Nonlinear Viscoelasticity Research Articles

Poroviscoelasto-plasticity of agarose-based hydrogels.

Agarose gels are excellent candidates for tissue engineering as they are tunable, viscoelastic, and show a pronounced strain-stiffening response. These characteristics make them ideal to create in vitro environments to grow cells and develop tissues. As in many other biopolymers, viscoelasticity and poroelasticity coexist as time-dependent behaviors in agarose gels. While the viscoelastic behavior of these hydrogels has been considered using both phenomenological and continuum models, there remains a lack of connection between the underlying physics and the macroscopic material response. Through a finite element analysis and complimentary experiments, we evaluated the complex time-dependent mechanical response of agarose gels in various conditions. We then conceptualized these gels as a dynamic network where the global dissociation/association rate of intermolecular bonds is described as a combination of a fast rate native to double helices forming between aligned agarose molecules and a slow rate of the agarose molecules present in the clusters. Using the foundation of the transient network theory, we developed a physics-based constitutive model that accurately describes agarose behavior. Integrating experimental results and model prediction, we demonstrated that the fast dissociation/association rate follows a nonlinear force-dependent response, whose exponential evolution agrees with Eyring's model based on the transition state theory. Overall, our results establish a more accurate understanding of the time-dependent mechanics of agarose gels and provide a model that can inform design of a variety of biopolymers with a similar network topology.

Linear and nonlinear rheology of liberase-treated breast cancer tumors.

Extracellular matrix (ECM) rigidity has been shown to increase the invasive properties of breast cancer cells, promoting transformation and metastasis through mechanotransduction. Reducing ECM stiffness via enzymatic digestion could be a promising approach to slowing breast cancer development by de-differentiation of breast cancer cells to less aggressive phenotypes and enhancing the effectiveness of existing chemotherapeutics via improved drug penetrance throughout the tumor. In this study, we examine the effects of injectable liberase (a blend of collagenase and thermolysin enzymes) treatments on the linear and nonlinear rheology of allograft 4T1 mouse mammary tumors. We perform two sets of in vivo mouse studies, in which either one or multiple treatment injections occur before the tumors are harvested for rheological analysis. The treatment groups in each study consist of a buffer control, free liberase enzyme in buffer, a thermoresponsive copolymer called LiquoGel (LQG) in buffer, and a combined, localized injection of LQG and liberase. All tumor samples exhibit gel-like linear rheological behavior with the elastic modulus significantly larger than the viscous modulus and both independent of frequency. Tumors that receive a single injection of localized liberase have significantly lower tumor volumes and lower tissue moduli at both the center and edge compared to buffer- and free liberase-injected control tumors, while tissue viscoelasticity remains relatively unaffected. Tumors injected multiple times with LQG and liberase also have lower tissue volumes but possess higher tissue moduli and lower viscoelasticities compared to the other treatment groups. We propose that a mechanotransductive mechanism could cause the formation of smaller but stiffer tumors after repeated, localized liberase injections. Large amplitude oscillatory shear (LAOS) experiments are also performed on tissues from the multiple injection study and the results are analyzed using MITlaos. LAOS analysis reveals that all 4T1 tumors from the multiple injection study exhibit nonlinear rheological behavior at high strains and strain rates. Examination of the Lissajous-Bowditch curves, Chebyshev coefficient ratios, elastic moduli, and dynamic viscosities demonstrate that the onset and type of nonlinear behavior is independent of treatment type and elastic modulus, suggesting that multiple liberase injections do not affect the nonlinear viscoelasticity of 4T1 tumors.

Nonlinear N – Compartments model of respiratory mechanics considering viscoelasticity, inertia and surface tension properties

Respiratory biomechanics constitutes an important topic in clinical practice. Different strategies like mathematical models have been implemented to understand and replicate scenarios allowing deeper analysis. In this paper, a nonlinear N - compartments model is presented, allowing to represent the lung in a heterogeneous way. It considers the resistance of each generation of the airway and each alveolar compartment characterized independently. Includes properties of nonlinear elastance, viscoelasticity, inertia, and surface tension. In this work, to show the functionality of the model, a simulation of four alveolar units coupled to the airway model is presented using pressure as input signal simulating mechanical ventilation. However, the model can be used to simulate any desired number of alveolar units. Values at airway output were compared to the linear model, obtaining a correlation close to 1. Also, was compared to a physical test lung using Hamilton - S1 mechanical ventilator obtaining a positive correlation. The model makes it possible to evaluate the effects of different properties during spontaneous respiration or mechanical ventilation, both at the airway opening and alveolar. These properties include viscoelasticity, surface tension, inertia, among others.

A more accurate fatigue characterization of GO-modified asphalt binder considering non-linear viscoelastic behaviour and UV exposure effects

The non-linear viscoelastic (NLVE) behaviour at high load levels is often neglected when characterizing the fatigue performance of asphalt materials, leading to a conservative or even underestimated assessment of the fatigue durability. The incremental stress sweep tests were conducted to define the threshold load amplitudes of the graphene oxide-modified asphalt binders (GO-MA) in the NLVE domain. The linear and non-linear dynamic shear modulus (|G*|LVE and |G*|NLVE) at fatigue test conditions were separately incorporated into the simplified viscoelastic continuum damage (S-VECD) model to rigorously quantify the fatigue life of asphalt binders. The damage evolution and the corresponding fatigue life of GO-MA binders in LVE-based and NLVE-based S-VECD models were analyzed comparatively. The outcomes manifested that GO nanoparticles could enhance the fatigue life of the asphalt binder. The comparison outcomes demonstrate an increase in fatigue life prediction for the base binder and GO-MA when both NLVE behavior and aging effects are taken into account.

Characterization of Nonlinear Viscoelastic Properties of Enhanced Oil Recovery Polymer Systems Using Steady-Shear Rheometry

SummaryEnhanced oil recovery (EOR) polymer systems such as hydrolyzed polyacrylamide (HPAM) solutions flowing in porous media at high fluxes were reported to cause shear-thickening, a nonlinear viscoelastic (NLVE) phenomenon. Bulk rheological studies are usually performed to characterize the viscous and viscoelastic behaviors of polymer solutions in porous media. To characterize the viscoelastic properties, oscillatory shear rheology based on linear viscoelastic (LVE) data and extensional rheology based on NLVE data have been used. Although both extensional flow and high-speed shear flow can stretch and thicken polymer solutions in a nonlinear fashion, steady-shear rheometry has been used to measure only the viscous and thinning behavior of HPAM systems. In this paper, (a) the thickening ability of HPAM polymer systems formulated with contrasting salinity and molecular weight (MW) concentration is characterized in bulk shear rheometry to analyze if the thickening in the pure shear field correlates with the thickening behavior reported in porous media and other rheometry and (b) the thickening intensity of the polymer solutions of varying salinity concentration in the bulk shear field is compared with the reported mechanical degradation effects in the literature.The shear-thickening index obtained by fitting a power-law model to thickening data in steady-shear rheograms is higher for the high-saline, high-MW low-concentration HPAM systems that have inherently higher nonlinear viscoelasticity. Furthermore, the thickening behavior observed due to salinity variation in bulk steady shear contrasts with linear oscillatory shear behavior but conforms to the thickening behavior observed in porous media and in the extensional field. This signifies that polymer-EOR researchers performing comparative studies on low-salinity and high-salinity polymer floods, and having a shear rheometer at their disposal, must look beyond linear oscillatory rheology and make use of nonlinear steady-shear rheology. There is a direct relation between the shear-thickening index of saline HPAM solutions and their mechanical degradation intensity. This paper shows that the high-speed data in steady-shear rheometry that are usually ignored in EOR literature have useful information and the notion that HPAM solutions are purely thinning in the bulk shear field needs to be reconsidered.

Localized Elasticity Governs the Nonlinear Rheology of Colloidal Supercooled Liquids

We propose a microscopic picture for understanding the nonlinear rheology of supercooled liquids with soft-repulsive potentials. Based on Brownian dynamics simulations of supercooled charge-stabilized colloidal suspensions, our analysis shows that the shear thinning of viscosity (eta) at large enough shear rates (sr), expressed as eta~sr^(-lambda), originates from the evolution of the localized elastic region (LER). An LER is a transient region composed of the first several coordination shells of a reference particle. In response to the external shear, particles within LER undergo nearly affine displacement before the yielding of LER. The characteristic strain (gamma) and size (xi) of LER respectively depend on the shear rate by gamma~sr^epsilon and xi~sr^(-nu). Three exponents, lambda, epsilon, and nu, are related by lambda=1-epsilon=4*nu. This simple relation connects the nonlinear rheology to the elastic properties and the microscopic configurational distortion of the system. The relaxation of the LER is promoted by the large-step nonaffine particle displacement along the extensional direction of the shear geometry with the step length of 0.4 particle diameter. The elastic deformation and the relaxation of the LER are ubiquitous and succesive in the flow, which compose the fundamental process governing the bulk nonlinear viscoelasticity. We apply this model to analyze the Rheo-Small Angle Neutron Scattering data of sheared charge-stabilized colloidal suspensions. It is seen that our model well explains the neutron spectra and the rheological data.

Insight of the non-linear viscoelasticity of noodle dough using large amplitude oscillatory extension tests and the correlation with noodle quality

Large Amplitude Oscillatory Extension (LAOE) experiments were used to analyze the influence of rolling speed on the non-linear viscoelasticity of the dough sheets with different water additions (34%, 38%), and then the correlations between LAOE parameters with noodle quality were investigated. The E′M and E′L values were ten times higher than the η′eM and η′eL values, and the dough sheet along the sheeting direction exhibited higher E′L, E′M, η′eL, η′eM, and S values than that perpendicular to the sheeting direction at the same rolling speed, water addition, frequency and strain amplitude. The E′L, E′M, η′eL, η′eM, and S values decreased as the rolling speed increased, and this phenomenon was more pronounced for the dough sheet with 34% water addition than that with 38% water addition. The elastic modulus and fracture stress of dry noodles, and hardness and tensile force of cooked noodles had highly linear correlations with LAOE parameters (E′L, E′M, η′eL, and η′eM) when the water addition was the same.

CONSTRAINTS ON THE FUNCTION CHARACTERIZING THE PHYSICAL PROPERTIES OF A NONLINEAR VISCOELASTIC MATERIAL DETERMINED FROM THE CONVERGENCE CONDITIONS OF THE METHOD OF SUCCESSIVE APPROXIMATIONS FOR SOLVING THE DYNAMIC EQUATION OF NONLINEAR VISCOELASTICITY

The dynamic one-dimensional problem of nonlinear viscoelasticity is reduced to a nonlinear Volterra integral of the second kind, which can be solved by the method of successive approximations. From the convergence conditions of the method, conditions can be obtained that are imposed on the function characterizing the degree of nonlinearity of the viscoelastic medium.

Quantitative investigation on the nonlinear viscoelasticity of magnetorheological gel under large amplitude oscillatory shear

Magnetorheological gel (MRG) is a kind of magneto-sensitive smart composite whose nonlinear rheological behavior is highly controllable by external magnetic fields. For filling the gap that most publications studied the nonlinear property of MR materials in a qualitative manner, this work adopts a quantitative analysis method, called Fourier-transform rheology (FTR), to investigate the nonlinear viscoelasticity of MRG under large amplitude oscillatory shear (LAOS) tests. The influences of magnetic field, strain amplitude and frequency on the nonlinearity of MRG are thoroughly discussed. Results indicate that MRG, under a relative smaller magnetic field, appears higher degree of nonlinearity in the high-frequency region. The magneto-mechanical coupling mechanism of microstructures in MRG is also proposed to explain the various nonlinear phenomena under different loading conditions. Furthermore, for remedy the limitation that higher-order harmonics in FTR lack of clear physical meanings, a geometrical nonlinear parameter, S factor, is utilized to disclose the intra-cycle strain stiffening characteristic of MRG. The effects of strain amplitude, frequency and magnetic field on S factor are similar with that on the third-order harmonic in FTR. Moreover, the energy dissipation density is calculated based on Lissajous curve (i.e. hysteretic stress-strain loop) to characterize the damping property or capacity to dissipate energy of MRG. It is found that frequency only has a great effect on energy dissipation density of MRG under relatively large strain amplitude.

Roles of repeating-unit interactions in the stress relaxation process of bulk amorphous polymers: 2. nonlinear viscoelasticity

Stress relaxation manifests itself as the most fundamental mechanical response of bulk amorphous polymers. We characterized polymer repeating units with four-set interaction parameters separately representing the thermodynamic and kinetic aspects of local intrachain and interchain interactions, and evaluated their relative importance in stress relaxation with linear viscoelasticity at high temperatures by means of kinetic Monte Carlo simulations (DOI: 10.1016/j.polym.2021.123740). Hereby we continued to evaluate their relative importance in the initiation and the deviation extent of nonlinear viscoelasticity at low temperatures. We observed that thermodynamic interchain interactions seem no effective, while the other three local interactions retard the later stage of stress relaxation for nonlinear viscoelasticity, responsible for the KWW indexes of polymer rubbery states around 0.5. Both the kinetic aspects of intrachain and interchain interactions dominate the initiation temperatures of nonlinear viscoelasticity, and their high barriers suppress the deviation extent of nonlinear viscoelasticity towards the strong liquids like metals and ceramics, while their low barriers leave the fragile liquids to more thermodynamically rigid polymers. Our work facilitates a better understanding of structure-property relationship in nonlinear viscoelasticity of bulk amorphous polymers.

Structural-Phenomenological Rheological Model for Engineering Calculations of Polymeric Media Flows

Studying the behavior of flows of solutions and polymer melts in the field of nonlinear viscoelasticity allows describing the rheological properties in more details and more accurately assess the adequacy of rheological models. A new structural-phenomenological model is proposed to describe the rheological behavior of melts of branched polymers. This model can be recommended for engineering calculations of flows of polymeric media. The model is obtained from the modified Vinogradov-Pokrovsky model which is based on the microstructur-al approach and describes the dynamics of a polymer fluid. Stationary viscometric functions for simple shear and uniaxial tension, as well as stationary shear viscosity, the first-difference coefficient of normal stresses, stationary viscosity at uniaxial tension, are calculated using the obtained model. Also, the influence of model parameters on the form of the functions has been studied. It is shown that the model describes with good accuracy the nonlinear viscoelastic behavior of flowing polymer systems: an anomaly in viscosity, a drop in the coefficient of the first difference of normal stresses, and a nonmonotonic nature of the dependence of the steady-state elongation viscosity on the tensile rate. The viscometric functions data are compared with the experimental data for an industrial polyethylene melt sample.

Proxy-based sliding-mode tracking control of dielectric elastomer actuators through eliminating rate-dependent viscoelasticity

Dielectric elastomer actuators (DEAs) usually suffer from rate-dependent viscoelastic nonlinearity, which manifests as hysteresis in their deformation cycles, leading to huge challenges in their modeling and control. In this work, we propose a model-free, proxy-based, sliding-mode tracking control approach to mitigate viscoelastic nonlinearity, achieving high-precision tracking control of DEAs. To this end, we first investigate the viscoelastic nonlinearity of DEAs, revealing its asymmetric and rate-dependent characteristics. Then, by combining the benefits of the PID control for small positioning errors and sliding-mode control for large errors, a proxy-based, sliding-mode tracking controller (PBSMC) is established. Finally, the stability of the controller is analyzed. To verify the effectiveness of the controller, several experiments are conducted to demonstrate the performance of DEAs in tracking sinusoidal trajectories under different frequencies. The experimental results demonstrate that with the PBSMC, the DEA can precisely track sinusoidal trajectories within a frequency range of 0.1 Hz–4.0 Hz by effectively minimizing the effect of inherent viscoelastic nonlinearity. Compared with open-loop tracking performance, the proxy-based, sliding-mode controlled DEA shows a significant reduction in maximum tracking errors from 45.87% to 8.72% and in root-mean-square errors from 24.46% to 3.88%. The main advantages of the proxy-based, sliding-mode control are: (a) it adopts a model-free approach, avoiding the need for complex dynamic modeling; (b) it can achieve high-precision tracking control of DEAs, thereby paving the way for the adoption of DEAs in several emerging applications.

The Ogden and the extended tube model as backbone in describing electroactive polymers: advancements in modelling nonlinear behaviour and fracture.

Hyperelastic constitutive relations form the basis of advanced models for novel materials. Such elastic deformation potentials are the backbone for complex material formulations at elastic and inelastic deformations, especially when embedded into powerful frameworks like generalized standard materials, as well as multiphysical and multiscale formulations. With the focus on electroactive polymers, the article at hand demonstrates the derivation of a variational, rate-dependent electromechanical model for quasi-incompressible polymers and the derivation of an electromechanical model for regularized fracture mechanics by means of the phase-field method. Starting at the prominent Ogden and the extended tube model, some developments from the last decades are revisited and presented via the principle of virtual power, for instance, the established mixed element formulation, nonlinear viscoelasticity and electromechanical coupling. An electromechanically fully coupled representative crack element is used to derive a novel phase-field model for fracture. A key property of the proposed model is the ability to describe the electrical free-space behaviour inside the crack gap, which is demonstrated by adopting three common crack-face conditions. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

Strain-dependent stress relaxation behavior of healthy right ventricular free wall

The increasing evidence of stress-strain hysteresis in large animal or human myocardium calls for extensive characterizations of the passive viscoelastic behavior of the myocardium. Several recent studies have investigated and modeled the viscoelasticity of the left ventricle while the right ventricle (RV) viscoelasticity remains poorly understood. Our goal was to characterize the biaxial viscoelastic behavior of RV free wall (RVFW) using two modeling approaches. We applied both quasi-linear viscoelastic (QLV) and nonlinear viscoelastic (NLV) theories to experimental stress relaxation data from healthy adult ovine. A three-term Prony series relaxation function combined with an Ogden strain energy density function was used in the QLV modeling, while a power-law formulation was adopted in the NLV approach. The ovine RVFW exhibited an anisotropic and strain-dependent viscoelastic behavior relative to anatomical coordinates, and the NLV model showed a higher capacity in predicting strain-dependent stress relaxation than the QLV model. From the QLV fitting, the relaxation term associated with the largest time constant played the dominant role in the overall relaxation behavior at most strains from early to late diastole, whereas the term associated with the smallest time constant was pronounced only at low strains at early diastole. From the NLV fitting, the parameters showed a nonlinear dependence on the strain. Overall, our study characterized the anisotropic, nonlinear viscoelasticity to capture the elastic and viscous resistances of the RVFW during diastole. These findings deepen our understanding of RV myocardium dynamic mechanical properties. Statement of significanceAlthough significant progress has been made to understand the passive elastic behavior of the right ventricle free wall (RVFW), its viscoelastic behavior remains poorly understood. In this study, we originally applied both quasi-linear viscoelastic (QLV) and nonlinear viscoelastic (NLV) models to published experimental data from healthy ovine RVFW. Our results revealed an anisotropic and strain-dependent viscoelastic behavior of the RVFW. The parameters from the NLV fitting showed nonlinear relationships with the strain, and the NLV model showed a higher capacity in predicting strain-dependent stress relaxation than the QLV model. These findings characterize the anisotropic, nonlinear viscoelasticity of RVFW to fully capture the total (elastic and viscous) resistance that is critical to diastolic function.

A Numerical Scheme for Anisotropic Reactive Nonlinear Viscoelasticity.

Reactive viscoelasticity is a theoretical framework based on the theory of reactive constrained mixtures that encompasses nonlinear viscoelastic responses. It models a viscoelastic solid as a mixture of strong and weak bonds that maintain the cohesiveness of the molecular constituents of the solid matter. Strong bonds impart the elastic response while weak bonds break and reform into a stress-free state in response to loading. The process of bonds breaking and reforming is modeled as a reaction where loaded bonds are the reactants and bonds reformed into a stress-free state are the products of a reaction. The reaction is triggered by the evolving state of loading. The state of stress in strong bonds is a function of the total strain in the material, whereas the state of stress in weak bonds is based on the state of strain relative to the time that these bonds were reformed. This study introduces two important practical contributions to the reactive nonlinear viscoelasticity framework: (1) normally, the evaluation of the stress tensor involves taking a summation over a continually increasing number of weak bond generations, which is poorly suited for a computational scheme. Therefore, this study presents an effective numerical scheme for evaluating the strain energy density, the Cauchy stress, and spatial elasticity tensors of reactive viscoelastic materials. (2) We provide the conditions for satisfying frame indifference for anisotropic nonlinear viscoelasticity, including for tension-bearing fiber models. Code verifications and model validations against experimental data provide evidence in support of this updated formulation.

A new non-contact method for calculating deformation resistance of tire tread rubber material under rolling condition

Background70% energy consumption of automobile tyre comes from the energy consumption generated by the viscoelasticity of tread rubber.The non-contact calculation method of rolling resistance of tire tread rubber block is studied, and the relationship between rolling resistance and global strain is analyzed. Materials and methodsA non-contact test bench for mechanical property of rubber tread block is developed.Stress-strain relationship and full-field distribution characteristics are obtained by means of digital image correlation under the influence of load and velocity.A Fourier series model is proposed to describe the non-linear viscoelasticity of rubber material.The model parameters is identified by using non-linear least squares. On this basis, the rolling resistance and the rolling resistance coefficient are calculated. ResultsThe experimental results show that the nonlinear fitting error of Fourier series model is less than 3%.The rolling resistance coefficient of rubber tread decreases with the increase of speed and increases with the increase of wheel load.The low strain areas is distributed at the trailing edge of contact zone, but the high strain is distributed at the leading edge of contact zone. ConclusionA new method for calculating the rolling resistance of rubber materials is presented. The results show that the rolling resistance is positively correlated with the high strain distribution of tread under the influence of velocity. Under the influence of load, it is positively correlated with the transverse deformation of tread.

Effect of Morphology/Structure on the Phase Behavior and Nonlinear Rheological Properties of NR/SBR Blends.

The evolution of the morphology/structure and the nonlinear viscoelasticity of rubber blends under large amounts of strain are key scientific issues for the design and manufacture of rubber blends. The rheological responses of natural rubber/styrene-butadiene rubber (NR/SBR) blends are traced over a wide range of blend compositions to gain an insight into the effect of blend morphology on their nonlinear viscoelasticity. We also prepare NR + SBR physical blends without melt mixing to distinguish the contributions of composition and blend morphology to the viscoelastic response. The microscopic heterogeneous gel-like structure of NR/SBR blends may remarkably weaken their strain softening and improve their modulus hysteretic recovery under large strain, which may be attributed to the heterogeneous microscopic deformation for the NR and SBR phases. Furthermore, additional elastic contribution resulted from the increasing interfacial energy of domain deformation. This may provide some new insights into the effect of blend morphology on the Payne effect of rubber blends.

Response of binder-filler systems into and beyond linear viscoelastic domain: Modeling and healing efficiency

This study is devoted to present insights into linear and nonlinear viscoelastic responses as well as the healing efficiency (HE) of binder-filler systems. To this aim, linear viscoelastic (LV) rheometric results were collected via implementing temperature and frequency sweep measurements, while for probing the nonlinear viscoelastic (NLV) response, large-amplitude oscillatory shear test was executed for various strain maxima. A parallel rheological framework assembled from 2 Yeoh models and hyperbolic-sine flow law, hereinafter abbreviated as 2Y-HS model, was explored to emulate the stress response for LV and NLV behavior of the binder-filler systems. In addition, a strain-dependent healing protocol was developed to test the HE of materials for varying strain-amplitudes. The tested binder-filler systems were blends of a plain binder and two mineral fillers, hydrated lime (HL) and silica fume (SF), added one at a time at different rates based on the best-practice limits. The binder-filler mastics undergone different behaviors into and beyond linear viscoelastic domain (LVD). The 2Y-HS model has efficiently constituted the rheometric results in a manner that elucidates the link between the stresses and strains for both LV and NLV behaviors. The proposed HE protocol showed its efficacy to evaluate the healability of materials at varying rest periods and stretch magnitudes. The damage-mending process at small-amplitude strains tended to improve better, and worst HE was attained as the strain level increases. The richer the asphalt binder with mineral filler, the less the HE is registered; however the binder-HL system is predisposed to heal much more than SF mastics.

Simplified dynamical model and experimental verification of an underwater hydraulic soft robotic arm

Inherent compliance equips soft robotic arms with such advantages as incomparable flexibility, good adaptability, and safe interaction with the environment, etc. However, the strong nonlinearity also brings challenges to predict their dynamic behaviors. This work presents a simplified dynamic model of an underwater soft robotic arm which has three fiber-reinforced hydraulic chambers distributed symmetrically in each section. By controlling the pressures in the chambers, the soft robotic arm can perform complex spatial motion with multiple degrees of freedom. The model is based on Lagrangian method and piecewise constant curvature hypothesis, and considers the nonlinear viscoelasticity of soft material. The model accuracy is verified by the experiments of a two-section soft robotic arm with different actuation modes. The effects of geometrical features on dynamic response are also investigated through model-based simulation and test verification, which can provide guidance to parameter optimization. The proposed dynamic model can be extended to multiple sections and contribute to behavior analysis, performance prediction, and motion control of the soft robotic arm.

Mechanical and rheological properties and CO2-foaming behavior of reactively modified TPEE with controlled chain entanglement

Thermoplastic polyether ester elastomer (TPEE) foams can be fabricated using supercritical carbon dioxide (CO2) as an environment-friendly blowing agent. In this study, we investigated the effect of chain entanglement on the mechanical properties, viscoelasticity, and CO2-foaming behavior of TPEE. A series of branched TPEE samples with controlled chain entanglement were prepared by reactive extrusion using modifiers with epoxy groups. The gel-permeation chromatography–intrinsic viscosity (GPC-IV) methodology was employed to determine branch density. The junction point of chain entanglement was obtained; it increased at higher branch densities. The tensile behavior revealed that the branched TPEE samples became more rigid and poorer ductility, with stronger chain entanglement. Small-amplitude oscillation rheology showed enhanced shear thinning and zero-shear viscosity, reduced loss factor, and slower relaxation; these parameters indicated an improvement in linear viscoelasticity. Furthermore, nonlinear viscoelasticity was studied using elongational rheology, and the results were analyzed in combination with molecular stress function (MSF) model. The experimental results revealed that strain hardening was steeper with stronger chain entanglement, as proved by increasing value of free parameters fmax2 and β from MSF model. The reactively modified TPEE samples exhibited a larger expansion ratio than that of raw TPEE during the CO2-foaming process. Additionally, broader foaming temperature window to fabricate high-fold TPEE foams at CO2-foaming process enable the reactively modified TPEE to be used in the industrial production of TPEE foam with stable quality like bead and molded foaming.