Fiber-reinforced Elastomers Research Articles

Pneumatic Multi-Pocket Elastomer Actuators for Metacarpophalangeal Joint Flexion and Abduction-Adduction

During recent years, interest has been rising towards developing fluidic fiber-reinforced elastomer actuators for wearable soft robotics used in hand rehabilitation and power-assist. However, they do not enable finger abduction-adduction, which plays an important role in activities of daily living, when grasping larger objects. Furthermore, the developed gloves often do not have separate control of joints, which is important for doing various common rehabilitation motions. The main obstacle for the development of a fully-assisting glove is moving a joint with multiple degrees of freedom. If the functions are built into the same structure, they are naturally coupled and affect each other, which makes them more difficult to design and complex to control than a simple flexion-extension actuator. In this study, we explored the key design elements and fabrication of pneumatic multi-pocket elastomer actuators for a soft rehabilitation glove. The goal was to gain more control over the metacarpophalangeal joint’s response by increasing the degree of actuation. Three main functional designs were tested for achieving both flexion and abduction-adduction. Five prototypes, with four different actuator geometries and four different reinforcement types, were designed and fabricated. They were evaluated by recording their free motion with motion capture and measuring their torque output using a dummy finger. Results showed the strengths and weaknesses of each design in separating the control of the two functions. We discuss the different improvements that are needed in order to make each design plausible for developing an actuator that meets the requirements for full assist of the hand’s motions. In conclusion, we show that it is possible to produce multi-pocket actuators for assisting MCP joint motion in both flexion and abduction-adduction, although coupling between the separate functions is still problematic and should be considered further.

Serially Actuated Locomotion for Soft Robots in Tube-Like Environments

Soft robots are able to complete tasks that traditional robots cannot, thus providing new opportunities for robots to navigate confined spaces. These tasks include pipe inspection and endoluminal surgical applications. The research objective of this letter is to present a design methodology for soft robots capable of traversing a cannula or pipe using only passive elements, a single pressure source, and while avoiding blockage, that is, avoiding full occlusion of the cannula to still allow fluid flow. The robot consists of three segments, each with actuators and valves, and is driven by hydraulics (water). The actuators were built using the FREE method and optimized for the specific task of traversing a cannula with a diameter of 19 mm. An experimental approach was used to create a pressure-volume relationship from the kinematic fiber-reinforced elastomer enclosure (FREE) model. The passive valves were built as flow restrictors and modeled with the nonlinear orifice equation. A simulation and grid search was performed over a range of valve coefficients. An objective function was then maximized to produce orifice coefficients that augmented extension of the robot per input pressure cycle. The physical robot was then constructed and tested in a cannula. This resulted in a robot that was serially actuated, never fully occluded the cannula, and was able to successfully locomote a cannula at a rate of 27 ± 4 mm per two-second cycle. This experimental result was close to the simulated result of 28 mm per cycle.

Development and testing of controlled adaptive fiber-reinforced elastomer composites

The integration of shape memory alloys (SMAs) into textile-reinforced composites produces a class of smart materials whose shape can be actively influenced. In this paper, Ni-Ti SMA wires are inserted during the weaving of a glass fiber reinforcement textile. This “active” reinforcement is then combined with an elastomeric matrix to produce a highly flexible composite sheet, which maintains high rigidity in the longitudinal direction. By activating the SMAs, high deflection ratios of up to 35% (relative to the component's length) are achieved. To adjust the composite's deflection to defined values, a closed-loop control is set up to adjust the current flow through the SMA wires. A control algorithm is designed and evaluated for several test cases. The high deformability and the controllable behavior show the high potential of these materials for applications such as aerodynamic flow control, automation and architecture.

Suppression of electromechanical instability in fiber-reinforced dielectric elastomers

The electromechanical instability of dielectric elastomers has been a major challenge for the application of this class of active materials. In this work, we demonstrate that dielectric elastomers filled with soft fiber can suppress the electromechanical instability and achieve large deformation. Specifically, we developed a constitutive model to describe the dielectric and mechanical behaviors of fiber-reinforced elastomers. The model was applied to study the influence of stiffness, nonlinearity properties and the distribution of fiber on the instability of dielectric membrane under an electric field. The results show that there exists an optimal fiber distribution condition to achieve the maximum deformation before failure.

On the isotropy of randomly generated representative volume elements for fiber-reinforced elastomers

The isotropy of different numerical simulations of fiber reinforced elastomers has been explored by explicitly applying stretch in different loading directions, in models with representative volume elements (RVEs) spanning a wide range of fiber volume fractions and system sizes. The results show that the homogenized response is not the same for all loading directions, and that the corresponding dependance takes the form of a sine. The anisotropy decreases with the RVE size, and so it can be used to asses if the scales can be separated in a given model. Considering the average response over all loading directions greatly reduces the variation between different RVEs, which can be used to improve the accuracy of the simulations in a way that is significantly more efficient than increasing the size of the RVE. The simulations have also shown a good correlation between the isotropy of each representative volume element at low and high values of the applied stretch. The result of linear simulations can therefore be used as an efficient indication of the anisotropy expected at high deformations.

Comparative study of fiber-reinforced elastomer composites subjected to accelerated aging in water

This work focuses on the study of the hydrothermal aging of fiber-reinforced rubber composites. Physical and mechanical properties of different rubber composites as well as their influence with aging conditions were studied. Four rubber matrices were used (ethylene propylene diene monomer (EPDM), silicone, EPDM/silicone, and neoprene) to make composite samples reinforced with glass fibers. Accelerated aging in water was performed using a hot tub under controlled temperature for few months. The decrement in mechanical properties was linked to water infiltration and degradation of the fiber–matrix interface. After 6 months of accelerated aging, some samples showed an important deviation from original properties, while others retained nearly homogeneous properties with time.

Rolling Resistance of a Nonpneumatic Tire Having a Porous Elastomer Composite Shear Band

ABSTRACT The shear band is the critical component of a nonpneumatic tire (NPT) when determining the rolling resistance resulting from the elastomer's shear friction. In an effort to reduce the rolling resistance of an NPT, a shear band made of a porous, fiber-reinforced elastomer is explored. The porous shear band is designed to have the same effective shear modulus as the shear modulus of a continuous shear band. The originality of the study in this article is in the design of a flexible, porous solid for fuel efficiency of a tire structure by including a low viscoelastic energy loss material—a carbon fiber that partially replaces the volume of high viscoelastic energy loss material—polyurethane. To make the NPT structure remain flexible, porous volumes were included. Finite element (FE)–based numerical experiments with ABAQUS were conducted to quantify the reduced energy loss of an NPT using hyperelastic and viscoelastic material models. Load carrying capacity of the NPT with the designed porous shear band is also discussed.

A study on fiber-reinforced elastomer with a biphasic loading behavior

AbstractA specific fiber-reinforced elastomer (FRE) composite was formed by inserting curved fibers into a rubber matrix. This material combined the hyperelastic behavior of a soft elastomer matrix with the high stiffness character of a fibrous reinforcement. A biphasic loading property could be realized physically. Based on the guided concept, experiments were performed on the specimens of pure and fiber-reinforced silicone rubber, respectively. Test results showed that this FRE composite first experienced an elastomer-dominant phase with a large recoverable deformation and then a fiber-dominant phase with rapid increasing loading. This biphasic behavior of the developed FRE composite was also identified by the constitutive equations based on the nonlinear solid mechanics. It was further discovered that the division of the two phases could be varied with the change of curved fiber length.

Mechanical Behavior of Continuous Fiber-Reinforced Elastomeric Materials at Finite Strain

A constitutive model is developed to characterize mechanical behavior of unidirectional continuous fiber-reinforced elastomeric materials at finite strains. Assuming transversely isotropic behavior, strain energy of elastomeric composite is expressed as polyconvex functions of principal invariants defined by tensors describing deformation field and fiber directions. Parameters of polyconvex functions are evaluated based on homogenization of incompressible elastomeric matrix reinforced with unidirectional inextensible continuous fibers. Heterogeneous microstructure is identified by a representative volume element subjected to equivalent macroscopic deformations. Micromechanical results show that the strain energy of unidirectional fiber-reinforced elastomers can accurately be described by additive decomposition into isotropic and anisotropic models.

Some Remarks on the Effect of Interphases on the Mechanical Response and Stability of Fiber-Reinforced Elastomers

In filled elastomers, the mechanical behavior of the material surrounding the fillers -termed interphasial material-can be significantly different (softer or stiffer) from the bulk behavior of the elastomeric matrix. In this paper, motivated by recent experiments, we study the effect that such interphases can have on the mechanical response and stability of fiber-reinforced elastomers at large deformations. We work out in particular analytical solutions for the overall response and onset of microscopic and macroscopic instabilities in axially stretched 2D fiber-reinforced nonlinear elastic solids. These solutions generalize the classical results of Rosen (1965, “Mechanics of Composite Strengthening,” Fiber Composite Materials, American Society for Metals, Materials Park, OH, pp. 37–75), and Triantafyllidis and Maker (1985, “On the Comparison between Microscopic and Macroscopic Instability Mechanisms in a Class of Fiber-Reinforced Composites,” J. Appl. Mech., 52, pp. 794–800), for materials without interphases. It is found that while the presence of interphases does not significantly affect the overall axial response of fiber-reinforced materials, it can have a drastic effect on their stability.

On Microstructure Evolution in Fiber-Reinforced Elastomers and Implications for Their Mechanical Response and Stability

Lopez-Pamies and Idiart (2010, “Fiber-Reinforced Hyperelastic Solids: A Realizable Homogenization Constitutive Theory,” J. Eng. Math., 68(1), pp. 57–83) have recently put forward a homogenization theory with the capability to generate exact results not only for the macroscopic response and stability but also for the evolution of the microstructure in fiber-reinforced hyperelastic solids subjected to finite deformations. In this paper, we make use of this new theory to construct exact, closed-form solutions for the change in size, shape, and orientation undergone by the underlying fibers in a model class of fiber-reinforced hyperelastic solids along arbitrary 3D loading conditions. Making use of these results, we then establish connections between the evolution of the microstructure and the overall stress-strain relation and macroscopic stability in fiber-reinforced elastomers. In particular, we show that the rotation of the fibers may lead to the softening of the overall stiffness of fiber-reinforced elastomers under certain loading conditions. Furthermore, we show that this geometric mechanism is intimately related to the development of long-wavelength instabilities. These findings are discussed in light of comparisons with recent results for related material systems.

Microscopic and macroscopic instabilities in finitely strained fiber-reinforced elastomers

The present work is a detailed study of the connections between microstructural instabilities and their macroscopic manifestations — as captured through the effective properties — in finitely strained fiber-reinforced elastomers, subjected to finite, plane-strain deformations normal to the fiber direction. The work, which is a complement to a previous and analogous investigation by the same authors on porous elastomers, ( Michel et al., 2007), uses the linear comparison, second-order homogenization (S.O.H.) technique, initially developed for random media, to study the onset of failure in periodic fiber-reinforced elastomers and to compare the results to more accurate finite element method (F.E.M.) calculations. The influence of different fiber distributions (random and periodic), initial fiber volume fraction, matrix constitutive law and fiber cross-section on the microscopic buckling (for periodic microgeometries) and macroscopic loss of ellipticity (for all microgeometries) is investigated in detail. In addition, constraints to the principal solution due to fiber/matrix interface decohesion, matrix cavitation and fiber contact are also addressed. It is found that both microscopic and macroscopic instabilities can occur for periodic microstructures, due to a symmetry breaking in the periodic arrangement of the fibers. On the other hand, no instabilities are found for the case of random microstructures with circular section fibers, while only macroscopic instabilities are found for the case of elliptical section fibers, due to a symmetry breaking in their orientation.

Finite Deformations of Tubular Dielectric Elastomer Sensors

This article describes a numerical model validated with experimental results for a large stretch tubular sensor. The sensor is a dielectric elastomer (DE) membrane with electrical properties that can be accurately correlated with mechanical strain, for strains well over 50%. The DE sensor is a passive capacitive sensor. To illustrate the concept, the sensor is attached to the inner surface of a fiber-reinforced elastomer actuator, which serves as the host substrate. Fiber-reinforced elastomers configured for pneumatic operation are employed as actuators in robotic, prosthetic, and morphing applications. An electromechanical model for the two-layer composite consisting of the fiber-reinforced elastomer and the sensor is derived. For several illustrative loading profiles, the model yields a strain output for an input capacitance value. Using identical loading cases, an experimental setup was designed to measure sensor output for two different sensor materials: silicone and polyacrylate. The sensitivity of the DE sensor was also evaluated for varying geometrical parameters and is mainly dependent on the initial thickness. Comparison of experimental data and numerical results is very good with an overall error of 3—6%. This work shows that the model is robust in the large strain range and furthermore predicts non-linear strain behavior.

Effect of interface fracture on the tensile deformation of fiber-reinforced elastomers

The influence of interface properties (strength and toughness) on the tensile behavior of fiber-reinforced elastomers deformed perpendicularly to the fibers was studied using computational micromechanics. Numerical simulations were performed by means of the finite element analysis of a representative volume element of the composite microstructure. The effect of finite deformations and of interface fracture was included in the simulations, the latter through a bidimensional and quadratic interface element inserted at the fiber/matrix interfaces. A parametrical study was carried out to assess the effect of interface strength and toughness on the tensile strength and damage micromechanisms. It was found that the onset of damage and tensile strength were controlled by interface strength while the evolution of damage depended on interface toughness.

Onset of macroscopic instabilities in fiber-reinforced elastomers at finite strain

In this paper, we investigate theoretically the possible development of instabilities in fiber-reinforced elastomers (and other soft materials) when they are subjected to finite-strain loading conditions. We focus on the physically relevant class of “macroscopic” instabilities, i.e., instabilities with wavelengths that are much larger than the characteristic size of the underlying microstructure. To this end, we make use of recently developed homogenization estimates, together with a fundamental result of Geymonat, Müller and Triantafyllidis linking the development of these instabilities to the loss of strong ellipticity of the homogenized constitutive relations. For the important class of material systems with very stiff fibers and random microstructures, we derive a closed-form formula for the critical macroscopic deformation at which instabilities may develop under general loading conditions, and we show that this critical deformation is quite sensitive to the loading orientation relative to the fiber direction. The result is also confronted with classical estimates (including those of Rosen) for laminates, which have commonly been used as two-dimensional (2-D) approximations for actual fiber-reinforced composites. We find that while predictions based on laminate models are qualitatively correct for certain loadings, they can be significantly off for other more general 3-D loadings. Finally, we provide a parametric analysis of the effects of the matrix and fiber properties and of the fiber volume fraction on the onset of instabilities for various loading conditions.

Finite deformation of incompressible fiber-reinforced elastomers: A computational micromechanics approach

The in-plane finite deformation of incompressible fiber-reinforced elastomers was studied using computational micromechanics. Composite microstructure was made up of a random and homogeneous dispersion of aligned rigid fibers within a hyperelastic matrix. Different matrices (Neo-Hookean and Gent), fibers (monodisperse or polydisperse, circular or elliptical section) and reinforcement volume fractions (10–40%) were analyzed through the finite element simulation of a representative volume element of the microstructure. A successive remeshing strategy was employed when necessary to reach the large deformation regime in which the evolution of the microstructure influences the effective properties. The simulations provided for the first time “quasi-exact” results of the in-plane finite deformation for this class of composites, which were used to assess the accuracy of the available homogenization estimates for incompressible hyperelastic composites.

A general hyperelastic model for incompressible fiber-reinforced elastomers

This work presents a new constitutive model for the effective response of fiber-reinforced elastomers at finite strains. The matrix and fiber phases are assumed to be incompressible, isotropic, hyperelastic solids. Furthermore, the fibers are taken to be perfectly aligned and distributed randomly and isotropically in the transverse plane, leading to overall transversely isotropic behavior for the composite. The model is derived by means of the “second-order” homogenization theory, which makes use of suitably designed variational principles utilizing the idea of a “linear comparison composite.” Compared to other constitutive models that have been proposed thus far for this class of materials, the present model has the distinguishing feature that it allows consideration of behaviors for the constituent phases that are more general than Neo-Hookean, while still being able to account directly for the shape, orientation, and distribution of the fibers. In addition, the proposed model has the merit that it recovers a known exact solution for the special case of incompressible Neo-Hookean phases, as well as some other known exact solutions for more general constituents under special loading conditions.

Homogenization estimates for fiber-reinforced elastomers with periodic microstructures

This work presents a homogenization-based constitutive model for the mechanical behavior of elastomers reinforced with aligned cylindrical fibers subjected to finite deformations. The proposed model is derived by making use of the second-order homogenization method [Lopez-Pamies, O., Ponte Castañeda, P., 2006a. On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: I—theory. J. Mech. Phys. Solids 54, 807–830], which is based on suitably designed variational principles utilizing the idea of a “linear comparison composite.” Specific results are generated for the case when the matrix and fiber materials are characterized by generalized Neo-Hookean solids, and the distribution of fibers is periodic. In particular, model predictions are provided and analyzed for fiber-reinforced elastomers with Gent phases and square and hexagonal fiber distributions, subjected to a wide variety of three-dimensional loading conditions. It is found that for compressive loadings in the fiber direction, the derived constitutive model may lose strong ellipticity, indicating the possible development of macroscopic instabilities that may lead to kink band formation. The onset of shear band-type instabilities is also detected for certain in-plane modes of deformation. Furthermore, the subtle influence of the distribution, volume fraction, and stiffness of the fibers on the effective behavior and onset of macroscopic instabilities in these materials is investigated thoroughly.

On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: II—Application to cylindrical fibers

In Part I of this paper, we presented a general homogenization framework for determining the overall behavior, the evolution of the underlying microstructure, and the possible onset of macroscopic instabilities in fiber-reinforced elastomers subjected to finite deformations. In this work, we make use of this framework to generate specific results for general plane-strain loading of elastomers reinforced with aligned, cylindrical fibers. For the special case of rigid fibers and incompressible behavior for the matrix phase, closed-form, analytical results are obtained. The results suggest that the evolution of the microstructure has a dramatic effect on the effective response of the composite. Furthermore, in spite of the fact that both the matrix and the fibers are assumed to be strongly elliptic, the homogenized behavior is found to lose strong ellipticity at sufficiently large deformations, corresponding to the possible development of macroscopic instabilities [ Geymonat, G., Müller, S., Triantafyllidis, N., 1993. Homogenization of nonlinearly elastic materials, macroscopic bifurcation and macroscopic loss of rank-one convexity. Arch. Rat. Mech. Anal. 122, 231–290]. The connection between the evolution of the microstructure and these macroscopic instabilities is put into evidence. In particular, when the reinforced elastomers are loaded in compression along the long, in-plane axis of the fibers, a certain type of “flopping” instability is detected, corresponding to the composite becoming infinitesimally soft to rotation of the fibers.

Second-Order Homogenization Estimates Incorporating Field Fluctuations in Finite Elasticity

This paper presents the applicaition of a recently proposed "second-order"homogenization method (Ponte Castañeda 2002; J. Mech. Phys. Solids 50, 737) to the estimation of the effective behavior of hypetrelastic composites subjected to finite deformations. The key idea is to introduce an optimally chosen "linear comparison composite" which can then be used to convert available homogenization estimates bor linear composites directly into new estimates for the nonlinear hyperelastic composites. More precisely, the method makes use of "generalized" secant moduli that are intermediate between the standard "secant" and "tangent" moduli of the nonlinear phases, and that depend not only on the averages, or first moments of the fields in the phases, but also on the second moments of the field fluctuations, or phase covariance tensors. The use of the method is illustrated in the context of carbon-black-filled, and fiber-reinforced elastomers, and estimates analogous to the well-known Hashin=-Shtrikman and self-consistent estimates for linear-elastic composites are generated. The new estimates are compared with corresponding estimates using an earlier version of the method (Ponte Castañeda and Tiberio 2000; J Mech. Phys. Solids 48, 1389) neglecting the use of fluctuations, and the new results are found to be superior. In particular, the new estimates, unlike the earlier ones, are found to satisfy a rigorous bound, and to give more realistic predictions in the important limit of incompressible behavior.