Soft Elastic Material Research Articles

High-speed ultrasound imaging of bubbly flows and shear waves in soft matter.

In this methods paper, we explore the capabilities of high-speed ultrasound imaging (USI) to study fast varying and complex multi-phase structures in liquids and soft materials. Specifically, we assess the advantages and the limitations of this imaging technique through three distinct experiments involving rapid dynamics: the underwater flow induced by an external jet, the dissolution of sub-micron bubbles in water, and the propagation of shear waves in a soft elastic material. The phenomena were simultaneously characterized using optical microscopy and USI. In water, we use compounded USI for tracking a multi-phase flow produced by a jetting bubble diving into a liquid pool at speeds around 20 m s-1. These types of jets are produced by focusing a single laser pulse below the liquid surface. Upon breakup, they create a bubbly flow that exhibits high reflectivity to the ultrasound signal, enabling the visualization of the subsequent turbulent flow. In a second experiment, we demonstrate the potential of USI for recording the diffusive shrinkage of micro- and nanobubbles in water that could not be optically resolved. Puncturing an elastic material with a liquid jet creates shear waves that can be utilized for elastography measurements. We analysed the shape and speed of shear waves produced by different types of jetting bubbles in industrial gelatin. The wave characteristics were simultaneously determined by implementing particle velocimetry in optical and ultrasound measurements. For the latter, we employed a novel method to create homogeneously distributed micro- and nanobubbles in gelatin by illuminating it with a collimated laser beam.

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.

An Integrative Computational Design Workflow and Validation Methodology for 3D-Printed Personalized Orthopedic Devices: Case Study of a Wrist–Hand Orthosis (WHO)

Additive manufacturing (AM) technologies enable the production of customized and personalized medical devices that facilitate users’ comfort and rehabilitation requirements according to their individual conditions. The concept of a tailor-made orthopedic device addresses the accelerated recovery and comfort of the patient through the utilization of personalized rehabilitation equipment. Direct modeling, with an increasing number of approaches and prototypes, has provided many successful results until now. The modeling procedure for 3D-printed orthoses has emerged as the execution of steady and continuous tasks with several design selection criteria, such as cutting, thickening the surface, and engraving the shell of the orthosis. This publication takes into consideration the aforementioned criteria and proposes the creation of a holistic methodology and automated computational design process for the customization of orthotic assistive devices, considering aspects such as material properties, manufacturing limitations, recycling, and patients’ requirements. This proposal leads to the designing and manufacturing of a wrist orthopedic device based on reverse engineering, Design for AM (DfAM), and Design for Recycling (DfR) principles. The proposed methodology can be adjusted for different limbs. A dual-material approach was attained utilizing rigid, mechanically enhanced feedstock material and soft elastic material with reduced skin irritation risks to achieve both mechanical requirements and adequate cushioning for user comfort during rehabilitation. Recyclable thermoplastic matrices were selected, which also allow for the option to create washable devices for product life extension. Then, 3D scanning procedures were implemented to acquire the initial anatomic measurements for the design of the WHO and ensure and assess the dimensional accuracy of the final product. Physical mechanical testing was implemented to evaluate the WHO’s mechanical behavior and verify its functionality during basic wrist movements. The extracted dimensional data for the two main orthosis components that indicated approximately 50% and 25% of the tolerance values, respectively, were within the range (−0.1 mm, 0.1 mm).

Nonlinear propagation of quasiplanar shear wave beams in soft elastic media with transverse isotropy.

Model equations are developed for shear wave propagation in a soft elastic material that include effects of nonlinearity, diffraction, and transverse isotropy. A theory for plane wave propagation by Cormack [J. Acoust. Soc. Am. 150, 2566 (2021)] is extended to include leading order effects of wavefront curvature by assuming that the motion is quasiplanar, which is consistent with other paraxial model equations in nonlinear acoustics. The material is modeled using a general expansion of the strain energy density to fourth order in strain that comprises thirteen terms defining the elastic moduli. Equations of motion for the transverse displacement components are obtained using Hamilton's principle. The coupled equations of motion describe diffraction, anisotropy of the wave speeds, quadratic and cubic plane wave nonlinearity, and quadratic nonlinearity associated with wavefront curvature. Two illustrative special cases are investigated. Spatially varying shear vertical wave motion in the fiber direction excites a quadratic nonlinear interaction unique to transversely isotropic soft solids that results in axial second harmonic motion with longitudinal polarization. Shear horizontal wave motion in the fiber plane reveals effects of anisotropy on third harmonic generation, such as beam steering and dependence of harmonic generation efficiency on the propagation and fiber directions.

A local-resonance elastic metamaterial for the transport of wheel-rail vertical vibrations

The subwavelength artificial elastic metamaterials can be used for efficient transmission of vibration energies in a tunable frequency range. A local-resonance equal-thickness elastic metamaterial plate is designed in this work. The triangular resonators in the rhombic unit cell are used to exploit the valley degeneracy of the out-of-plane locally resonant modes under hexagonal symmetry conditions. The resonators consist of high-density cores wrapped by soft elastic material, and the differences in the intrinsic frequencies produce a topological band gap caused by the double resonant effect. The reversal of the energy bands proves that the band gap has a non-trivial topology effect, i.e., there exists edge states with robustness and high transmission efficiency. This structure can be utilized in railway transportation as an advanced elastic wave medium material to improve the efficiency of sensing and harvesting the energy of vertical vibrations between vehicles and rails.

Sound radiation from a cylindrical shell with a multilayered resonant coating

The vibroacoustic response of a structurally excited cylindrical shell submerged in water is presented. The shell is coated with a soft elastic material embedded with circumferential arrays of resonant inclusions. The coating is modelled as a multilayered equivalent fluid composed of homogeneous layers of the host soft material and homogenised layers comprising voids or hard inclusions. The radiated acoustic pressure is analytically derived by assembling and solving continuity and kinematic conditions at the interfaces between the cylindrical shell and the multilayered coating. Coating designs with different combinations of homogenised layers are examined. Physical mechanisms governing acoustic performance of the various coating designs are described. We show that the material of the inclusions, tuning the local resonances of the inclusions and the distribution of the homogenised layers within the coating have a significant effect on the shell vibroacoustic response.

Acoustic radiation from a cylindrical shell with a voided soft elastic coating.

An analytical framework for sound radiation from a fluid-loaded cylindrical shell covered with an acoustic coating is presented. The coating is composed of a soft elastic material embedded with a circumferential layer of equispaced voids. The layer of voids is modeled as an effective fluid medium sandwiched between two layers of the host material. Expressions for the effective impedance of the coating, radial displacement of the elastic shell, and the structure-borne radiated pressure for harmonic excitation of the shell are derived. Results show that the coating design can be tuned to reduce the radiated sound in a broad frequency range.

Flexible Low‐Melting Point Radiation Shielding Materials: Soft Elastomers with GaInSnPbBi High‐Entropy Alloy Inclusions

AbstractA polydimethylsiloxane (PDMS) matrix soft elastic composite material with low‐melting‐point GaInSnPbBi high‐entropy alloy (LHEA) inclusions is prepared to evaluate its radiation shielding performance. The LHEA is composed of two different three‐component eutectic microstructures, which are grown in a mixed manner to form a complex eutectic structure. The inclusions have excellent mechanical properties that matched the deformation of the PDMS matrix. To evaluate the interaction of the shielding material with photons, the Monte Carlo N‐Particle Extended and XCOM codes are used to determine the shielding parameters of the LHEA/PDMS composites, such as mass attenuation coefficient, linear attenuation coefficient, half‐value layer, tenth value layer, mean free path, and effective atomic number. The composite with 50‐vol% LHEA has the best radiation shielding properties, validated by medical X‐ray imaging experiments. The excellent shielding properties of the flexible lightweight composites are attributed to the higher mass attenuation coefficient of the LHEA inclusions than that of lead.

Constitutive modeling of magneto-viscoelastic polymers, demagnetization correction, and field-induced Poynting effect

Magneto-active polymers are polymer-based composites consisting of magnetizable micro-particles embedded in an elastomeric matrix material. The presence of magnetic particles provides strong tunability to the stiffness and damping properties of the polymeric composites under the magnetic field. We propose here a novel free energy-based phenomenological modeling for magneto-active polymers. Coupled mechanical and magnetization constitutive equations are derived by considering magneto-viscoelasticity in a finite deformation framework. The model calibration takes into account the demagnetization effect, which depends on the specimen size, shape, and its own magnetization. The model prediction is verified with the available experimental data. Finally, a coupled simple shear problem is solved to demonstrate the influence of magnetic field on the Poynting effect. Classical nonlinear soft elastic material shows positive Poynting effect, i.e., shearing planes try to expand. We found the possibilities of field-induced reverse or negative Poynting effect in shear for magneto-active polymers. Such a negative Poynting effect could potentially affect a very diverse range of applications from the performances of miniature sensors and actuators to controlled drug delivery.

Soft Robotics: Research, Challenges, and Prospects

The soft robot is a kind of continuum robot, which is mainly made of soft elastic material or malleable material. It can be continuously deformed in a limited space, and can obtain energy in large bending or high curvature distortion. It has obvious advantages such as high security of human-computer interaction, strong adaptability of unstructured environment, high driving efficiency, low maintenance cost, etc. It has wide application prospects in the fields of industrial production, defense military, medical rehabilitation, exploration, and so on. From the perspective of the bionic mechanism, this paper introduces the soft robots corresponding to insect crawling, snake crawling, fish swimming, elephant trunk, arm, etc. According to different driving modes, the soft robots can be classified into pneumatic-hydraulic driven, intelligent material driven, chemical reaction driven, and so on. The mechanical modeling, control strategy, material, and manufacturing methods of soft robot are summarized, and the application fields of soft robot are introduced. This paper analyzes the main challenges faced by the research on the key technologies of soft robots, summarizes and analyzes them, and puts forward the prospects for the future research of soft robots. The development trend of the future is to develop the soft robot with the characteristics of micro-scale, rigid-flexible coupling, variable stiffness, multi-functional, high integration, and intelligence of driving sensor control.

Responses of suction buckets subjected to sustained vertical uplift loads in sand

This study presents finite element analysis (FEA) results of suction buckets subjected to vertical sustained uplift loads, focusing on the suction pressure and the displacement responses. The accumulative seepage of water and the heave of the soil in the bucket are the key components of the displacement. The accumulative seepage of water is modelled using a layer of soft elastic material (water elements) beneath the bucket lid. The model is first used to investigate the suction pressure and the displacement responses under drained, partially drained, and undrained conditions. The components of the displacement are subsequently explained under different drained conditions. A critical uplift force is then defined when heave of the soil occurs. The influences of the key parameters on the displacement rates are analyzed. The fitting equations of the displacement rates with and without heave of the soil are presented, and the results calculated by equations are compared with those from available centrifuge tests and previous FEA.

Influence of interface phenomena on the features of interaction between the probe of atomic force microscope and soft material

A new model of the interaction of AFM sharp probe with a soft incompressible elastic material is proposed. The model takes into account the finite deformations of the material. The novelty is the consideration of bending and increasing of the material-air interface during the process of indentation. The work performed by the probe is spent both on the elastic deformation of the sample and on changing the geometry of the material-air interface. The paper proposes an explanation of possibility to simulate the phase boundary by a thin elastic layer under the condition of its large shrinkage. The obtained approximation dependences allow quick computer calculations. The presented arguments justify the possibility of neglecting the probe jump to the sample surface. It is established that the Deryagin-Muller-Toporov model is a special case of the proposed model.

Heavily loaded line EHL contacts with thin adsorbed soft layers

Studies of thin soft polymeric or metal layers adsorbed on the surfaces of lubricated solids showed lower friction coefficients and energy losses. The degree to which this reduction happens depends on the coating material nature, its rheology, and coating thicknesses, as well as other factors. To an extent, the application of such soft coatings is in its infancy and it is still not clear which parameters affect the performance of lubricated joints, and how. This paper attempts to model such coated lubricated contacts and to understand how soft coatings affect the joint performance. The paper presents a model of heavily loaded elastohydrodynamically lubricated (EHL) contacts of solids made of elastic homogeneous materials, the surfaces of which are covered by thin coating layers made of soft elastic material. The model incorporates not only normal but also tangential contact stresses and displacements. First, the effect of tangential contact stresses and displacements on the problem parameters is determined, and then the EHL problem is formulated and analyzed. It is necessary to account for variations in the solid surface linear velocities caused by tangential contact stresses. The deformation and displacement processes in thin coating layers are asymptotically modeled by certain boundary conditions. This is done using the Fourier transform with respect to the coordinate along the contact and making the necessary simplifications of the equations. The formulated EHL problem incorporates the normal and tangential contact surface displacements caused by normal and tangential contact stresses. The difference between the classic EHL problems and the problem at hand is due to variations in the linear surface velocities compared with the nominal ones. This causes significant changes in the contact friction parameters. The solution of the EHL problem is obtained numerically. A parametric analysis of the EHL problem solution is performed.

Polymer gel with a flexible and highly ordered three-dimensional network synthesized via bond percolation.

Gels are a soft elastic material consisting of a three-dimensional polymer network with nanometer-sized pores and are used in a variety of applications. However, gel networks typically have a substantial level of defects because the network formation reaction proceeds stochastically. In this study, we present a general scheme to fabricate gels with extremely low levels of defects by applying geometric constraints into pregel solution based on the "bond percolation" concept. In the formed gel, stationary laser speckles, which are an indicator of spatial defects, were not observed at all. In addition, we found that the concentration fluctuations of the polymer chains were ergodic across the whole gel network. In such a homogeneous gel, both the spatial and temporal correlations of polymer chains are the same before and after gelation.

Multimaterial 3D Printing for Microrobotic Mechanisms.

Multimaterial mechanisms are seen throughout natural organisms across all length scales. The different materials in their bodies, from rigid, structural materials to soft, elastic materials, enable mobility in complex environments. As robots leave the lab and begin to move in real environments, including a range of materials in 3D robotics mechanisms can help robots handle uncertainty and lessen control requirements. For the smallest robots, soft materials combined with rigid materials can facilitate large motions in compact spaces due to the increased compliance. However, integrating various material components in 3D at the microscale is a challenge. We present an approach for 3D microscale multimaterial fabrication using two-photon polymerization. Two materials with three orders of magnitude difference in Young's moduli are printed in consecutive cycles. Integrating a soft elastic material that is capable of more than 200% strain along with a rigid material has enabled the formation of hybrid elements, strongly adhered together, with layer accuracy below 3-μm resolution. We demonstrate a multilink multimaterial mechanism showing large deformation, and a 3D-printed 2-mm wingspan flapping wing mechanism, showing rapid prototyping of complex designs. This fabrication strategy can be extended to other materials, thus enhancing the functionality and complexity of small-scale robots.

Preparation of high-damping soft elastomer based on Eucommia ulmoides gum

This paper focus on the nature of a high-damping soft elastic material based on Eucommia ulmoides gum (EUG) obtained by epoxidation of EUG first and then in situ reaction between epoxy group and sodium bisulfite. The influence of degree of modification (M mol%) and degree of sulfonation (S mol%) of the product sulfonated E. ulmoides gum (SEUG) on the melting–crystallization behavior, tensile properties and dynamic mechanical properties is analyzed mainly. The results show that M mol% is the key factor in controlling the aggregation structure and static or dynamic mechanical behavior of SEUG, while the introduced sodium bisulfite groups show strengthening and toughening effect to some extent. Besides, the SEUG with high M mol% shows dramatically high tanδ value. With M mol% increasing, the tensile strength and Shore A hardness of SEUG decrease sequentially, while the elongation at break increases visibly. SEUGs with M mol% above 20.3 display soft and elastic stress–strain behavior. At similar M mol% level, SEUG with higher S mol% shows higher tensile strength and lower elongation at break than the one with lower S mol% value. These are attributed to the transformation of the aggregate structure and the introduction of ion interaction. The maximum tanδ value of SEUG reaches up to 2.19. The removal of the restriction effect of crystal region on the molecular motion of amorphous and the increased intermolecular interaction are thought to be main causes.

Mixed-mode crack propagation during needle penetration for surgical interventions

An accurate description of the penetration mechanics of flexible needles into target soft tissues is a complex task, including friction at the needle-tissue interface, large strains, non-predetermined penetration trajectories, fracture under mixed-mode loading and so on. In the present work, a finite element algorithm is employed to simulate the two-dimensional deep penetration of a flexible needle in a soft elastic material. The fracture process of the target material during penetration is described by means of a cohesive zone model, with a suitable mixed-mode criterion for determining the propagation direction of the crack. To illustrate the potential of the numerical algorithm, we have performed some simulations of the insertion of a flexible needle with an asymmetric tip, and the results are presented in terms of force-penetration curves as well as of the obtained penetration paths in the target tissue.

Effect of the Strength of Stickers on Rheology and Adhesion of Supramolecular Center-Functionalized Polyisobutenes.

In order to systematically investigate the effect of the strength of the supramolecular interactions on the debonding properties of associative polymers, a series of model systems have been characterized by probe-tack tests. These model materials, composed of linear and low dispersity poly(isobutylene) chains ( Mn ≈ 3 kg/mol) center-functionalized by a single bis-urea sticker, are able to self-assemble by four hydrogen bonds. Three types of stickers are used in the present study: a bis-urea with a methylene diphenyl (MDI) spacer, a bis-urea with a tolyl (TOL) spacer, and a bis-urea with a xylyl (XYL) spacer. In order to investigate the influence of stickers in depth, both the nanostructure of the materials and the linear rheology were investigated by small-angle X-ray scattering (SAXS) and oscillatory shear, respectively. For two types of stickers (TOL and XYL), the association of polymers via hydrogen bonds induces the formation of bundles of rodlike aggregates at room temperature and the behavior of a soft elastic material was observed. For bis-urea MDI, no structure is detected by SAXS and a Newtonian behavior is observed at room temperature. In probe-tack experiments, all these materials show a cohesive mode of failure, a signature of flowing materials as previously observed for tri-urea center-functionalized poly(butylacrylate) (PnBA3U). However, XYL center-functionalized polyisobutene shows much higher debonding energies than PnBA3U, revealing the importance of the strength of noncovalent bonds in the scission/recombination dynamics. On the basis of the analysis of the debonding images, this effect is discussed via the mechanical behavior at large deformation.

Soft elastic superhydrophobic cotton: A new material for contact time reduction in droplet bouncing

Reducing the contact time while water droplets impact on solid surface has become a vital object concerned by many researchers in recent years. However, previous methods of preparing superhydrophobic surfaces for shortening the contact time, with low efficiency and high expense, are not suitable for large-area fabrication and some obtained surfaces cannot work unless droplets just impact on the specific textures which limits their application in the field of anti-icing from freezing rain. Moreover, the contact time reduction has been mostly observed on metals, but rarely on nonmetals. Here, a facile method of fabricating superhydrophobic cotton was first conducted to largely reduce the contact time between droplet and substrate surface, which obviously eliminated the previous weakness. The treated cotton showed an excellent self-cleaning property and water droplet could also easily roll off the surface. The subsequent impact experiments show that the contact time was shortened by ~ 36% compared with that on the regular hard superhydrophobic surface. Moreover, the influence of the impact velocity and droplet radius on the overall contact time or spreading time and recoiling time had been also observed. And the elasticity of soft elastic superhydrophobic material plays a significant role in making the droplet early bounce off the surface causing a large contact time reduction, which leads to a new way to understand the dynamics of bouncing droplets.

Extreme Toughening of Soft Materials with Liquid Metal.

Soft and tough materials are critical for engineering applications in medical devices, stretchable and wearable electronics, and soft robotics. Toughness in synthetic materials is mostly accomplished by increasing energy dissipation near the crack tip with various energy dissipation techniques. However, bio-materials exhibit extreme toughness by combining multi-scale energy dissipation with the ability to deflect and blunt an advancing crack tip. Here, we demonstrate a synthetic materials architecture that also exhibits multi-modal toughening, whereby embedding a suspension of micron sized and highly deformable liquid metal (LM) droplets inside a soft elastomer, the fracture energy dramatically increases by up to 50x (from 250 ± 50 J m-2 to 11,900 ± 2600 J m-2 ) over an unfilled polymer. For some LM-embedded elastomer (LMEE) compositions, the toughness is measured to be 33,500 ± 4300 J m-2 , which far exceeds the highest value previously reported for a soft elastic material. This extreme toughening is achieved by (i) increasing energy dissipation, (ii) adaptive crack movement, and (iii) effective elimination of the crack tip. Such properties arise from the deformability of the LM inclusions during loading, providing a new mechanism to not only prevent crack initiation, but also resist the propagation of existing tears for ultra tough, soft materials.