Soft Viscoelastic Materials Research Articles

Development of a piezo stack – Laser doppler vibrometer sensing approach for characterizing shear wave dispersion and local viscoelastic property distributions

Laser Doppler vibrometry and wavefield analysis have recently shown great potential for nondestructive evaluation, structural health monitoring, and studying wave physics. However, there are limited studies on these approaches for viscoelastic soft materials, especially, very few studies on the laser Doppler vibrometer (LDV)-based acquisition of time–space wavefields of dispersive shear waves in viscoelastic materials and the analysis of these wavefields for characterizing shear wave dispersion and evaluating local viscoelastic property distributions. Therefore, this research focuses on developing a piezo stack-LDV system and shear wave time–space wavefield analysis methods for enabling the functions of characterizing the shear wave dispersion and the distributions of local viscoelastic material properties. Our system leverages a piezo stack to generate shear waves in viscoelastic materials and an LDV to acquire time–space wavefields. We introduced space-frequency-wavenumber analysis and least square regression-based dispersion comparison to analyze shear wave time–space wavefields and offer functions including extracting shear wave dispersion relations from wavefields and characterizing the spatial distributions of local wavenumbers and viscoelastic properties (e.g., shear elasticity and viscosity). Proof-of-concept experiments were performed using a synthetic gelatin phantom. The results show that our system can successfully generate shear waves and acquire time–space wavefields. They also prove that our wavefield analysis methods can reveal the shear wave dispersion relation and show the spatial distributions of local wavenumbers and viscoelastic properties. We expect this research to benefit engineering and biomedical research communities and inspire researchers interested in developing shear wave-based technologies for characterizing viscoelastic materials.

Stress distribution in a multi-layer soft viscoelastic material under sliding motion of a spherical indenter tip

Stress distribution in a multi-layer soft viscoelastic material under sliding motion of a spherical indenter tip

Investigation of the Motion of a Spherical Object Located at Soft Elastic and Viscoelastic Material Interface for Identification of Material Properties

Measuring the properties of soft viscoelastic materials is challenging. Here, the motion of a spherical object located at the soft elastic and viscoelastic material interface for the identification of material properties is thoroughly investigated. Formulations for different loading cases were derived. First, the theoretical models for a spherical object located at an elastic medium interface were derived, ignoring the medium viscosity. After summarizing the model for the force reducing to zero following the initial loading, we developed mathematical models for the force reducing to a lower non-zero value or increasing to a higher non-zero value, following the initial loading. Second, a similar derivation process was followed to evaluate the response of a spherical object located at a viscoelastic medium interface. Third, by performing systematic analyses, the theoretical models obtained via different approaches were compared and evaluated. Fourth, the measured and predicted responses of a spherical object located at a gelatin phantom interface were compared and the viscoelastic material properties were identified. It was seen that the frequency of oscillations of a spherical object located at the sample interface during loading was 10–15% different from that during unloading in the experimental studies here. The results showed that different loading cases have immense practical value and the formulations for different loading cases can provide an accurate determination of material properties in a multitude of biomedical and industrial applications.

Modeling cracks in viscoelastic materials at finite strains

AbstractViscosity is a manifestation of internal friction in materials. Such friction is accompanied by the dissipation of energy, which affects deformation and fracture. In the present work, we develop a new theoretical formulation and its numerical implementation for modeling fracture in viscoelastic soft materials. Concerning the theory, we extend the material‐sink approach by including a viscosity description at finite strains. Concerning numerical methods, we introduce a mixed finite‐element formulation based on the relative deformation gradient and implement it in Abaqus. Representative numerical examples show that the proposed approach captures the viscous behavior of material and demonstrates the coupling between viscosity and fracture. Simulations reveal that the viscous dissipation suppresses minor crack branching as compared to the purely hyperelastic case, when the strain rate is relatively small. That said, when the strain rate is relatively large, viscoelastic and hyperelastic materials fracture consonantly.

Multichannel resonant acoustic rheometry system for quantification of coagulation of multiple human plasma samples

Resonant Acoustic Rheometry (RAR), a newly developed ultrasound-based technique for non-contact characterization of soft viscoelastic materials, has shown promise for quantitative viscoelastic assessment of temporally changing soft biomaterials in real time, and may be used to monitor blood coagulation process. Here, we report the development of a novel, multichannel RAR (mRAR) system for simultaneous measurements of multiple temporally evolving samples and demonstration of its use for monitoring the coagulation of multiple small-volume plasma samples. The mRAR system was constructed using an array of 4 custom-designed ultrasound transducers at 5.0 MHz and a novel electronic driving system that controlled the generation of synchronized ultrasound pulses for real time assessment of multiple samples simultaneously. As a proof-of-concept of the operation of the mRAR system, we performed tests using pooled normal human plasma samples and anti-coagulated plasma samples from patients treated with warfarin with a range of International Normalized Ratio (INR) values as well-characterized samples with different coagulation kinetics. Our results show that simultaneous tracking of dynamic changes in 4 plasma samples triggered by either kaolin or tissue factor was achieved for the entire duration of coagulation. The mRAR system captured distinct changes in the samples and identified parameters including the clotting start time and parameters associated with the stiffness of the final clots that were consistent with INR levels. Data from this study demonstrate the feasibility of the mRAR system for efficient characterization of the kinetic coagulation processes of multiple plasma samples.

Complex band structure in viscoelastic thin plate phononic crystals

Phononic crystals (PnCs) are artificial composites designed by a periodic arrangement of two or more materials with different properties and/or geometry, in order to tailor the propagation of mechanical waves. The complex band structures of PnC thin plates, consisting of a hard matrix material reinforced by inclusions of soft viscoelastic material (HS-PnC), and vice-versa (SHPnC), are investigated. In general, elastic plate structures can be modelled using the Kirchhoff- Love theory, which is suitable for thin plates in low frequencies. However, there is a lack of knowledge concerning the effects of viscoelastic constituents on the complex band structure of flexural Bloch waves in PnC thin plates. In this study, an extended plane wave expansion (EPWE) method is used to compute the complex band structures of VPnC thin plates. The evanescent behaviour of periodic plates for the cases HS-PnC and SH-PnC is calculated, and the results show that the first creates flat bands for wave localization and the second opens up complete and partial Bragg scaterring band gaps.

Inverse design of acoustic coatings using Bayesian inference

A Bayesian approach for the inverse design of acoustic coatings for underwater noise control is presented. The coating model comprises a periodic arrangement of voids embedded in a soft viscoelastic material. The viscoelastic material is attached to a steel backing with water on its incidence side and air on its transmission side. The acoustic performance of the coating is strongly dependent on the geometric properties of the voided inclusions as well as the number of layers of voids in the direction of sound propagation. The geometric optimization process using Bayesian inference proceeds inversely from a target absorption coefficient spectrum to the required number of voided layers, the geometric design parameters in each layer, and the distance between each layer. The Bayesian design process demonstrates that broadband sound absorption can be achieved using a multilayered coating with a gradient change in both void diameter and distance between each layer. Optimized designs using the Bayesian approach are validated against results obtained numerically as well as experimental results from the literature.

Research on the Dynamic Behaviors in the Sliding Friction of Silicone

With the promotion of soft viscoelastic materials in the field of flexible bionic robots, the behavior of sliding friction between soft viscoelastic materials and rigid materials such as metals has attracted great attention. In this study, the research object was silicone, and a research method combining a dynamic force testing technique and a non-contact optical testing technique for deformation and strain was proposed to study the frictional behavior of silicone and the effect of the tooth structure surface on the sliding friction. We analyzed the temporal changes in the friction force for different loads, the dynamic characteristics of large deformation and micro-strain on the front side (define the contact surface as the bottom surface) of the silicone. The results showed that within a certain range, the sliding friction coefficient of the silicone increased monotonically with increasing load, and there were stick-slip and deformation waves during the relative motion. The larger the load was, the faster the deformation wave propagated, and the tooth structure surface had sliding friction anisotropy.

Identification of the viscoelastic properties of a hydrogel in sol–gel transition by vibration experiments

Soft viscoelastic materials, such as hydrogels, are widely used by biomedical and agri-food industries. The characterization of their transition from solution (liquid) to gel (solid) state is often necessary for manufacturing processes and quality control. This study aims at characterizing the viscoelastic properties of a hydrogel in sol–gel transition by measuring the vibration response of the bottom silicone membrane of a rigid circular cylindrical container subjected to base excitation. The static deflection of the membrane for increasing sample filling height was measured. The frequency-responses of the membrane alone and of the membrane coupled to a hydrogel during sol–gel transition were measured for increasing filling heights. A finite-element numerical model was built for the identification of the storage shear modulus and loss tangent of the hydrogel. Both a slip and a no-slip conditions of the hydrogel at the inner wall of the container were applied and their effects were compared. The static deflection was calculated and compared to the experiments. The parameters of a dynamic model of the coupled membrane–hydrogel were identified. The evolution of the identified material parameters enables to follow the sol–gel transition of the hydrogel. Results show that the membrane vibration can be used to characterize the viscoelastic mechanical properties of a hydrogel in sol–gel transition through a more versatile approach.

Friction Dynamics of Foams under Nonlinear Motion

Foams are viscoelastic soft materials with complex mechanical properties. Here, we evaluated the friction dynamics of foams between acrylic plates using a sinusoidal motion friction evaluation system and we found some interesting characteristics under accelerated conditions. On a typical solid surface, a symmetrical friction profile, in which static and kinetic frictions are observed, is obtained under reciprocating nonlinear motion. Meanwhile, significant lubricant effects and velocity-dependent friction profiles without static friction were observed in foams. The friction force in foams increased in proportion to the power of velocity, with a power index of <1. These characteristic and dynamic phenomena in foams were observed in this study. They had been caused by the formation of a thick lubricant film and various dissipative modes including surfactant diffusion, viscous dissipation, and wall slip of bubbles. Moreover, the addition of a thickener increased the friction force and the delay time of friction response and improved the foam durability against normal force and shear. These findings are useful for understanding dynamic phenomena in soft materials.

Correction: Plateau-Rayleigh instability in a soft viscoelastic material.

Correction for 'Plateau-Rayleigh instability in a soft viscoelastic material' by S. I. Tamim et al., Soft Matter, 2021, DOI: .

Fiber-Reinforced Soft Bending Actuator Control Utilizing On/Off Valves

Soft fluid-driven robots have great potential for safe interaction with humans, and for adaptation to complex and unpredictable environments with the compliance brought about by soft materials. However, the respective complex structure and massive use of nonlinear and viscoelastic soft materials, and the nonlinear fluid-driven dynamics, result in the nonlinear dynamic behavior of soft robots, and thus pose great challenges to system modeling and dynamic control. In this study, a complete model is first established by considering the nonlinear behavior of fiber-reinforced soft bending actuator (FRSBA) and the nonlinear dynamics of pneumatic system regulated by two high-speed on/off valves. Notably, the nonlinear dynamic behavior of FRSBA is first identified as parametric uncertainties using the multi-sine pressure excitation signal, and the effects of nonlinear pneumatic system are fully taken into account. Then, an adaptive robust controller is designed to handle the system nonlinearities with a guaranteed transient and steady-state performance. Finally, the comparative experiments demonstrate the effectiveness of proposed modeling method and high performance of adaptive robust controller.

Solutions to ramp-hold dynamic oscillation indentation tests for assessing the viscoelasticity of hydrogel by Kelvin-Voigt fractional derivative modeling

Indentation type dynamic mechanical analysis (IT-DMA) is an attractive approach to characterizing viscoelastic properties of soft matter under both quasi-static and dynamic loadings. Frequency-dependent viscoelastic properties are usually characterized by storage and loss moduli whereas extracting inherent viscoelastic model parameters from dynamic loadings remains unsolved. In this study, closed-form solutions to dynamic oscillation loadings were first derived and adapted to a variety of excitations for arbitrary shape indenters. A uniform theoretical framework for ramp-hold-oscillation-relaxation/creep indentation tests are established and Kelvin-Voigt fractional derivative (KVFD) solutions are presented to predict the viscoelastic behavior for both quasi-static loadings (creep, relaxation) and dynamic loadings (sinusoidal displacement/force cycles at 5,10,15,20,30 Hz). Four gelatin-cream hydrogel samples were investigated under ramp-hold-oscillation-relaxation and ramp-hold-oscillation-creep testing conditions. Viscoelastic quantities of elasticity E0, fluidity α, and viscosity τ were extracted by fitting the experimental curves to KVFD predictions. The results show that KVFD models can accurately depict the viscoelastic behavior under both dynamic and quasi-static loadings with high goodness of fit (R2>0.936). To assess the proposed method, comparison of the viscoelastic quantities from different experimental protocols were conducted. Statistical results revealed viscoelastic parameters from different loading are in close agreement. For dynamic loadings, significant differences were found for [E0, α] estimates at different frequencies. For different experimental protocols, estimations were consistent in that E0 showed maximum value on Gel5Cream15 sample, and α was increased with increasing cream percentage. Moreover, viscoelastic quantities extracted from dynamic relaxation were correlated with those of the dynamic creep (r = 0.977, p < 0.001 for E0, and r = 0.969, p < 0.001 for α). Viscoelastic quantities from quasi-static relaxation were highly correlated with those from quasi-static creep (r = 0. 910, p < 0.001 for E0, and r = 0.979, p < 0.001 for α). The complex modulus from KVFD estimations was found to be correlated with that of the DMA measurement (for dynamic relaxation, r = 0.603, p < 0.001 for E′ and r = 0.818, p < 0.001 for E″; for dynamic creep, r = 0.756, p < 0.001 for E′ and r = 0.762, p < 0.001 for E″). Cross validation and assessment by alternative DMA method confirmed that KVFD solutions provided a method for relating viscoelastic measurements at load frequencies from quasi-static to dynamic for soft viscoelastic tissue-like materials.

Topology optimization of dissipative metamaterials at finite strains based on nonlinear homogenization

This study presents a novel computational framework for designing optimal dissipative (damping) metamaterials under time-dependent loading conditions at finite deformations. In this framework, finite strain computational homogenization is integrated with a density-based multimaterial topology optimization. In addition, a thermodynamically consistent finite strain viscoelasticity model is incorporated together with an analytical path-dependent sensitivity analysis. Optimization formulations with and without stiffness and mass constraints are considered, and various new damping metamaterial designs are obtained that combine soft viscoelastic and stiff hyperelastic material phases. Multiscale stability analysis using the Bloch wave analysis and rank-1 convexity checks is also carried out to investigate stability of the optimized designs. Stability analyses demonstrate that the inclusion of voids or soft material phases can make a metamaterial more prone to lose micro and macro-stability. Furthermore, the concept of tunable metamaterials is explored wherein metamaterial’s response is steered towards a stable deformation path by tailoring the design with a preselected micro buckling mode.

Development and Characterization of Calmodulin-Based Copolymeric Hydrogels.

Recently, there has been growing interest in harnessing genetically engineered polymers to develop responsive biomaterials, such as hydrogels. Unlike their synthetic counterparts, genetically engineered polymers are produced without the use of toxic reagents and can easily be programmed to incorporate desirable hydrogel properties, including bioactivity, biodegradability, and monodispersity. Herein, we report the development of a copolymeric hydrogel that is based on the calcium-dependent protein, calmodulin (CaM). For our system, CaM and M13, a CaM-binding peptide, were incorporated into genetically engineered polymers with intervening linkers containing cleavable sequences. Spectroscopic and multiple-particle tracking (MPT) studies demonstrate that these polymers self-assemble through calcium-stabilized, noncovalent crosslinking to form a soft viscoelastic material. MPT further revealed that gelation is concentration-dependent. Collagenase digests show that the protein polymers are selectively degraded through specific cleavage. The modularity and stimuli-responsiveness of this system suggest its potential as a flexible scaffold for biomedical applications.

A Proprioceptive Bellows (PB) Actuator With Position Feedback and Force Estimation

Soft robot is known for great safety in human-centered environments due to its inherent compliance. However, the compliance resulting from the soft continuum structure and viscoelastic material also induces challenges for sensing and control of soft robots. In this letter, we propose a proprioceptive soft actuator design approach based on 3D printed conductive material and 3D printed deformable structure, such as bellows. The conductive bellow exhibits effective resistance change and structural deformation, thus provides a promising solution for the challenge of deformable soft robots that need integrated actuation and sensing. The proposed proprioceptive bellow actuator (PB actuator) achieves effective position feedback and real-time output force estimation. Using a dedicated control logic of the pressure controller, the PB actuator can not only provide anticipated motion but also estimate the interactive force based on real-time position sensing and input pressure. The design, fabrication, modeling, control, and experimental validation of our proposed PB actuator are discussed in detail in this letter. The parameters of PB actuator are highly customizable depending on the intended applications. Based on the proposed PB actuator, two specialized grippers, T and Y gripper, are designed and prototyped to demonstrate the grasping force estimation capability. The proposed proprioceptive soft robotic approach provides a promising solution to design behavior steerable soft robots.

X-ray elastography by visualizing propagating shear waves

Elastography, an imaging modality for mapping elastic modulus in soft viscoelastic materials, has been developed using magnetic resonance imaging and ultrasound imaging, but few studies were reported on using X-ray imaging. We report on dynamic X-ray elastography, which relies on shear-wave propagation. We pneumatically vibrated polyacrylamide gel phantoms and obtained two-dimensional maps of storage and loss moduli, which were determined from temporal variation in displacement vectors of the vibrating particles in the phantoms. Our experiment provided storage moduli with a precision of 30% and a spatial resolution was one order of magnitude higher than other imaging modalities.

Nonlinear theory of wetting on deformable substrates.

The spreading of a liquid over a solid material is a key process in a wide range of applications. While this phenomenon is well understood when the solid is undeformable, its "soft" counterpart is still misunderstood and no consensus has been reached with regard to the physical mechanisms ruling the spreading of liquid drops over soft deformable materials. In this work we provide a theoretical framework, based on the nonlinear theory of discontinuities, to describe the behavior of a triple line on a soft material. We show that the contact line motion is opposed both by nonlinear localized capillary and visco-elastic forces. We give an explicit analytic formula relating the dynamic contact angle of a moving drop to its velocity for arbitrary rheology. We then specialize this formula to the experimentally relevant case of elastomers with the Chasset-Thirion (power-law) type of rheologies. The theoretical prediction is in very good agreement with experimental data, without any adjustable parameters. We then show that the nonlinear force balance presented in this work can also be used to recover classical models of wetting. Finally we provide predictions for the dynamic behavior of the yet largely unexplored case of a viscous drop spreading over a soft visco-elastic material and predict the emergence of a new form of apparent hysteresis.

Viscoelastic tribopairs in dry and lubricated sliding friction.

Soft contacts present different tribological responses compared to stiff materials, especially when soft materials exhibit viscoelastic behaviour, as viscoelastic materials have intermediate mechanical properties between viscous liquids and elastic solids. In this work, we investigated the influence of viscoelasticity of soft materials on sliding friction in dry and lubricated conditions. To achieve this, soft tribopairs with varying viscoelasticity were obtained by tuning the weight ratios of polydimethylsiloxane (PDMS) base and curing agent. The real-time friction force and preload were observed over multiple conditions, with systematic control of lubricant viscosity, preload, and sliding velocity. Tribopairs with a higher proportion of viscous character had more oscilliations in the friction force. They also presented a higher friction coefficient due to the increased contribution of viscoelastic hysteresis losses on friction. Through regression analysis, the models of the friction coefficient were found, which are in good agreement with experimental results. From the models, we found that in both dry and lubricated conditions, viscoelasticity of tribopairs, indicated as the loss modulus or loss tangent, plays a key role in determining the friction coefficient. This influence is particularly significant for dry contacts due to the direct interactions between surfaces of tribopairs. This study provides empirical proof and a focused analysis on the role of viscoelasticity in tribological contacts.

RHEOS.jl -- A Julia Package for Rheology Data Analysis

Rheology is the science of deformation and flow, with a focus on materials that do not exhibit simple linear elastic or viscous Newtonian behaviours. Rheology plays an important role in the empirical characterisation of soft viscoelastic materials commonly found in the food and cosmetics industry, as well as in biology and bioengineering. A broad range of theoretical tools exist to extract material parameters and interpret them thanks to data analysis and/or physical modelling. RHEOS (RHEology, Open-Source) is a software package designed to make the analysis of rheological data simpler, faster and more reproducible. RHEOS is currently limited to the broad family of linear viscoelastic models. A particular strength of the library is its ability to handle rheological models containing fractional derivatives which have demonstrable utility for the modelling of biological materials but have hitherto remained in relative obscurity-possibly due to their mathematical and computational complexity. RHEOS is written in Julia, which greatly assists achievement of our aims as it provides excellent computational efficiency and approachable syntax. RHEOS is fully documented and has extensive testing coverage. It should be noted that RHEOS is not an optimisation package. It builds on another optimisation package, NLopt, by adding a large number of abstractions and functionality specific to the exploration of viscoelastic data.