acoustomechanical instability and bifurcation behavior of soft materials enables innovative design of programmable mechanical metamaterials. PACS numbers: 43.35.+d, 43.25.+y, 46.70.De, 61.41.+e.

Wave dispersion in non-linear pantographic beams

In this paper, amplitude-dependent dispersion relations for flexural and axial waves travelling along a pantographic beam in non-linear deformation regime are computed. The kinetic energy of the pantographic beam, including a gradient micro-inertia contribution, is derived by homogenization. In the limit of travelling waves with infinitesimal amplitude, well-known amplitude-independent wave dispersion relations for linear deformation regime are recovered. Our analysis concludes that exotic wave propagation is observed in pantographic beams and deserves further studies.

Consequences of Delayed Chain Retraction on the Rheology and Stretch Dynamics of Entangled Polymer Liquids under Continuous Nonlinear Shear Deformation

We generalize our recent new ideas for the continuous startup shear rheology of entangled polymer liquids in the transient stress overshoot regime to formulate a theory for the full constitutive response and nonequilibrium dynamics over all time scales, deformation rates, and degrees of entanglement. The convective constraint release (CCR) idea that chain retraction locally triggers disentanglement in a shear-rate-dependent manner is significantly modified to be physically consistent with our nonclassical treatment of delayed retraction due to an entanglement grip force. A detailed numerical study of the predictions of the theory is presented for the full stress–strain response, scaling behavior of the stress overshoot and undershoot features, orientational stress, primitive path contour length dynamics, and nonequilibrium steady-state properties spanning the slow and fast nonlinear deformation regimes. For deformations slow enough there is little or no chain stretch, our results are qualitatively the sam...

Computer Simulations of Bottle Brushes: From Melts to Soft Networks

Using a combination of molecular dynamics simulations and analytical calculations, we study dense bottle- brush systems in a melt and network state. Analysis of our simulation results shows that bottle-brush macromolecules in melt behave as ideal chains with effective Kuhn length bK. Simulations show that the bottle-brush-induced bending rigidity is due to an entropy decrease caused by redistribution of the side chains upon backbone bending. The Kuhn length of the bottle brushes increases with increasing the side-chain degree of polymerization nsc as bK ∝ nsc 0.46 . This model of bottle-brush macromolecules is extended to describe mechanical properties of bottle-brush networks in linear and nonlinear deformation regimes. In the linear deformation regime, the network shear modulus scales with the degree of polymerization of the side chains as G0 ∝ (nsc +1 ) −1 as long as the ratio of the Kuhn length, bK, to the size of the fully extended bottle-brush backbone between cross-links, Rmax, is smaller than unity, bK/Rmax ≪ 1. Bottle-brush networks with bK/Rmax ∝ 1 demonstrate behavior similar to that of networks of semiflexible chains with G0 ∝ nsc −0.5 . In the nonlinear network deformation regime, the deformation-dependent shear modulus is a universal function of the first strain invariant I1 and bottle-brush backbone deformation ratio β describing stretching ability of the bottle-brush backbone between cross-links.

Large strain behaviour of nanostructured polyelectrolyte hydrogels

The mechanical properties of nanostructured polyelectrolyte hydrogels have been investigated targeting specifically the nonlinear deformation regime at large strains and the fracture properties. The hydrogels were synthesized using a thiol-ene cross-linking chemistry of polyacrylic acid precursor chains previously functionalized with double bonds. Some polymers were also grafted with C12 side chains able to form hydrophobic clusters in water. The large strain deformation of these nanostructured gels was tested in uniaxial compression by performing loading/unloading cycles at different strain rates and up to different maximum strains. All hydrogels displayed a pronounced strain hardening before fracture and a strain dependent hysteresis but the magnitude of these effects depended on the details of the composition. The most pronounced strain hardening was observed for the unmodified hydrogels in pure water while the largest hysteresis was found for the gels containing the highest concentration of nanoclusters. These dissipative processes barely influence the mechanical behaviour at small strains where the gel remains very elastic but become important at large strains and improve the resistance to fracture of the gels.

Spicules and the Effect of Rigid Rods on Enclosing Membrane Tubes

Membrane tubes (spicules) arise in cells, or artificial membranes, in the nonlinear deformation regime due to, e.g., the growth of microtubules, actin filaments, or sickle hemoglobin fibers towards a membrane. We calculate the axial force f exerted by the tube, and its average radius, taking into account steric interactions between the fluctuating membrane and the enclosed rod. We find a smooth crossover of the axial force between f approximately square root of (sigma) and f approximately sigma as the membrane tension sigma increases and the tube radius shrinks. This crossover occurs around the most physiologically relevant membrane tensions. Our work may be important in (i) interpreting experiments in which axial force is related to the tube radius or membrane tension, and (ii) constructing dynamical theories for biopolymer growth in narrow tubes where these fluctuation effects control the tube radius.

Studies of gel viscoelasticity by a wave interference technique

A new technique involving high-frequency shear wave interferometry has been used to investigate the viscoelastic properties of gels formed from aqueous dispersions of a synthetic hectorite-type clay colloid. The technique facilitates studies of stress relaxation phenomena under a range of strains and strain rates, in both linear and nonlinear deformation regimes. Measurements of the group and phase velocities of frequency-multiplexed shear waves, conducted in the presence and absence of steady shear fields, provide visco elastic-solid-like relaxation spectra. Under shear, the relaxation spectra indicate a trend to fluidization of the system as shear rate increases. A viscoelastic solid model is used to interpret the wave dispersion and the results, which constitute the first rheometrical exploitation of the `beat' phenomenon, support conclusions drawn from light scattering and small-angle neutron scattering studies concerning the origin of viscoelasticity in this system.

Off-Axis Inelastic Behavior of Hybrid Composite GLARE 2 and Classical Lamination Theory Taking Into Account Ply Failure.

Inelastic and fracture behaviors of a new fiber-metal composite GLARE 2, a unidirectional hybrid laminate of glass/epoxy laminae and aluminum alloy sheets, have been examined under various off axis static tensile loading conditions. The classical laminated plate theory (CLT) has been applied to describe the off-axis inelastic behavior of GLARE 2, in which the failure-induced elastic degradation of GFRP plies was taken into account. For all off-axis angles, a clear transition from the linear to nonlinear deformation regime appears. The stress level of this sharp transition almost coincides with the yield stress of the constituent aluminum layers. The anisotropy in the fracture stress can be predicted using the Tsai-Hill theory. Taking into account the observation that for a 90°C off-axis specimen the tangent modulus in the nonlinear regime is almost in agreement with that of the monolithic aluminum alloy, we have considered transverse cracking in the GFRP plies and modified the CLT so as to include the instantaneous degradation of the transverse and shear elastic moduli due to the transverse fracture. The results obtained using the CLT with ply failure accurately described the characteristic behavior of GLARE 2.

Visco‐Elastic properties of blends of crystalline polymers possessing a weak phase coupling. Studies on blends of poly(ethylene) and poly(oxymethylene)

AbstractThe investigations reported in this paper aimed at evaluating the impact of a weak interfacial strength on visco‐elastic properties in multiphase polymer blends both in the linear and nonlinear deformation regime. Blends of poly(ethylene) and poly(oxymethylene) were used as model systems. The particular choice of the components of the blend was based on the fact that the two components are incompatible, possess strong interfacial energies and thus narrow and weak interfacial layers, and finally that their individual visco‐elastic properties are within the same order of magnitude. This allows to evaluate the contributions of the phase boundaries to the visco‐elastic properties in a transparent way.We investigated the visco‐elastic properties of blends of various compositions by analyzing the stress‐strain behavior, the dynamical torsional behavior as well as by determinating their cyclic stress‐strain behavior. The experimental finding is that most of the properties studied vary linearly with the composition and are not influenced by the weakness of the interfacial strength–contrary to the expectation. An exception is the elongation at break which varies nonlinearly with the composition and which shows a minimum value at intermediate compositions. The impact of a weak phase coupling on visco‐elastic properties is thus rather limited.

Polarization-optical investigation of polymers in fluid and high-elastic states under oscillatory deformation

The relationship was investigated between birefringence and oscillatory shear deformation of linear high molecular mass polymers exemplified by narrow- and broad-distribution polybutadienes and polyisoprenes. Polymer deformation at different frequencies and amplitudes was carried out in an annular gap. The stress field uniformity was not below 95%. It was shown that in oscillatory deformation of polymers in the fluid and high-elastic states, birefringence contains a time-independent steady component and an oscillatory component with a frequency equal to that of the assigned oscillation. A linear interrelation was found to exist between the amplitude of the oscillatory component of birefringence and that of the shear stresses, with a proportionality factor equal to the stress-optical coefficient of the polymers. The phase of the oscillatory component of birefringence coincides with that of the shear stresses. Measurements of the steady component of the birefringence make it possible to find the steady component of the first normal stress difference resulting from the assignment of shear oscillations to the polymer. On the basis of the experimental data obtained for polybutadienes and polyisoprenes, and the literature data for polystyrene solutions, a master curve was constructed that generalizes the dependence of the steady component of the first normal stress difference in the linear and nonlinear deformation regimes on the product of the square of the deformation amplitude and the storage modulus measured at low amplitudes. This dependence is valid in the linear and nonlinear deformation regimes. It is invariant with frequency, amplitude deformation, molecular mass, and molecular mass distribution of the polymers. It is shown by visual observation of deformation that the abrupt drop in resistance of polymer to shear in large-amplitude deformation is due to polymer rupture near the surface of the inner cylinder and is accompanied by a slip-stick process. This is the phenomenon of spurt early observed in capillary viscometers at high shear stresses and recently investigated in coaxial cylinder devices at large amplitude deformation.