The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young’s modulus and the Poisson’s ratio, which can be derived by ...simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests. These parameters represent changes in the material properties as the deformation progresses, and can be identified with their linear equivalent when the deformations are small. Universal relations between certain of these parameters are further established, and then used to quantify nonlinear elastic responses in several hyperelastic models for rubber, soft tissue and foams. The general parameters identified here can also be viewed as a flexible basis for coupling elastic responses in multi-scale processes, where an open challenge is the transfer of meaningful information between scales.
Nanocomposites, especially natural rubber (NR), have been extensively studied for their unique features and superior performance in tire applications. The present research investigated the impact of ...zinc oxide nanoparticles (ZnO) on the performance of typical rotary machine seals made of chloroprene rubber / natural rubber (CR/NR) composites. An ordinary standard rubber two-roll mill and hydraulic press were used to prepare high-temperature vulcanized CR/NR samples filled with ZnO nanoparticles. Tensile strength, tear resistance, abrasion resistance, resilience, and hardness were measured to determine the effects of nanoparticles on these physical and mechanical properties. Based on the various hyperelastic modeling schemes, enhancement in multiple characteristics of the control sample, such as overhaul properties, was observed. Furthermore, results show that increasing nanoparticle content in the vulcanisates increased the physicomechanical characteristics, such as hardness, resilience, tensile strength, and elastic Modulus at 200% strain. Moreover, hyperelastic analytical modeling shows that the differences with experimental results are less than 5%.
The development of biocompatible hydrogels with high strength and toughness is an ongoing challenge in many tissue engineering and drug delivery applications. Glutaraldehyde crosslinking of gelatin ...is widely used but increases cell toxicity. We crosslinked bovine gelatin using glutaraldehyde (Control) and methylglyoxal (MGO), a metabolic by-product during non-enzymatic collagen crosslinking, and assessed changes in the material properties of the hydrogels. Scanning electron micrographs show large pores with plate-like walls in MGO hydrogels that help retain water. Monotonic compression tests demonstrate nonlinear stress-strain behaviors. MGO samples had 96% higher moduli as compared to Control hydrogels that had moduli of 4.77 ± 0.73 kPa (n = 4). A first-order Ogden model fits the data from Control and MGO hydrogels well as compared to the Mooney-Rivlin model and neo-Hookean hyperelastic models that fit the Control samples alone. We used cavitation rheology to quantify the maximum pressure for bubble failure in the hydrogels using blunt needles with inner radii of 75, 150, 230, and 320 μm, respectively. Pressures in the bubbles increased linearly with time and dropped sharply following a critical value. High-speed videography studies demonstrate a symmetry break from large spherical bubbles in soft control hydrogels to small ellipsoidal bubbles in stiffer MGO samples. We used the critical pressures to quantify the fracture energies of the hydrogels. MGO treatment increased the fracture energy by 274% from 12.92 J/m2 for control gels. Finally, we show that analytical equations for cavitation based on Ogden and Mooney-Rivlin models present challenges when computing the fracture toughness of hydrogels.
•Methylglyoxal (MGO) crosslinks increased modulus of gelatin hydrogels. Ogden hyperelastic model provides better fit to experimental results.•Plate like structures correlated with higher strength of MGO hydrogels.•Cavitation rheology shows higher fracture toughness for MGO samples.•Bubble shapes change from spherical to ellipsoidal during inflation in the hydrogels.•Ogden and Mooney-Rivlin material models for cavitation have unbound critical pressures.
Many soft robots are composed of soft fluidic actuators that are fabricated from silicone rubbers and use hydraulic or pneumatic actuation. The strong nonlinearities and complex geometries of soft ...actuators hinder the development of analytical models to describe their motion. Finite element modeling provides an effective solution to this issue and allows the user to predict performance and optimize soft actuator designs. Herein, the literature on a finite element analysis of soft actuators is reviewed. First, the required nonlinear elasticity concepts are introduced with a focus on the relevant models for soft robotics. In particular, the procedure for determining material constants for the hyperelastic models from material testing and curve fitting is explored. Then, a comprehensive review of constitutive model parameters for the most widely used silicone rubbers in the literature is provided. An overview of the procedure is provided for three commercially available software packages (Abaqus, Ansys, and COMSOL). The combination of modeling procedures, material properties, and design guidelines presented in this article can be used as a starting point for soft robotic actuator design.
Herein, the literature on finite element modeling of soft fluidic actuators is reviewed. The combination of modeling procedures with commercial software packages, hyperelastic material parameters, and design guidelines presented in this article can be used as a starting point for soft robotic actuator design, while saving fabrication cost and time.
This paper reports an energy-based method for the dynamic pull-in instability analysis of a spherical dielectric elastomer (DE) balloon subjected to a quasi-statically applied inflation pressure and ...a Heaviside step voltage across the balloon wall. The proposed technique relies on establishing the energy balance at the point of maximum stretch in an oscillation cycle, followed by the imposition of an instability condition for extracting the threshold parameters. The material models of the Ogden family are employed for describing the hyperelasticity of the balloon. The accuracy of the critical dynamic pull-in parameters is established by examining the saddle-node bifurcation in the transient response of the balloon obtained by integrating numerically the equation of motion, derived using the Euler–Lagrange equation. The parametric study brings out the effect of inflation pressure on the onset of the pull-in instability in the DE balloon. A quantitative comparison between the static and dynamic pull-in parameters at four different levels of the inflation pressure is presented. The results indicate that the dynamic pull-in instability gets triggered at electric fields that are lower than those corresponding to the static instability. The results of the present investigation can find potential use in the design and development of the balloon actuators subjected to transient loading. The method developed is versatile and can be used in the dynamic instability analysis of other conservative systems of interest.
The study investigates the structural characterisation of flexible membranes used in oscillating water column (OWC) wave energy converters (WECs). Four commonly utilised elastomers – natural rubber, ...nitrile rubber, silicone, and latex – were subjected to a novel hyperelastic model selection process. A custom bulge test setup enabled the selection of second-order Mooney-Rivlin (SOMR) and Yeoh models for relevant accuracy (RMSE<0.018 MPa), stability and numerical validation. A 1:20 scale OWC model with latex was tested in a water tank to examine the effects of waves with a frequency range of 0.25–1.4 Hz and up to 0.24m amplitude. Water tank experiments demonstrated smooth frequency responses for OWC with membrane, beneficial for consistent power generation. A dry test rig was designed and built to replicate OWC inflation conditions and apply cyclic loadings up to 1.5 Hz, overcoming pressure limitations of the water tank, exploring wider material options, and validating numerical simulation. An optical motion capture system, Qualisys, supported the validation process by providing precise data on membrane deformation during experiments. Furthermore, finite element analysis (FEA) was utilised to conduct stress analysis and parametric studies, assessing the suitability of these materials for flexible OWC application.
This work focuses on the mechanical characterisation of adhesives with hyperelastic behaviour and on the determination of the behavioural laws that best represent it, in order to introduce them in ...simulation models. First, a test plan is carried out on simple specimens: uniaxial and planar configuration. These are designed to measure the non-linear behaviour of adhesives in both tensile and pure shear. Unlike the uniaxial specimen, which is governed by a test standard (UNE-ISO 37) that defines its geometry, the planar specimen does not have a standard that defines its dimensions. Therefore, in this research it is proposed to carry out tests with specimens of different width-length sizes to evaluate how these dimensions affect the stress-strain curves.For mechanical characterisation, finite element programs provide the tool to evaluate the predicted behaviour of a hyperelastic material from the experimental results, displaying in the same graph the degree of approximation obtained for the results of each test (Dumbbell and planar) with different hyperelastic models, allowing us to select the hyperelastic model that best fits the experimental data.The Mooney-Rivlin model was found to be the best fitting model and therefore the most appropriate to describe the behaviour of hyperelastic adhesives used in this study. To conclude this study, the obtained law was validated by comparing the results of tests carried out on single lap joint (SLJ) specimens of different thickness.
Likely equilibria of the stochastic Rivlin cube Mihai, L Angela; Woolley, Thomas E; Goriely, Alain
Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences,
05/2019, Letnik:
377, Številka:
2144
Journal Article
Recenzirano
Odprti dostop
The problem of the Rivlin cube is to determine the stability of all homogeneous equilibria of an isotropic incompressible hyperelastic body under equitriaxial dead loads. Here, we consider the ...stochastic version of this problem where the elastic parameters are random variables following standard probability laws. Uncertainties in these parameters may arise, for example, from inherent data variation between different batches of homogeneous samples, or from different experimental tests. As for the deterministic elastic problem, we consider the following questions: what are the likely equilibria and how does their stability depend on the material constitutive law? In addition, for the stochastic model, the problem is to derive the probability distribution of deformations, given the variability of the parameters. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.
•A general approach for the stochastic finite element analysis of soft tissue deformation is presented.•Sensitivity derivative Monte Carlo method to propagate uncertainty through hyperelastic models ...with stochastic parameters.•The proposed method is up to two orders of magnitude faster than the standard Monte Carlo approach.•The method is able to provide the user with statistical results on quantities of practical interest.•We applied the approach to a simple academic example and to the stochastic deformation of a brain.
We present a simple open-source semi-intrusive computational method to propagate uncertainties through hyperelastic models of soft tissues. The proposed method is up to two orders of magnitude faster than the standard Monte Carlo method. The material model of interest can be altered by adjusting few lines of (FEniCS) code. The method is able to (1) provide the user with statistical confidence intervals on quantities of practical interest, such as the displacement of a tumour or target site in an organ; (2) quantify the sensitivity of the response of the organ to the associated parameters of the material model. We exercise the approach on the determination of a confidence interval on the motion of a target in the brain. We also show that for the boundary conditions under consideration five parameters of the Ogden–Holzapfel-like model have negligible influence on the displacement of the target zone compared to the three most influential parameters. The benchmark problems and all associated data are made available as supplementary material.
The examination of hyperelastic materials’ behavior, such as polydimethylsiloxane (PDMS), is crucial for applications in areas as biomedicine and electronics. However, the limitations of hyperelastic ...models for specific stress scenarios, with stress concentration, are not well explored on the literature. To address this, firstly, three constitutive models were evaluated (Neo-Hookean, Mooney-Rivlin, and Ogden) using numerical simulations and Digital Image Correlation (DIC) analysis during a uniaxial tensile test. The samples were made of PDMS with stress concentration geometries (center holes, shoulder fillets, and edge notches). Results of ANOVA analysis showed that any of the three models can be chosen for numerical analysis of PDMS since no significant differences in suitability were found. Finally, the Ogen model was chosen to obtain the stress concentration factors for these geometries, a property which characterize how discontinuities change the maximum stress supported by an element. Our study provides new values for variables needed to analyze and design hyperelastic elements and produce a foundation for understanding PDMS stress-strain behavior.
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