Rubber-like Materials Research Articles

A model for rubber-like materials with three parameters obtained from a tensile test

Based on our recent findings on the chains orientational distribution in deformed rubber-like materials, we present a novel, accurate and simple non-affine model for isotropic, incompressible polymers. The model has only three material parameters that are easily calibrated from the characteristic behaviour of a tensile test: the initial slope, the slope of the mid-range, and the locking stretch. Once calibrated, the proposal reproduces accurately the behaviour of the material under the general deformation states for moderately large stretches measured by Kawabata (rubber) and Kawamura (silicone), and at least for three deformation states approaching the locking behaviour (Treloar’s tests on rubber).

STUDY OF SELF-DRYING EFFECT OF PACKER INSTALLATIONS IN EXPLOITATION WELLS

The article considers the effect of self-compacting of packer structures in production wells. In order to reduce the high costs of oil and gas companies, the issues of self-compacting packers in producing production wells are being studied. The design used here is centered in the open hole, and the rubber elements of the packers prevent leakage in the event of a pressure drop. In general, the sealing assembly consists of a sealing surface, sealing elements, an auxiliary protective structure and a power mechanism. Under downhole conditions, the operating pipeline is not part of the seal assembly and varies from well to well. For this reason, the principle of operation of the packer's sealing unit cannot be justified from the point of view of the roughness of the sealing surface and the specified limits on the nature of the gas-liquid medium to be separated. This indicates that the operating conditions of the well packer are significantly different from the operating conditions of other sealing structures. Despite the effectiveness of the use of packers, the low manufacturability of the sealing elements does not allow them to be widely used. Most often, this manifests itself in special difficult conditions, at the same time, in operating conditions, when the sealing material is broken, the rubber material flows onto the metal part of the packer, the rubber sticks to the wall of the production string, in some cases, tubing is captured. The performance of packer equipment is determined by the performance of its sealing elements. Since the sealing elements are mainly rubber-like construction materials, their design is unreliable in mountain conditions. The packer is released into the well by tubing. When the required depth is reached, water is pumped into the packer barrel (through the NCU). In this case, the valve is connected to the fluid pressure in the packer hydraulic cylinder, and the piston moves, compresses the rubber cuffs through the support washer and delivers them to the inner surface of the working belt. He pushes the cone under the plates and thus shrinks the packer. To drive the lower layer into the packer, the pressure is increased by an additional 3.5 MPa (23 ... 25 MPa from the landing pressure) and the mortise screws are cut off, the ball and seat are released from the packer. The packer channel opens. At this time, under the pressure of the well product (oil or gas), the round plates in the anchor are pressed against the belt, which prevents the packer from slipping upwards. To release the packer from the well, just pull it up. The packer consists of the mechanisms of the upper and lower devices, the clamping collar assembly, the saddle valve, the hydraulic cylinder, the circulation valve. Relevance. The study of the shaping units of packer structures and the choice of criteria that provide the shaping effect is a topical issue. Keywords: conditioning elements, wellbore, packer assembly, horizontal well, open hole staged fracturing.

Development and Validation of a Nonlinear Model to Describe the Tension–Compression Behavior of Rubber-Like Base Isolators

The fractional-order derivative Zener (FDZ) model can reasonably predict the frequency dependence behavior of rubber-like materials. However, its capability to capture nonlinear behaviors is limited. In our previous work, we built a horizontal shear model of a multidimensional rubber-like base isolation bearing, modifying the FDZ model to compensate for its inability to reproduce the nonlinear behaviors of amplitude dependence and slow stabilization. In this paper, the tension-compression behavior of the same bearing in the vertical direction is studied, where strain-stiffening nonlinear behavior is exhibited. A different strategy is used to establishing the modified tension-compression FDZ (CFDZ) model, which is shown to have good agreement with experimental results. State-space representation of the CFDZ model is presented and included in modelling a train-bridge-bearing system for dynamic analysis. Simulation results demonstrate that the proposed bearing achieves a high base isolation performance in the vertical direction.

Large Isotropic Elastic Deformations: On a Comprehensive Model to Correlate the Theory and Experiments for Incompressible Rubber-Like Materials

A comprehensive model, i.e., a model that: (i) suitably captures the mechanical behaviour of various types of rubber-like materials; (ii) describes the constitutive behaviour of a subject rubber-like specimen under different deformation modes via a single set of model parameter values, and (iii) is parent to many of the existing models of distinct types, is presented in this paper for application to the finite deformation of incompressible isotropic rubber-like materials. The model breaks away from Rivlin’s principal invariants I_{i} and Valanis-Landel’s separable function of principal stretches lambda _{i} representations, and instead adopts a general non-separable functional form W( lambda _{1}, lambda _{2}, lambda _{3} ), subject to the incompressibility constraint. By way of example, the application of the model to extant datasets from four types of rubber-like materials that exhibit discernible mechanical behaviours, namely natural unfilled and filled rubbers, hydrogels and (extremely) soft tissue specimens, will be considered. The favourable correlation between the model predictions and the considered experimental datasets, obtained via simultaneous fitting of the model to the data of various deformations, will be demonstrated. It will be shown that most of the landmark models in the literature including the W( I_{1}, I_{2} ) form Mooney-Rivlin, the Gent-like limiting chain extensibility, the nonaffine tube and the separable principal stretches-based type Ogden models are all a special sub-set of the presented parent model, and are all recovered from this model. An important implication of the non-separable functional form of the model will be conferred, through a specific dataset, where the predictions of the separable functions prove inherently inadequate. The consequences of these improvements for a more accurate modelling of the finite deformation of incompressible isotropic rubber-like materials will also be discussed.

АНАЛИЗ ПРИМЕНЕНИЯ ПРОГРАММНОГО ОБЕСПЕЧЕНИЯ ДЛЯ РАСЧЕТА ГИПЕРУПРУГИХ МАТЕРИАЛОВ

The article discusses the use of software for the nonlinear analysis of hyperelastic material used in the soft capture mechanisms for robots working with agricultural products. Soft capture elements are made of rubber-like materials. Such materials have the ability to retain their elastic properties at high strain. The research reviewed various data resources, particularly, the reports on the development of soft grip elements for robots used to work with agricultural products. Internet resources were also studied to analyse the availability of data on the software for the nonlinear analysis of hyperelastic materials. The review has found that Abaqus, Ansys, and Comsol multiphysics software packages are used for the nonlinear analysis of hyperelastic elements. Abaqus is the most commonly used tool, although the programme training materials are not easily accessible. The Ansys software package ranks second with the highest data availability in the Internet. The review has found that the number of studies into Comsol multiphysics programme is the smallest though the availability of information on the tool in Internet sources ranks second.

Explicitly Modeling Stress Softening and Thermal Recovery for Rubber-like Materials

Rubber-like materials exhibit stress softening when subject to loading–unloading cycles, i.e., the Mullins effect. However, this phenomenon can be recovered after annealing the previously stretched sample under a stress-free state. The aim of this paper is to establish a constitutive model with thermodynamic consistency to account for the stress softening and thermal recovery. Towards this goal, (i) an explicit form of Helmholtz free energy can be found such that the restrictions from thermodynamic law can be satisfied; (ii) a compressible, multi-axial strain-energy function considering energy dissipation is proposed by introducing specific invariants; (iii) a unified shape function based on the symmetry property of the test data in a one-dimensional case with stress softening and thermal recovery is provided by introducing a weight variant; (iv) it is proven that the new potential can automatically reduce to the one-dimensional case, i.e., uniaxial tension, equal biaxial, or plane strain; (v) numerical results for model validation are exactly matched with classical experimental data.

Frequency- and temperature-dependent Payne effect and hysteresis loss of carbon black filled rubbers: Experimental study and model prediction

Many constitutive models have been proposed to model the Payne effect and to predict the hysteresis loss of the carbon black (CB)-filled rubber-like materials, but few works are related to clarifying which model is the more suitable one to model the Payne effect and to predict the energy dissipation. To this end, we present detailed comparisons of the classic quantitative models of the Payne effect proposed by Kraus, Huber-Vilgis and Maier-Göritz. The Payne effect is experimentally investigated under various frequency and temperature conditions, and the corresponding hysteresis loss loops are determined by DMA measurements. Classic quantitative models are used to describe the Payne effect and a viscoelastic model consisting of dynamic strain amplitude and loss modulus is used to calculate the energy dissipation, which can be used to verify the applicability of the classic quantitative models. The results show that the Maier-Göritz model is more suitable to describe the Payne effect, especially for the loss modulus. After comparison of the calculated energy dissipation with the experimental data, the Maier-Göritz model has the ability to predict the hysteresis loss.

Pneumatic soft phononic crystals with tunable band gap

Tuning the band gap by mechanically generating deformation of soft phononic crystals provides an effective means to manipulate the propagation of acoustic waves. In this paper, a pneumatic soft phononic crystal is computationally designed to realize tunable band gap. It consists of a line of soft inflatable silicone cylinders surrounded by air. In detail, there is no band gap in the soft phononic crystal when it is unpressurized. By applying the air pressure, the scatterer in the soft phononic crystal is deformed, then a new reversible band gap appears in the phononic crystal. By adjusting the air pressure, the opening and closing of the band gap can be controlled. In addition, the width of the band gap can be tuned by the application of air pressure. We obtained the mechanical parameters of the rubber-like material from the experimental data. On this basis, the variation of the band gap of phononic crystals with applied different air pressures to the soft scatterer is investigated numerically. The effect of scatterer geometry on the band gap evolution of phononic crystals is also parametrically studied. Compared with traditional mechanical deformation means, such as tension and compression, the pneumatic manipulation is low-cost, fast in response and easy to integrate. This work introduces a feasible design of tunable soft phononic crystals.

Reprogrammable flexible mechanical metamaterials

Mechanical metamaterials are artificial structures with structure-dependent properties. They often harness zero-energy deformation modes, e.g., a single shape change that limits their applications, resulting in the need for changeable mechanical responses. We address this limitation by using a flexible material, called light-responsive shape-memory polydimethylsiloxane (SM-PDMS), to introduce reprogrammability into flexible mechanical metamaterials. The SM-PDMS is a rubber-like functional material with shape-memory and photothermal effects. Specfically, we propose three different reprogrammable SM-PDMS metamaterials with different mechanical responses, namely, an auxetic SM-PDMS, a chiral SM-PDMS, and a buckling-induced SM-PDMS. Finally, a buckling-induced SM-PDMS was harnessed to make a soft actuator with a reprogrammable preferred locomotion direction. Despite focusing on reprogramming flexible metamaterials using the light-induced SM effect, our strategy can be easily extended to other structures and smart materials. More importantly, our strategy paves the way to change the mechanical responses for similar architectures. Furthermore, our designed flexible metamaterials have the potential for different applications, such as soft robots, actuation, adaptive safety, and sports equipment.

Constitutive modeling of particle reinforced rubber-like materials

The present study is focused on the constitutive modeling for the mechanical behavior of rubber reinforced with filler particles. A filler-dependent energy density function is proposed with all the continuum mechanics-based necessities of an effective hyperelastic material model. The proposed invariant-based energy function comprises a single set of material parameters for a material subjected to several modes of loading conditions. The model solution agrees well with existing experimental results. Later, the effect of varying concentrations of filler particles in the rubber matrix is also studied.

Hyperelasticity and the radial point interpolation method via the Ogden model

Rubber-like and biological materials could show a hyperelastic behaviour, often studied using the Finite Element Method (FEM), limitations still exist due to the large deformations that this type of material experiment. Conversely, meshless methods are suitable for large deformations. The Ogden hyperelastic model can also represent the Neo-Hookean and Mooney–Rivlin models with ease, making it versatile but its implementation into meshless methods is yet to be done.In this work, the Ogden model was implemented into the Radial Point Interpolation Method (RPIM), a robust and accurate meshless method, within its iterative process allowing for future simulation of multi-material domains. Then, the implementation was tested with small deformations cases. The implementation was validated using three examples and a different hyperelastic model was used for each example, Mooney–Rivlin, Neo-Hookean, and Ogden, whilst their material properties were taken from the literature.The results were compared to FEM solutions and the literature, a good agreement was achieved with differences below 2%, indicating a successful implementation. This is the first implementation of the Ogden model into the RPIM. The ability to model hyperelastic structures together with the inherent advantages of meshless methods provides a good alternative for the analysis of industrial and biological structures.

Constitutive modeling of rubber-like materials: an alternative material model

ABSTRACT This article proposes an alternative strain energy density function to describe the hyperelastic behavior of rubber-like materials under various deformations. This proposed strain energy function fulfilled all the necessary characteristics of a hyperelastic material model. This function consists of four material parameters and represents an invariant-based material model. Also, the material parameters are kept constant for the different modes of loading conditions. The model solution based on the proposed energy function is mathematically simple and well suited for all stretching ranges. The model solution is further tested with the existing experimental data and compared with the results of available model solutions. The findings of the model solution agree well with both experimental and theoretical results available in the literature.

A generalized Ogden model for the compressibility of rubber-like solids.

The aim of this paper is to further demonstrate the advantages and effectiveness of the constitutive formulation proposed by Huang (Huang 2014 J. Appl. Mech. 59, 902-908 (doi:10.1115/1.2894059)). In this formulation, any strain-energy function for an incompressible material can be easily generalized to include the effect of material compressibility, in which only a few material parameters and material functions to be fitted with the experimental data are required. To this end, the Ogden model for incompressible rubber-like solids is chosen as the starting point. By means of this formulation, the generalized Ogden strain-energy function, which takes into account material compressibility, can conveniently be constructed so long as its incompressible counterpart is given. The obvious advantage shown in this paper is that only a few material parameters and material functions are needed, i.e. in addition to the material parameters used in the original Ogden model for incompressible solids, only one material function depending on the volume ratio is involved to characterize the effect of compressibility. Both the material parameters in the original Ogden model and the material function suggested in this paper can be determined by fitting the experimental data for uniaxially tensile test and hydrostatic deformation test of rubbers, respectively. The present model considering compressibility is general since it can be applied to predict the stress-strain responses of rubber-like materials and porous rubbers in various loading conditions. With the present formulation, the applicable range of the celebrated Ogden model can be further broadened, which should be of practical importance for accurately describing the mechanical behaviour of rubber-like solids. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

Silica Masterbatches Produced with Liquid Phase Mixing; Part III. Quasi-Static Stress-Softening

The stress-softening effect of rubber-like materials is a phenomenon such that the stress required to attain a given elongation is less during the second cycle of deformation. In practice, stress-softening effects are used as a quantitative measure of strain energy loss. Both rubber reinforcement by fillers and the failure properties of vulcanizates, such as ultimate strength, tearing, cracking, abrasion, and fatigue, are closely related to the processes of energy dissipation during deformation. This paper reports the results of our research on the quasi-static stress-softening effect of vulcanizates of solution-polymerized styrene butadiene rubber (SSBR)/cis-polybutadiene rubber (BR)/silica masterbatches named Eco-Visco-Elastomer composite (EVEC) produced by a continuous liquid phase mixing, taking dry-mixed silica- and carbon black-filled vulcanizates as references. With this liquid phase mixing, the silanization efficiency of EVEC was greatly improved. Compared with the conventional silica filled vulcanizates, the stress softening effect of EVEC was significantly lower at low strain and rose more rapidly with increasing strain, which could be explained by the effects of filler agglomeration and polymer-filler interaction. The less energy dissipation at low strain is mainly due to fewer filler agglomerates, whereas at high strain, for EVEC, it is attributed to more rupture of polymer crosslinks and polymer chains in the matrix with increasing extension, due to higher polymer-filler interaction resulting in less slippage of polymer chains along the filler surfaces.

Polydimethylsiloxane-based stretchable conductive elastomer fiber by using oil bath-spinning for wearable devices

Flexible stretchable conductors are widely used in various wearable devices and flexible electronic components due to their unique engineering structure adaptability. Fiber has anisotropic stretchability due to its linear structure and it is used in the study of stretchable conductors. However, traditional fibers have low axial stretchability and poor adhesion to conductive particles, so they are not suitable for high-strain engineering structures. Here, a simple and fast preparation method with oil bath thermal curing and a blade coating method is proposed to obtain polydimethylsiloxane-based stretchable elastomer fibers. The fibers have excellent flexibility, stretchability (greater than 100%), elasticity (recovery rate greater than 96%), conductivity (176.5 S/m), and rapid electromechanical response. In particular, the fibers have good weaving ability for their stable performance under bending and twisting load, which is important to weave flexible high conductivity fabric. The effect of conductive particle types (carbon black, carboxylated multi-arm carbon nanotubes) on the fiber properties is also studied. The results show that the carbon nanotube/polydimethylsiloxane fiber has better stable performance under bending and twisting load due to a uniform and dense conductive layer formed. This work provides a research basis for the preparation of silicone rubber-like fibrous composite materials, and the prepared polydimethylsiloxane-based stretchable conductive elastomer fibers have broad application prospects in flexible wearable electronic devices.

Hybrid of monolithic and staggered solution techniques for the computational analysis of fracture, assessed on fibrous network mechanics

The computational analysis of fiber network fracture is an emerging field with application to paper, rubber-like materials, hydrogels, soft biological tissue, and composites. Fiber networks are often described as probabilistic structures of interacting one-dimensional elements, such as truss-bars and beams. Failure may then be modeled as strong discontinuities in the displacement field that are directly embedded within the structural finite elements. As for other strain-softening materials, the tangent stiffness matrix can be non-positive definite, which diminishes the robustness of the solution of the coupled (monolithic) two-field problem. Its uncoupling, and thus the use of a staggered solution method where the field variables are solved alternatingly, avoids such difficulties and results in a stable, but sub-optimally converging solution method. In the present work, we evaluate the staggered against the monolithic solution approach and assess their computational performance in the analysis of fiber network failure. We then propose a hybrid solution technique that optimizes the performance and robustness of the computational analysis. It represents a matrix regularization technique that retains a positive definite element stiffness matrix while approaching the tangent stiffness matrix of the monolithic problem. Given the problems investigated in this work, the hybrid solution approach is up to 30 times faster than the staggered approach, where its superiority is most pronounced at large loading increments. The approach is general and may also accelerate the computational analysis of other failure problems.

A class of periodic lattices for tuning elastic instabilities

With in mind microstructures exhibiting unconventional macroscopic mechanical behaviors, characterized by overall auxetic responses and strain localization due to local elastic instabilities, in this work we conceived a simple two-dimensional non-chiral architecture in the form of a periodic lattice, whose drawing is decided by varying the thickness ratios of the cells’ walls and in turn their slenderness. Inspired by nature, which often uses supposedly naive geometries that conceal complex functions, and focusing the attention on two limit geometrical configurations of main interest, we show how these non-chiral settings, as a function of the prescribed boundary conditions, might lead to symmetry breaking associated to a variety of non-trivial deformation modes, which in some cases also retrace and generalize chiral as well as auxetic responses already observed in literature in simpler microstructures. Interestingly, for both the above mentioned limit cases, we were able to idealize the mechanical response of the system through geometrically nonlinear beam-based models, in this way obtaining helpful analytical solutions and explicit formulas to estimate the tangent effective stiffness of the lattice as well as the critical load at the onset of instability. The post-buckling was instead analyzed and discussed in detail through parametric numerical finite element simulations and ad hoc laboratory experiments, performed by faithfully realizing 3D printed prototypes, constructed via additive manufacturing technologies and made of rubber-like material, to follow extreme deformation patterns, including multi-stable states, localization and compaction with possible self-contact/touching of the elements. At the end, we exploited the obtained closed-form solutions and some associated inequalities to derive the transition from the discrete lattice to its continuum limit, which – together with the multiple equilibrium bifurcation points exhibited by the proposed microstructure – could be used to broaden the spectrum of metamaterial geometries designed to exhibit complex tunable properties.

Pseudo rigid body model for a nonlinear folding compliant mechanism

Folding compliant mechanisms have the potential to be used for innovative designs tailored for specific applications such as energy absorption, shape morphing, or stress relief. This tailorability relies on multiple variables that define the geometric and material behavior. The combined effort of the geometric and material nonlinearity can emphasize certain features in the design that, individually, would not be possible. Folding as a concept is very important in origami engineering and requires careful choice in the design variables when it comes to dimensions and material properties. Finite element analyses for folding at the level of a unit cell, as well as the overall structural design, can be cumbersome and computationally expensive. Therefore, in this work, a segmented pseudo rigid body model that captures a high level of flexibility is developed for both a superelastic material, which is characterized using a shape memory alloy, and a hyperelastic, rubber-like material. By increasing the number of segments, the model allows the structure to undergo large deformations. The results from the segmented model are compared with FEA for the folding compliant mechanism. 3D-printing and experimental testing of the compliant mechanism is also explored.

Linearization of elasticity models for incompressible materials

We obtain linear elasticity as Gamma -limit of finite elasticity under incompressibility assumption and Dirichlet boundary conditions. The result is shown for a large class of energy densities for rubber-like materials.

Parameters Identification of Rubber-like Hyperelastic Material Based on General Regression Neural Network.

In this study, we present a systematic scheme to identify the material parameters in constitutive model of hyperelastic materials such as rubber. This approach is proposed based on the combined use of general regression neural network, experimental data and finite element analysis. In detail, the finite element analysis is carried out to provide the learning samples of GRNN model, while the results observed from the uniaxial tensile test is set as the target value of GRNN model. A problem involving parameters identification of silicone rubber material is described for validation. The results show that the proposed GRNN-based approach has the characteristics of high universality and good precision, and can be extended to parameters identification of complex rubber-like hyperelastic material constitutive.