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Journal articles on the topic 'Mooney Rivlin Model'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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Yu, Chun Jin. "Comparison Study of Membrane Flapping Wing Based on Mooney-Rivlin Model and Linear Model." Advanced Materials Research 753-755 (August 2013): 1842–45. http://dx.doi.org/10.4028/www.scientific.net/amr.753-755.1842.

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The maximum deformation and stress are compared based on Mooney-Rivlin Model and Linear Model for flapping wing. One flapping cycle was divided into twelve segments, and maximum deformation and stress were calculated in each segment. The results show that max deformation and stress all occur at the beginning of downstroke, the max deformation adopted Mooney-Rivlin model is 25 percent of the max deformation adopted the linear model, and the max stress adopted Mooney-Rivlin model is only 0.37 percent of the max stress adopted the linear model. Mooney-Rivlin Material is very suitable for the membrane flapping wing.

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Noor, Siti Noor Azizzati Mohd, and Jamaluddin Mahmud. "Skin Prestretch Evaluation Adapting Mooney-Rivlin Model." Journal of Medical and Bioengineering 4, no. 1 (2015): 31–35. http://dx.doi.org/10.12720/jomb.4.1.31-35.

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He, Bin, Chenghong Zhang, Yanmin Zhou, and Zhipeng Wang. "A Computing Method to Determine the Performance of an Ionic Liquid Gel Soft Actuator." Applied Bionics and Biomechanics 2018 (2018): 1–11. http://dx.doi.org/10.1155/2018/8327867.

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A new type of soft actuator material—an ionic liquid gel (ILG) that consists of BMIMBF4, HEMA, DEAP, and ZrO2—is polymerized into a gel state under ultraviolet (UV) light irradiation. In this paper, we first propose that the ILG conforms to the assumptions of hyperelastic theory and that the Mooney-Rivlin model can be used to study the properties of the ILG. Under the five-parameter and nine-parameter Mooney-Rivlin models, the formulas for the calculation of the uniaxial tensile stress, plane uniform tensile stress, and 3D directional stress are deduced. The five-parameter and nine-parameter Mooney-Rivlin models of the ILG with a ZrO2 content of 3 wt% were obtained by uniaxial tensile testing, and the parameters are denoted as c10, c01, c20, c11, and c02 and c10, c01, c20, c11, c02, c30, c21, c12, and c03, respectively. Through the analysis and comparison of the uniaxial tensile stress between the calculated and experimental data, the error between the stress data calculated from the five-parameter Mooney-Rivlin model and the experimental data is less than 0.51%, and the error between the stress data calculated from the nine-parameter Mooney-Rivlin model and the experimental data is no more than 8.87%. Hence, our work presents a feasible and credible formula for the calculation of the stress of the ILG. This work opens a new path to assess the performance of a soft actuator composed of an ILG and will contribute to the optimized design of soft robots.

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Liu, I.-Shih. "A note on the Mooney–Rivlin material model." Continuum Mechanics and Thermodynamics 24, no. 4-6 (2011): 583–90. http://dx.doi.org/10.1007/s00161-011-0197-6.

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Azarov, Daniil. "Stretching of the mechanical-geometric model and two common nonlinear elastic solids." E3S Web of Conferences 273 (2021): 07019. http://dx.doi.org/10.1051/e3sconf/202127307019.

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The variety of hyperelastic materials and the design of new modifications and technical applications requires the development of a description of nonlinear deformation properties. The most commonly used constitutive relations of the Mooney-Rivlin and Yeoh models are based on polynomial decompositions. Mechanical-geometric modeling (hereinafter - MGM) is a new way of constructing constitutive relations and strain energy densities within the nonlinear theory of elasticity. In this paper, a comparison of the deformation behavior of MGM with the traditional Mooney-Rivlin and Yeoh models was carried out. Comparative analysis is accompanied by diagrams for uniaxial and biaxial stretching. The effectiveness of the new model was proved.

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Li, Songyu, Liquan Wang, Shaoming Yao, et al. "Modelling, simulation and experiment of the spherical flexible joint stiffness." Mechanical Sciences 9, no. 1 (2018): 81–89. http://dx.doi.org/10.5194/ms-9-81-2018.

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Abstract. The spherical flexible joint is extensively used in engineering. It is designed to provide flexibility in rotation while bearing vertical compression load. The linear rotational stiffness of the flexible joint is formulated. The rotational stiffness of the bonded rubber layer is related to inner radius, thickness and two edge angles. FEM is used to verify the analytical solution and analyze the stiffness. The Mooney–Rivlin, Neo Hooke and Yeoh constitutive models are used in the simulation. The experiment is taken to obtain the material coefficient and validate the analytical and FEM results. The Yeoh model can reflect the deformation trend more accurately, but the error in the nearly linear district is bigger than the Mooney–Rivlin model. The Mooney–Rivlin model can fit the test result very well and the analytical solution can also be used when the rubber deformation in the flexible joint is small. The increase of Poisson's ratio of the rubber layers will enhance the vertical compression stiffness but barely have effect on the rotational stiffness.

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Fazli Adull Manan, Nor, Linasuriani Muhamad, Zurri Adam Mohd Adnan, Mohd Azman Yahaya, and Jamaluddin Mahmud. "Characterisation of Skin Biomechanical Properties via Experiment-Numerical Integration." International Journal of Engineering & Technology 7, no. 4.26 (2018): 205. http://dx.doi.org/10.14419/ijet.v7i4.26.22168.

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By having specific mechanical properties of skin, computational program and analysis become more reliable by showing the real skin behaviour. Up to date, mechanical properties of biological soft tissues (skin) haven’t been accepted solely for official usage. Therefore, characterisation of the skin biomechanical properties might contribute a new knowledge to the engineering and medical sciences societies. This paper highlights the success in characterising the hyperelastic parameters of leporine (rabbit) skin via experimental-numerical integration. A set of five sample of leporine skin were stretched using the conventional tensile test machine to generate the load-displacement graphs. Based on the Ogden’s constitutive equation and Mooney-Rivlin hyperelastic model, a stress-stretch equation was developed and a programme was written using Matlab. By varying the Ogden’s and Mooney-Rivlin’s parameters, the programme was capable of plotting stress-stretch and load-displacement graphs. The graphs that best match the experimental results will constitut to the corresponding coefficient, µ, and α for Ogden Model and C1 and C2 material parameter for Mooney-Rivlin Model that will best describe the behaviour of the leporine skin. The current results show that the Ogden’s coefficient and exponent for the subject was estimated to be (μ = 0.048MPa, α = 7.073) & (μ = 0.020MPa, α = 9.249) for Anterior-Posterior (AP) and Dorsal-Ventral (DV) respectively for Ogden Model. Meanwhile the value for Mooney-Rivlin Model were estimated to be (C1 = 1.271, C2 = 1.868) & (C1 = 1.128, C2 = 1.537) for AP and DV respectively, which is in close agreement to results found by other researchers. Further analyses for comparison could be carried out by developing mathematical model based on other constitutive equation such as Arruda-Boyce and Neo-Hookean. Nevertheless, this study has contributed to the knowledge about skin behaviour and the results are useful for references.

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Kamarul Bahrain, Siti Humairah, and Jamaluddin Mahmud. "Parametric Investigation of Mooney-Rivlin Material Constants on Silicone Biocomposite." Materials Science Forum 882 (January 2017): 51–55. http://dx.doi.org/10.4028/www.scientific.net/msf.882.51.

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Hyperelastic materials are unique materials that have high tendency to stretch and its highly non-linear behaviour is commonly investigated using hyperelastic constitutive models. The aim of this paper is to investigate the sensitivity of Mooney-Rivlin material constants; C1 and C2 values in order to observe the behavior and pattern of the stress-stretch graph for silicone-kenaf composite. There were no previous studies done in regards to assess the mechanical behaviour of the stress-stretch curve for silicone-kenaf biocomposite by varying the Mooney-Rivlin material constants. The material constant, C1 and C2 are varied into few cases and the patterns of stress-stretch curves are studied. It was found that variations of C1 and C2 material constants could contribute differently on the mechanical properties of silicone-kenaf composite. Thus, the results and findings of this study could be further enhanced by future study to gain deeper understanding on the hyperelastic materials behaviour and Mooney-Rivlin hyperelastic constitutive model.

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Śliwa-Wieczorek, Klaudia, Bogusław Zając, and Tomasz Kozik. "Tests on the Mechanical Properties of Polymers in the Aspect of an Attempt to Determine the Parameters of the Mooney-Rivlin Hyperelastic Model." Civil and Environmental Engineering Reports 30, no. 2 (2020): 1–14. http://dx.doi.org/10.2478/ceer-2020-0016.

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AbstractThe article presents testing of the mechanical properties of SIKA® polymer adhesives of the type PBM, PMM, PM, and PSM in the aspect of an attempt to determine the parameters of the Mooney-Rivlin hyperelastic model. The article contains a literature review on developed models for hyperelastic materials as well as a description of the author’s own results obtained in monaxial tensile and monaxial compression tests conducted on oars and cylindrical samples, respectively. Furthermore, the results of modeling of Mooney-Rivlin hyperelastic model parameters are shown in relation to the value of average parameters for polymers after both a week and a month-and-a-half of ripening.

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Irastorza, Ramiro M., Bernard Drouin, Eugenia Blangino, and Diego Mantovani. "Mathematical Modeling of Uniaxial Mechanical Properties of Collagen Gel Scaffolds for Vascular Tissue Engineering." Scientific World Journal 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/859416.

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Small diameter tissue-engineered arteries improve their mechanical and functional properties when they are mechanically stimulated. Applying a suitable stress and/or strain with or without a cycle to the scaffolds and cells during the culturing process resides in our ability to generate a suitable mechanical model. Collagen gel is one of the most used scaffolds in vascular tissue engineering, mainly because it is the principal constituent of the extracellular matrix for vascular cells in human. The mechanical modeling of such a material is not a trivial task, mainly for its viscoelastic nature. Computational and experimental methods for developing a suitable model for collagen gels are of primary importance for the field. In this research, we focused on mechanical properties of collagen gels under unconfined compression. First, mechanical viscoelastic models are discussed and framed in the control system theory. Second, models are fitted using system identification. Several models are evaluated and two nonlinear models are proposed: Mooney-Rivlin inspired and Hammerstein models. The results suggest that Mooney-Rivlin and Hammerstein models succeed in describing the mechanical behavior of collagen gels for cyclic tests on scaffolds (with best fitting parameters 58.3% and 75.8%, resp.). When Akaike criterion is used, the best is the Mooney-Rivlin inspired model.

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Brown, C. P., T. C. Nguyen, H. R. Moody, R. W. Crawford, and A. Oloyede. "Assessment of common hyperelastic constitutive equations for describing normal and osteoarthritic articular cartilage." Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 223, no. 6 (2009): 643–52. http://dx.doi.org/10.1243/09544119jeim546.

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With the aim of providing information for modelling joint and limb systems, widely available constitutive hyperelastic laws are evaluated in this paper for their ability to predict the mechanical responses of normal and osteoarthritic articular cartilage. Load—displacement data from mechanical indentation were obtained for normal and osteoarthritic cartilage at 0.1 s−1 and 0.025 s−1 and converted to the stress—stretch ratio. The data were then fitted to the ArrudA—Boyce, Mooney—Rivlin, neo-Hookean, Ogden, polynomial, and Yeoh hyperelastic laws in the MATLAB environment. Although each of the hyperelastic laws performed satisfactorily at the higher rate of loading, their ability to fit experimental data at the lower loading rate varied considerably. For the preferred models, coefficients were provided for stiff, soft, and average tissues to represent normal and degraded tissue at high and low loading rates. The present authors recommend the use of the Mooney—Rivlin or the Yeoh models for describing both normal and degraded articular cartilage, with the Mooney—Rivlin model providing the best compromise between accuracy and required computational power.

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Du, Xian Bin, You Qun Zhao, Fen Lin, and Zhen Xiao. "Parameters Determination of Mooney-Rivlin Model for Rubber Material of Mechanical Elastic Wheel." Applied Mechanics and Materials 872 (October 2017): 198–203. http://dx.doi.org/10.4028/www.scientific.net/amm.872.198.

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In order to improve the driving safety of vehicles, a non-pneumatic safety tire named mechanical elastic wheel was developed, and the structural components of mechanical elastic wheel and the method of determining the rubber material parameters of Mooney-Rivlin model were introduced. Uniaxial tensile tests of the rubber in different parts of mechanical elastic wheel were carried out with a stretch test machine and the material parameters and of the Mooney-Rivlin model were determined by fitting the experimental data. Finite element method (FEM) was used to validate the stability of the fitted data. The results show that the obtained material parameters have high accuracy and can be a reference for the subsequent finite element simulation of mechanical elastic wheel.

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Ryu, Jong Eun, Eduardo Salcedo, Hyeok Jong Lee, et al. "Material models and finite analysis of additively printed polymer composites." Journal of Composite Materials 53, no. 3 (2018): 361–71. http://dx.doi.org/10.1177/0021998318785672.

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There are urgent needs to characterize and model the mechanical property of additively manufactured composite materials, known as the digital materials, for the computational design and simulation. In this study, most utilized digital material samples, which are the mixture of base polymers, Tango Black+ and Vero White+, by PolyJet (Stratasys) are chosen. Four polynomial models (Neo Hookean model, and two-, three-, and five-parameter Mooney–Rivlin models) are used to fit mechanical tensile test results up to 30% of strain. The material models were adopted in the finite element analysis simulating the tensile test to validate their accuracy. The simulation results based on the two-parameter Mooney–Rivlin model predict the stress at 30% strain with small errors (8.2, 10.5, 0.9, 5.0, and 8.0 for Tango Black+, DM40, DM50, DM60, and DM70, respectively). Additionally, scanning electron microscopy was utilized to analyze the fracture surface of the base materials (Tango Black+ and Vero White+) and the digital materials.

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Yu, Chun Jin. "Stress Study of Membrane Flapping Wing Based on Mooney-Rivlin Model." Advanced Materials Research 538-541 (June 2012): 83–87. http://dx.doi.org/10.4028/www.scientific.net/amr.538-541.83.

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The stress change of membrane flapping-wing aerial vehicle that used Moon-Rivlin model was calculated in one flapping cycle. One flapping cycle was divided into twelve segments, aerodynamic force and inertia force in each segment were calculated, the stress distribution could be gotten. The results show that: at the beginning of upstroke and at the beginning of downstroke, the stress of flapping-wing is maximum; the stress of downstroke near the flapping symmetry position is minimum, and the stress of upstroke near flapping symmetry position is another minimum peak stage.

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Keerthiwansa, Rohitha, Jakub Javořík, Soňa Rusnáková, Jan Kledrowetz, and Petr Gross. "Hyperelastic Material Characterization: How the Change in Mooney-Rivlin Parameter Values Effect the Model Curve." Materials Science Forum 994 (May 2020): 265–71. http://dx.doi.org/10.4028/www.scientific.net/msf.994.265.

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Mooney-Rivlin is the most frequently used model from all models used for mechanical characterization of the hyperelestic materials. Simplicity, applicability in a large rage of strains are the key reasons for regular use of this model. However, depending on the number of parameters, the Mooney model can take several forms. While, nine parameter being the highest order noticed, two parameter model is the most commonly found form in the current research domain. Since two parameter model used repetitively, we investigated the effect of incremental change in two material constant values one at a time, on model curve. As Drucker Stability Criterion is governing the extreme values of material parameters, changes in the model curves are discussed related to it. Resultant effects on stress-strain curves due to change in parameter values were examined and physical effect on the characterization is interpreted accordingly.

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Diaz-Calleja, Ricardo, Damián Ginestar, Vícente Compañ Moreno, et al. "Viscoelastic Effects on the Response of Electroelastic Materials." Polymers 13, no. 13 (2021): 2198. http://dx.doi.org/10.3390/polym13132198.

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Electroelastic materials, as for example, 3M VHB 4910, are attracting attention as actuators or generators in some developments and applications. This is due to their capacity of being deformed when submitted to an electric field. Some models of their actuation are available, but recently, viscoelastic models have been proposed to give an account of the dissipative behaviour of these materials. Their response to an external mechanical or electrical force field implies a relaxation process towards a new state of thermodynamic equilibrium, which can be described by a relaxation time. However, it is well known that viscoelastic and dielectric materials, as for example, polymers, exhibit a distribution of relaxation times instead of a single relaxation time. In the present approach, a continuous distribution of relaxation times is proposed via the introduction of fractional derivatives of the stress and strain, which gives a better account of the material behaviour. The application of fractional derivatives is described and a comparison with former results is made. Then, a double generalisation is carried out: the first one is referred to the viscoelastic or dielectric models and is addressed to obtain a nonsymmetric spectrum of relaxation times, and the second one is the adoption of the more realistic Mooney–Rivlin equation for the stress–strain relationship of the elastomeric material. A modified Mooney–Rivlin model for the free energy density of a hyperelastic material, VHB 4910 has been used based on experimental results of previous authors. This last proposal ensures the appearance of the bifurcation phenomena which is analysed for equibiaxial dead loads; time-dependent bifurcation phenomena are predicted by the extended Mooney–Rivlin equations.

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Vishvanathperumal, S., V. Navaneethakrishnan, G. Anand, and S. Gopalakannan. "Evaluation of Crosslink Density Using Material Constants of Ethylene-Propylene-Diene Monomer/Styrene-Butadiene Rubber with Different Nanoclay Loading: Finite Element Analysis-Simulation and Experimental." Advanced Science, Engineering and Medicine 12, no. 5 (2020): 632–42. http://dx.doi.org/10.1166/asem.2020.2567.

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Nanoclay is used to enhance the mechanical properties of ethylene-propylene-diene rubber (EPDM)/styrene-butadiene rubber (SBR) blends. Sulphur (S), dicumyl peroxide (P), and mixed systems (S + P) were used as crosslinking or vulcanizing agents for the EPDM/SBR nanocomposites. The experimental data of the stress–strain behavior of EPDM/SBR blends with different nanoclay loading have been determined through a tension test. Nonlinear mechanical behaviors of the rubbers are described by strain energy functions in order to assurance that rigid body motions play no role in the constitutive law. The mathematical model such as the Mooney-Rivlin model based on the existence of strain energy density functions depends on the right Cauchy-Green's deformation tensor or Green's strain tensor. The experimental data are fitted to the Mooney-Rivlin model in order to find the rubber material constants. These constants are used to find the crosslinking density. A comparison between the experimental stress–strain behavior and finite element analysis of a uniaxial tension test at different nanoclay loading is presented.

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Pereira, Carlos E. L., and Marco L. Bittencourt. "Topological sensitivity analysis for a two-parameter Mooney-Rivlin hyperelastic constitutive model." Latin American Journal of Solids and Structures 7, no. 4 (2010): 391–411. http://dx.doi.org/10.1590/s1679-78252010000400002.

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Zhang, Ce, Shi Min Zhang, Dai Geng, Jian Ming Zheng, and Wen Bin Fan. "FEM Analysis of Plug Packer Based on the Model of Mooney-Rivlin." Advanced Materials Research 201-203 (February 2011): 326–31. http://dx.doi.org/10.4028/www.scientific.net/amr.201-203.326.

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The technology of Pipeline high-pressure intelligent isolation is a new technology which has been developed by Company PSI since the 1990’s, and the core technology, packer’s sealing performance has been blocked from then on. In this paper, we study the Polyurethane columns specimen of different hardness though ANSYS, then fit with the curve from the experiments, in order to get the Polyurethane columns’ Mechanical constants of Model Mooney-Rivlin. Calculate the deformation between two statuses, then according to isolation pressure and anti-convexity of packer we choose the packer of appropriate hardness. Finally, analysis the packer under different pressure, get the working curve of isolation ability, and the outlet can be used in the design of packer.

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Chen, Chao-Hsun, and Yu-Chung Wang. "An extended nonlinear mechanical model for solid-filled Mooney-Rivlin rubber composites." Polymer 38, no. 3 (1997): 571–76. http://dx.doi.org/10.1016/s0032-3861(96)00539-3.

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Suraj, Abhishek Kumar, Bikas Prasad, and Kaushik Kumar. "Effect of change of material model in Mooney Rivlin hyper-elastic material." Materials Today: Proceedings 26 (2020): 2511–14. http://dx.doi.org/10.1016/j.matpr.2020.02.534.

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Dai, H. H. "Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod." Acta Mechanica 127, no. 1-4 (1998): 193–207. http://dx.doi.org/10.1007/bf01170373.

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Eriksson, Anders, and Arne Nordmark. "Non-unique response of Mooney–Rivlin model in bi-axial membrane stress." Computers & Structures 144 (November 2014): 12–22. http://dx.doi.org/10.1016/j.compstruc.2014.07.021.

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Li, Ming, Xiao Ling Hu, Wen Bo Luo, You Jian Huang, and Ji Ling Bu. "Comparison of Two Hyperelastic Models for Carbon Black Filled Rubber." Applied Mechanics and Materials 275-277 (January 2013): 28–32. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.28.

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Mooney-Rivlin model and Ogden model are frequently used by engineers for finite element analysis of rubber material. Before simulation, simple, biaxial and planar extension tests are always done to get the model parameters. In this paper, we compare these two hyperelastic models with experimental data produced under simple, biaxial extension and planar extension loading conditions. The ability of the two models to reproduce different deformation modes is analyzed. Both material parameters and the stretch range of validity of each model are determined.

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Kim, Beomkeun, Seong Beom Lee, Jayone Lee, et al. "A comparison among Neo-Hookean model, Mooney-Rivlin model, and Ogden model for chloroprene rubber." International Journal of Precision Engineering and Manufacturing 13, no. 5 (2012): 759–64. http://dx.doi.org/10.1007/s12541-012-0099-y.

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Merkulov, Dmitrii. "Research of the deformation of a thin body with a magnetizable elastomer in the magnetic field of a coil." EPJ Web of Conferences 185 (2018): 09009. http://dx.doi.org/10.1051/epjconf/201818509009.

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Deformation of a thin cylindrical body with a magnetizable elastomer based on silicone in the magnetic field of an electromagnetic coil is investigated experimentally and theoretically. It is observed that a bistability of the thin body equilibrium shape exists at some values of the coil current. The method of measuring elasticity coefficients of the magnetizable elastomer in the Mooney – Rivlin model is proposed.

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Valencia, Alvaro, Patricio Burdiles, Miguel Ignat, et al. "Fluid Structural Analysis of Human Cerebral Aneurysm Using Their Own Wall Mechanical Properties." Computational and Mathematical Methods in Medicine 2013 (2013): 1–18. http://dx.doi.org/10.1155/2013/293128.

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Computational Structural Dynamics (CSD) simulations, Computational Fluid Dynamics (CFD) simulation, and Fluid Structure Interaction (FSI) simulations were carried out in an anatomically realistic model of a saccular cerebral aneurysm with the objective of quantifying the effects of type of simulation on principal fluid and solid mechanics results. Eight CSD simulations, one CFD simulation, and four FSI simulations were made. The results allowed the study of the influence of the type of material elements in the solid, the aneurism’s wall thickness, and the type of simulation on the modeling of a human cerebral aneurysm. The simulations use their own wall mechanical properties of the aneurysm. The more complex simulation was the FSI simulation completely coupled with hyperelastic Mooney-Rivlin material, normal internal pressure, and normal variable thickness. The FSI simulation coupled in one direction using hyperelastic Mooney-Rivlin material, normal internal pressure, and normal variable thickness is the one that presents the most similar results with respect to the more complex FSI simulation, requiring one-fourth of the calculation time.

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CORRALES MAGALLANES, ADI, LUIS DEL LLANO VIZCAYA, CELSO EDUARDO CRUZ GONZALEZ, VICENTE BRINGAS RICO, ALDO AUGUSTO LOPEZ MARTINEZ, and EUSEBIO JIMENEZ LOPEZ. "NUMERICAL-EXPERIMENTAL EVALUATION OF A HYPERELASTIC POLYURETHANE ADHESIVE." DYNA 96, no. 3 (2021): 246–49. http://dx.doi.org/10.6036/9783.

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This article presents the results of the experimental tests carried out on a polyurethane hyperelastic adhesive. The Mooney-Rivlin, Ogden and Yeoh models were analyzed between others, with different order and parameters using the finite element method and the Ansys V17.1 package, with the aim of evaluating the convergence of a general hyperelastic model, to subsequently manufacture specimens and perform experimental uniaxial stress tests. The information obtained from the tests was supplied to a curve fitting model for several hyperelastic models, seeking to obtain a correlation between these tests. New analyzes were performed with the finite element method with the materials considered and the curves adjusted. The results were studied and the numerical hyperelastic model closest to reality was selected, observing that the 1st order Yeoh model presented significant deviations between -30% to 60% in the experimental stiffness, the 3rd order Yeoh model presented deviations of -5% to -30%, while Ogden models of 1st and 3rd order presented deviations of -3.5% to 25% and -3% to 20%, before approaching the critical load, where the model of Ogden of 1st order presented a deviation of 0.66% and that of 3rd order of -3.59%. The 2 parameter Mooney-Rivlin model presents a deviation of 3.9% when it approaches the critical load, but values from -2.04% to 15% during the development of the stress test, so that model proved to be the most appropriate to analyze the material investigated in this work. Key Words: Hyperelastic material, Experimental Methods, Numerical Methods, FEA

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Qu, Jia, Geng Chen, and Yu Wei Yang. "Finite Element Analysis of Rubber Sealing Ring Resilience Behavior." Advanced Materials Research 705 (June 2013): 410–14. http://dx.doi.org/10.4028/www.scientific.net/amr.705.410.

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In this paper, hyper-elastic constitutive models of rubber material have been summed up based on constitutive relation and the Mooney-Rivlin model has been pay more attention. Then through the tension experimental test, data of sealing material under axial experimental are obtained, and M-R model parameters C10 and C01 are fitted by ANSYS. After obtaining the material parameters, compression deformation behavior and the distribution of stress field and resilience behavior of the seal ring are simulated by using ANSYS/LS-DYNA software under different loading conditions.

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Yeoh, O. H. "Some Forms of the Strain Energy Function for Rubber." Rubber Chemistry and Technology 66, no. 5 (1993): 754–71. http://dx.doi.org/10.5254/1.3538343.

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Abstract According to Rivlin's Phenomenological Theory of Rubber Elasticity, the elastic properties of a rubber may be described in terms of a strain energy function which is an infinite power series in the strain invariants I1, I2 and I3. The simplest forms of Rivlin's strain energy function are the neo-Hookean, which is obtained by truncating the infinite series to just the first term in I1, and the Mooney-Rivlin, which retains the first terms in I1 and I2. Recently, we proposed a strain energy function which is a cubic in I1. Conceptually, the proposed function is a material model with a shear modulus that varies with deformation. In this paper, we compare the large strain behavior of rubber as predicted by these forms of the strain energy function. The elastic behavior of swollen rubber is also discussed.

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Luo, Hua An, Hua Ming Wang, Jian Ying Zhu, and You Peng You. "Characterization of Hyperelastic Dielectric Elastomer Based on Biaxial Tensile Bench." Advanced Materials Research 97-101 (March 2010): 884–88. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.884.

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Usually model parameters from uniaxial experiments are not suitable for dielectric elastomer under biaxial loading condition. To characterize the mechanical behavior of dielectric elastomer, a biaxial tensile bench is established, on which uniaxial tests can be performed too. On the basis of the analysis of viscous effect of elastomer, experimental condition for data acquirement is determined. Then equi-biaxial and uniaxial experimental data are obtained to fit three constitutive models, i.e. Mooney-Rivlin, Yeoh and Ogden model. Also, least square minimization method is used to obtained model parameters, which are applicable to both uniaxial and equi-biaxial experimental data.

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Kalayeh, Kourosh, and Panos Charalambides. "A Non-Linear Model of an All-Elastomer, in-Plane, Capacitive, Tactile Sensor Under the Application of Normal Forces." Sensors 18, no. 11 (2018): 3614. http://dx.doi.org/10.3390/s18113614.

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In this work, a large deformation, non-linear semi-analytical model for an all-elastomer, capacitive tactile unit-sensor is developed. The model is capable of predicting the response of such sensors over their entire sensing range under the application of normal forces. In doing so the finite flat punch indentation model developed earlier is integrated with a capacitance model to predict the change-in-capacitance as a function of applied normal forces. The empirical change-in-capacitance expression, based on the parallel plate capacitance model, is developed to account for the fringe field and saturation effects. The elastomeric layer used as a substrate in these sensors is modeled as an incompressible, non-linear, hyperelastic material. More specifically, the two term Mooney-Rivlin strain energy function is used as a constitutive response to relate the stresses and strains. The developed model assumes both geometrical as well as material non-linearity. Based on the related experimental work presented elsewhere, the inverse analysis, combining finite element (FE) modeling and non-linear optimization, is used to obtain the Mooney-Rivlin material parameters. Finally, to validate the model developed herein the model predictions are compared to the experimental results obtained elsewhere for four different tactile sensors. Great agreements are found to exist between the two which shows the model capabilities in capturing the response of these sensors. The model and methodologies developed in this work, may also help advancing bio-material studies in the determination of biological tissue properties.

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Major, Izabela. "Numerical Analysis of Wave Phenomena in Hyperelastic Mooney-Rivlin and Zahorski Materials." Civil and Environmental Engineering 10, no. 1 (2014): 44–50. http://dx.doi.org/10.2478/cee-2014-0006.

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Abstract This paper focuses on presentation of waves phenomena that occur during propagation of disturbance in continuous incompressible hyperelastic structures, described with elastic potential. Numerical analysis demonstrated differences during the propagation of disturbances in the commonly used model of Mooney-Rivlin material compared to less popular Zahorski material. The obtained result is also likely to contribute to development of new forms of practical application of nonlinear rubber and rubber-like materials for technological solutions, including those used in the broadly understood construction sector.

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Wang, Wen Tao, and Wen Bin Shang Guan. "The Study on Rubber’s Constitutive Model about Parameters Identification and the Effect of Fitting Error." Advanced Materials Research 503-504 (April 2012): 1094–99. http://dx.doi.org/10.4028/www.scientific.net/amr.503-504.1094.

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Fitting accuracy of hyper-elastic constitutive models of rubber and parameter identification of the models play important roles in the finite element analysis of rubber components. In this paper, to obtain stress-strain characteristics, uniaxial and planar as well as biaxial tension of a standard rubber sample are measured. Model parameters of three kinds of classic constitutive models are identified using least square method. Then, the fitting accuracy among different models is compared. The comparison shows that the fitting accuracy is getting higher when the test material strain is increased. Also, it can be concluded that Mooney-Rivlin model and Van der Waals model as well as third-order Ogden model have relatively stable fitting accuracy.

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R. Cipolatti, I-Shih Liu, and M. A. Rincon. "MATHEMATICAL ANALYSIS OF SUCCESSIVE LINEAR APPROXIMATION FOR MOONEY-RIVLIN MATERIAL MODEL IN FINITE ELASTICITY." Journal of Applied Analysis & Computation 2, no. 4 (2012): 363–79. http://dx.doi.org/10.11948/2012027.

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Xu, P., and J. E. Mark. "Biaxial Extension Studies Using Inflation of Sheets of Unimodal Model Networks." Rubber Chemistry and Technology 63, no. 2 (1990): 276–84. http://dx.doi.org/10.5254/1.3538258.

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Abstract Measurements of uniaxial extension and compression were made on model poly(dimethylsiloxane) (PDMS) [−Si(CH3)2−O−]x networks to examine the molecular theories of rubber elasticity. The stress-strain isotherms showed that the Flory-Erman theory of rubber elasticity is in good agreement with experimental data from extension to compression (α−1: 0.3–13), while the Mooney-Rivlin relation is useful only in a specific region of extension ratio (α−1: 0.3–0.8). The experimental results strongly support the theory of Flory-Erman, rather than those of phantom and affine networks. It is thus evident that the Flory-Erman theory of rubber elasticity is the more nearly correct.

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Klute, Glenn K., and Blake Hannaford. "Accounting for Elastic Energy Storage in McKibben Artificial Muscle Actuators." Journal of Dynamic Systems, Measurement, and Control 122, no. 2 (1998): 386–88. http://dx.doi.org/10.1115/1.482478.

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The McKibben artificial muscle is a pneumatic actuator whose properties include a very high force to weight ratio. This characteristic makes it very attractive for a wide range of applications such as mobile robots and prosthetic appliances for the disabled. In this paper, we present a model that includes a nonlinear, Mooney–Rivlin mathematical description of the actuator’s internal bladder. Experimental results show that the model provides improvement in the ability to predict the actuator’s output force. However, a discrepancy between model and experiment, albeit smaller than previous models, still exists. A number of factors are identified that may be responsible for this discrepancy. [S0022-0434(00)00902-3]

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Rassoli, Aisa, Nasser Fatouraee, and Mohammad Shafigh. "UNIAXIAL AND BIAXIAL MECHANICAL PROPERTIES OF THE HUMAN SAPHENOUS VEIN." Biomedical Engineering: Applications, Basis and Communications 27, no. 05 (2015): 1550050. http://dx.doi.org/10.4015/s1016237215500507.

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Cardiovascular diseases are one of the major causes of death in the world and are closely related to blood dynamics and wall mechanical properties of vessels. This makes the study of mechanical properties of arteries and veins essential. In this regard, study on common vessels used in bypass grafting operations is of special importance due to the frequency of this surgery. Human saphenous vein is one of the vessels used for bypass surgeries. The objective of the present study is to characterize the behavior of human saphenous vein using uniaxial and biaxial planar tests. Forty human saphenous samples were obtained after coronary artery bypass surgery (CABG). The planar tensile tests were performed on the tissue specimens by applying loads along two directions. These tests provided the force-displacement curves. The stress-strain curves from uniaxial tests were modeled with a mathematical function and the Young modulus was obtained in both longitudinal and circumferential directions. Measured data of uniaxial tests were then fitted into a hyperelastic four-parameter Fung-type model and also an isotropic Mooney–Rivlin model. The biaxial stress-stretch curves were fitted to a hyperelastic anisotropic four-parameter Fung-type model and a five-parameter Mooney–Rivlin model. The specimens showed some degrees of anisotropy. In both uniaxial and biaxial tests, specimens showed stiffer behaviour in longitudinal as opposed to circumferential directions. The stretch ratio in the circumferential direction was much higher than in the longitudinal orientation.

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Ng, Soon Seng, Chuan Li, and Vincent Chan. "Experimental and numerical determination of cellular traction force on polymeric hydrogels." Interface Focus 1, no. 5 (2011): 777–91. http://dx.doi.org/10.1098/rsfs.2011.0036.

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Anchorage-dependent cells such as smooth muscle cells (SMCs) rely on the transmission of actomyosin-generated traction forces to adhere and migrate on the extracellular matrix. The cellular traction forces exerted by SMCs on substrate can be measured from the deformation of substrate with embedded fluorescent markers. With the synchronous use of phase-contrast and fluorescent microscopy, the deformation of polyacrylamide (PAM) gel substrate can be quantitatively determined using particle image velocimetry. This displacement map is then input as boundary conditions for the stress analysis on PAM gel by the finite-element method. In addition to optical microscopy, atomic force microscopy was also used to characterize the PAM substrate using the contact mode, from which the elasticity of PAM can be quantified using Hertzian theory. This provides baseline information for the stress analysis of PAM gel deformation. The material model introduced for the computational part is the Mooney–Rivlin constitutive law because of its long proven usefulness in predicting polymers' mechanical behaviour. Numerical results showed that adhesive stresses are high around the cell edges, which is in accordance with the general phenomena of cellular focal adhesion. Further calculations on the total traction forces indicate a slightly contact-dominated regime for a broad range of Mooney–Rivlin stiffnesses.

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Shearer, Tom, William J. Parnell, and I. David Abrahams. "Antiplane wave scattering from a cylindrical cavity in pre-stressed nonlinear elastic media." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2182 (2015): 20150450. http://dx.doi.org/10.1098/rspa.2015.0450.

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The effect of a longitudinal stretch and a pressure-induced inhomogeneous radial deformation on the scattering of antiplane elastic waves from a cylindrical cavity is determined. Three popular nonlinear strain energy functions are considered: the neo-Hookean, the Mooney–Rivlin and a two-term Arruda–Boyce model. A new method is developed to analyse and solve the governing wave equations. It exploits their properties to determine an asymptotic solution in the far-field, which is then used to derive a boundary condition to numerically evaluate the equations local to the cavity. This method could be applied to any linear ordinary differential equation whose inhomogeneous coefficients tend to a constant as its independent variable tends to infinity. The effect of the pre-stress is evaluated by considering the scattering cross section. A longitudinal stretch is found to decrease the scattered power emanating from the cavity, whereas a compression increases it. The effect of the pressure difference depends on the strain energy function employed. For a Mooney–Rivlin material, a cavity inflation increases the scattered power and a deflation decreases it; for a neo-Hookean material, the scattering cross section is unaffected by the radial deformation; and for a two-term Arruda–Boyce material, both inflation and deflation are found to decrease the scattered power.

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Sahu, Raj Kumar, and Karali Patra. "Estimation of Elastic Modulus of Dielectric Elastomer Materials Using Mooney-Rivlin and Ogden Models." Advanced Materials Research 685 (April 2013): 331–35. http://dx.doi.org/10.4028/www.scientific.net/amr.685.331.

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Elastomers have low elastic modulus, high specific energy density, light weight, high dielectric constant and high electrical breakdown strength. Due to these properties, elastomers are currently recognized as the future materials for actuator technology and actuators based on these materials are known as dielectric elastomer actuators (DEA). Based on Maxwell stress principle, these actuators transform electric energy directly into mechanical work. Modeling large actuation of this material depends on accurate estimation of E-modulus which varies with strain. In this work, E-modulus values at different strain are estimated based Mooney-Rivlin & Ogden Models. The model predicted values of E-modulus are compared with experimentally estimated values of E-modulus and found to be in good agreement.

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Žmindák, Milan, Pavol Novák, and Vladimir Dekýš. "Repair of Composite Structure Using Cold Sleeve with Polymer Filling Material." Advanced Materials Research 897 (February 2014): 83–86. http://dx.doi.org/10.4028/www.scientific.net/amr.897.83.

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This paper describes the failure analysis of a cold sleeve using modified adhesive layer of polymer Protegol. The tensile test was carried out to estimate material properties of the polymer and the two-parameter Mooney-Rivlin constitutive model was used. An axisymmetric FEM model with additional plane symmetry was developed for simulation of cold sleeve. Cohesive zone material failure modeling uses contact elements to model interface delamination. The bilinear behaviour of sleeve material with normal tractions and separation distances and material nonlinearities together with contact were considered. Commercial finite element software ANSYS was utilized to carry out the static nonlinear analysis.

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Chow, C. L., W. H. Tai, and C. T. Liu. "Prediction of Mixed-mode Fracture in Participate Composite Using a Damage Criterion." Tire Science and Technology 29, no. 2 (2001): 79–90. http://dx.doi.org/10.2346/1.2135233.

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Abstract In this paper, a damage-coupled Mooney-Rivlin hyperelastic material model and a damage failure criterion are developed based on the theory of damage mechanics. The model is applied to predict the crack initiation angle and fracture load of particulate composite plate under mixed load. The prediction is achieved by implementing the damage model in a finite element package ABAQUS through its user-specified material subroutine. The inclined angles of the pre-crack are θ = 0, 15, 30, 45, 60, and 75°. The predictions are compared with the test results and found to be in satisfactory agreement.

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Fan, Longling, Jing Yao, Chun Yang, Di Xu, and Dalin Tang. "Patient-Specific Echo-Based Left Ventricle Models for Active Contraction and Relaxation Using Different Zero-Load Diastole and Systole Geometries." International Journal of Computational Methods 16, no. 03 (2019): 1842014. http://dx.doi.org/10.1142/s0219876218420148.

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A new modeling approach using two different zero-load geometries (diastole and systole) was introduced to properly model active contraction and relaxation for more accurate stress/strain calculations. Ventricle diastole and systole material parameter values were also determined based on in vivo data. Echo-based computational two-layer left ventricle (LV) models using one zero-load geometry (1G) and two zero-load geometries (2G) were constructed. Material parameter values in Mooney–Rivlin models were also adjusted to match echo LV volume data. Effective Young’s moduli (YM) were calculated for ventricle materials for easy comparison. The 2G models may lead to more accurate ventricle stress/strain calculations and material parameter value estimations.

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Li, Zhi Miao, Ju Bao Liu, and Yu Qi Ding. "Finite Element Analysis of the Packer at Fracturing." Applied Mechanics and Materials 385-386 (August 2013): 159–62. http://dx.doi.org/10.4028/www.scientific.net/amm.385-386.159.

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According to the working principle and structural feature of compressive packer, mechanic analysis of rubber tubes was done with adopting Mooney-Rivlin model. The contact stress between rubber tube and the casing and axial compression distance were figured out at 83MPa of the differential pressure between inside and outside string. The results show that the middle tube has the function of beginning to set the paker and the lower tube seals and separate the layers. Upper tubing should be installed the equipment to prevent shoulder protruding.

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Muslov, S. A., A. I. Lotkov, S. D. Arutyunov, and T. M. Albakova. "Calculation of the parameters of mechanical properties of the heart muscle." Perspektivnye Materialy 12 (2020): 42–52. http://dx.doi.org/10.30791/1028-978x-2020-12-42-52.

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A review of studies of the mechanical properties of human and animal heart tissues has been performed. Based on literature data, a form of approximating function is found for the dependence of the Young’s modulus of the ventricles of the human heart on the magnitude of the deformation. The average values of the Young’s modulus and other elastic constants were calculated and compared with the known experimental values. The coefficients C1 and C2 of the two-parameter hyperelastic myocardial Mooney-Rivlin model are calculated.

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Nazali, Nur Nabila Mohd, Nur Ani Aniqah Anirad, and Nor Fazli Adull Manan. "The Mechanical Properties of Mimic Skin." Applied Mechanics and Materials 899 (June 2020): 73–80. http://dx.doi.org/10.4028/www.scientific.net/amm.899.73.

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This paper focuses on the characterized of the mechanical properties and hyper elastic behavior of lab made skin. Bovine Serum Albumin (BSA) combined with gelatin as a base. BSA is a plasma lead concentrations or heparin plasma which is separated from blood sample and it is not associated with significant changes in iron or hemoglobin concentrations. In general, the gelatin is widely used as the best material for skin substitution since it exhibits the characteristic of human skin. However, the lab made skin layer was made of non-halal type gelatin (Type B). The methodology process started by adding the BSA and using the type A gelatin to carry out the mechanical properties and hy-per elastic behavior of halal lab made skin layer. A uniaxial tensile test standard that being used in this study is ASTM D412. The raw data (Load-Extension) from computational was plotted on graph stress-strain. The numerical approach such as Mooney-Rivlin model and Yeoh’s model were selected to analyze a stress-stretch of composition gelatin and BSA. From the results Mooney-Rivlin model, the con-stant, C1 is in the range of (0.0187-0.0658) MPa and C2 is in the range of (0.0628-0.0737) MPa. Meanwhile the constant, CP for Yeoh model is in the range of (0.0748-0.0861) MPa. As a conclusion, the composition of gelatin and Bovine Serum Albumin is a best combina-tion as it increases the strength of the lab made skin layer. Therefore, the most suitable composition is 10 wt.% of gelatin and Bovine Serum Albumin.

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Valencia, Alvaro, Benjamin Blas, and Jaime H. Ortega. "Modeling of Brain Shift Phenomenon for Different Craniotomies and Solid Models." Journal of Applied Mathematics 2012 (2012): 1–20. http://dx.doi.org/10.1155/2012/409127.

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This study investigates the effects of different solid models on predictions of brain shift for three craniotomies. We created a generic 3D brain model based on healthy human brain and modeled the brain parenchyma as single continuum and constrained by a practically rigid skull. We have used elastic model, hyperelastic 1st, 2nd, and 3rd Ogden models, and hyperelastic Mooney-Rivlin with 2- and 5-parameter models. A pressure on the brain surface at craniotomy region was applied to load the model. The models were solved with the finite elements package ANSYS. The predictions on stress and displacements were compared for three different craniotomies. The difference between the predictions of elastic solid model and a hyperelastic Ogden solid model of maximum brain displacement and maximum effective stress is relevant.

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Keerthiwansa, R., J. Javorik, J. Kledrowetz, and P. Nekoksa. "Elastomer testing: the risk of using only uniaxial data for fitting the Mooney-Rivlin hyperelastic-material model." Materiali in tehnologije 52, no. 1 (2018): 3–8. http://dx.doi.org/10.17222/mit.2017.085.

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WANG, MONAN, XIANJUN AN, and NING YANG. "MODELING AND SIMULATION OF SKELETAL MUSCLE BASED ON COMBINED EXPONENTIAL AND POLYNOMIAL MODEL." Journal of Mechanics in Medicine and Biology 17, no. 07 (2017): 1740025. http://dx.doi.org/10.1142/s0219519417400255.

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With the aim to build an accurate skeletal muscle simulation model, the biomechanical modeling and solution method of skeletal muscle were developed. First, the Mooney–Rivlin model, polynomial model, exponential model, logarithmic model, combined exponential and polynomial model were compared. The biomechanical model of skeletal muscle was built by combining the exponential and polynomial models. Second, the geometric non-linearity problem and material non-linearity problem of the biomechanical model were solved by using the finite element method. The program for this solution was implemented using Visual Studio 2012. Finally, the simulation results were compared to the experimental results. The maximum error between the simulation curve and the experiment stress–strain curve was 0.00149[Formula: see text]MPa. Finite element simulation for the lateral femoral muscle was conducted using the program developed in this study.

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