Journal articles: 'Murnaghan hyperelastic material model'

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Jemioło, Stanisław, and Aleksander Franus. "Numerical implementation of the Murnaghan material model in ABAQUS/Standard." MATEC Web of Conferences 196 (2018): 01042. http://dx.doi.org/10.1051/matecconf/201819601042.

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The paper presents a numerical implementation of the Murnaghan material model (M) [1] in the finite element method software ABAQUS / Standard v. 6.14 [2]. The UHYPER user subroutine is employed, which is suitable for the class of isotropic hyperelastic models [3]. As a special case of the M model, the Saint Venant-Kirchhoff (SVK) model is considered [4]. Formal verification on the basis of elementary tests is performed. Among others, a special attention is paid to a simple shear deformation. In all tested types of deformation, analytical values confirms results based on the finite element procedure within assumed numerical precision and accuracy. It should be noted that the stored-energy function of the M and SVK models do not meet any requirements of the mathematical theory of non-linear elasticity [4, 5]. Therefore, these models are suitable for relatively small deformations, while there are no restrictions on finite rotations. As an example of applications, a tube under axial compression is considered in two cases. Various starting parameters for the Riks procedure [6, 7] are adopted to obtain different solutions of corresponding boundary value problem. Material parameters of steel are considered according to Lurie [8].

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Rushchitsky, J. J. "On the Constants of the Nonlinear Murnaghan’s Hyperelastic Material Model." International Applied Mechanics 52, no. 5 (September 2016): 508–19. http://dx.doi.org/10.1007/s10778-016-0771-5.

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Yuan, Maodan, Anbang Dai, Lin Liao, Yan Chen, and Xuanrong Ji. "Numerical Study on Surface Roughness Measurement Based on Nonlinear Ultrasonics in Through-Transmission and Pulse-Echo Modes." Materials 14, no. 17 (August 26, 2021): 4855. http://dx.doi.org/10.3390/ma14174855.

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Ultrasonic is one of the well-known methods for surface roughness measurement, but small roughness will only lead to a subtle variation of transmission or reflection. To explore sensitive techniques for surfaces with small roughness, nonlinear ultrasonic measurement in through-transmission and pulse-echo modes was proposed and studied based on an effective unit-cell finite element (FE) model. Higher harmonic generation in solids was realized by applying the Murnaghan hyperelastic material model. This FE model was verified by comparing the absolute value of the nonlinearity parameter with the analytical solution. Then, random surfaces with different roughness values ranging from 0 μm to 200 μm were repeatedly generated and studied in the two modes. The through-transmission mode is very suitable to measure the surfaces with roughness as small as 3% of the wavelength. The pulse-echo mode is sensitive and effective to measure the surface roughness ranging from 0.78% to 5.47% of the wavelength. This study offers a potential nondestructive testing and monitoring method for the interfaces or inner surfaces of the in-service structures.

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Zhao, Chengwei, Sunia Tanweer, Jian Li, Min Lin, Xiang Zhang, and Yang Liu. "Nonlinear Guided Wave Tomography for Detection and Evaluation of Early-Life Material Degradation in Plates." Sensors 21, no. 16 (August 16, 2021): 5498. http://dx.doi.org/10.3390/s21165498.

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In this paper, the possibility of using nonlinear ultrasonic guided waves for early-life material degradation in metal plates is investigated through both computational modeling and study. The analysis of the second harmonics of Lamb waves in a free boundary aluminum plate, and the internal resonance conditions between the Lamb wave primary modes and the second harmonics are investigated. Subsequently, Murnaghan’s hyperelastic model is implemented in a finite element (FE) analysis to study the response of aluminum plates subjected to a 60 kHz Hanning-windowed tone burst. Different stages of material degradation are reflected as the changes in the third order elastic constants (TOECs) of the Murnaghan’s model. The reconstructed degradations match the actual ones well across various degrees of degradation. The effects of several relevant factors on the accuracy of reconstructions are also discussed.

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Jemiolo, Stanislaw, Aleksander Franus, and Wlodzimierz Domanski. "Attempt to Assess the Scope of Applicability of a Hyperelastic Murnaghan’s Material Model in the Case of Elastomers." IOP Conference Series: Materials Science and Engineering 661 (November 20, 2019): 012040. http://dx.doi.org/10.1088/1757-899x/661/1/012040.

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Major, Izabela, and Maciej Major. "Application of the Perturbation Method for Determination of Eigenvalues and Eigenvectors for the Assumed Static Strain." Civil and Environmental Engineering 10, no. 2 (December 1, 2014): 111–20. http://dx.doi.org/10.2478/cee-2014-0020.

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Abstract The paper presents the perturbation method which was used for computation of eigenvalues and eigenvectors for the assumed homogeneous state of strain in the hyperelastic Murnaghan material. The values calculated might be used for determination of the rate of propagation of unit vectors of wave amplitude for other non-linear

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Соколова, Марина Юрьевна, and Юрий Владимирович Астапов. "Elastic waves in the Hencky-Murnaghan material." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 3(45) (December 29, 2020): 108–20. http://dx.doi.org/10.37972/chgpu.2020.26.33.011.

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Рассмотрены динамические методы идентификации модели нелинейно упругого деформируемого тела. По эффективным фазовым скоростям продольных и поперечных волн, распространяющихся вдоль и поперек оси сжимаемого стержня, возможно определить пять констант упругости второго и третьего порядков, входящих в соотношения модели. В статье получены расчетные формулы и приведен пример определения зависимости фазовых скоростей для полиамида 6. The dynamic methods for selecting models of a nonlinear elastic deformable body are considered. Depending on the model, five elastic constants of the second and third orders, which are available in the relations of the models, can be determined. The calculation formulas and the given example of determining the dependence of phase velocities for polyamide 6 are obtained in the article.

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Соколова, Марина Юрьевна, and Юрий Владимирович Астапов. "Elastic waves in the Hencky-Murnaghan material." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 3(45) (December 29, 2020): 108–20. http://dx.doi.org/10.37972/chgpu.2020.26.33.011.

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Рассмотрены динамические методы идентификации модели нелинейно упругого деформируемого тела. По эффективным фазовым скоростям продольных и поперечных волн, распространяющихся вдоль и поперек оси сжимаемого стержня, возможно определить пять констант упругости второго и третьего порядков, входящих в соотношения модели. В статье получены расчетные формулы и приведен пример определения зависимости фазовых скоростей для полиамида 6. The dynamic methods for selecting models of a nonlinear elastic deformable body are considered. Depending on the model, five elastic constants of the second and third orders, which are available in the relations of the models, can be determined. The calculation formulas and the given example of determining the dependence of phase velocities for polyamide 6 are obtained in the article.

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Rugsaj, Ravivat, and Chakrit Suvanjumrat. "Finite Element Analysis of Hyperelastic Material Model for Non-Pneumatic Tire." Key Engineering Materials 775 (August 2018): 554–59. http://dx.doi.org/10.4028/www.scientific.net/kem.775.554.

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This research aimed to find an appropriated hyperelastic material model for the finite element analysis (FEA) of a non-pneumatic tire (NPT). The innovative method involving water jet cutting technique was performed to prepare the tensile and compressive test specimens from the non-pneumatic tire, TWEEL, which was developed by Michelin. The stress-strain relationship of material testing results was fitted to select the suitable constitutive model. The FEA was performed and compared to the physical experiment to validate the hyperelastic material model. The suitable hyperelastic material model can be used in the development of NPT for the further work.

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Sumelka, Wojciech, and George Z. Voyiadjis. "A hyperelastic fractional damage material model with memory." International Journal of Solids and Structures 124 (October 2017): 151–60. http://dx.doi.org/10.1016/j.ijsolstr.2017.06.024.

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Çalışkan, Kemal, Erhan Ilhan Konukseven (1), and Y. Samim Ünlüsoy. "Product Based Material Testing for Hyperelastic Suspension Jounce Bumper Design with FEA." Key Engineering Materials 450 (November 2010): 119–23. http://dx.doi.org/10.4028/www.scientific.net/kem.450.119.

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The basic problem in the finite element analysis of parts made of hyperelastic materials is the identification of mathematical material model coefficients. Furthermore, selection of a suitable mathematical hyperelastic material model may not be straightforward. In this study, a systematic design methodology is presented for hyperelastic suspension jounce bumpers. The presented methodology involves a critical examination of material testing procedures, material model selection, and coefficient identification. The identified material model coefficients are verified through comparison of the finite element analysis results with actual tests.

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Chen, Wei, Lin Wang, and Huliang Dai. "Nonlinear Free Vibration of Hyperelastic Beams Based on Neo-Hookean Model." International Journal of Structural Stability and Dynamics 20, no. 01 (November 28, 2019): 2050015. http://dx.doi.org/10.1142/s0219455420500157.

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The investigation of hyperelastic responses of soft materials and structures is essential for understanding of the mechanical behaviors and for the design of soft systems. In this paper, by considering both the material and geometrical nonlinearities, a new neo-Hookean model for the hyperelastic beam is developed with focus on its nonlinear free vibration with large strain deformations. The neo-Hookean model is employed to capture the large strain deformation of the hyperelastic beam. The governing equations of the hyperelastic beam are derived by using Hamilton’s principle. To avoid expensive calculations for solving the nonlinear governing equations, a simplified Taylor-series expansion model is proposed. The effects of two key system parameters, i.e. the initial displacement amplitude and the slenderness ratio, on the nonlinear free vibrations of the hyperelastic beam are numerically analyzed. The bifurcation diagrams, displacement time traces, phase portraits and power spectral diagrams are presented for the nonlinear free vibrations of the hyperelastic beam. For small initial displacement amplitudes, it is found that the hyperelastic beam will undergo limit cycle oscillations, depending on the initial amplitude employed. For initial displacement amplitudes large enough, interestingly, the free vibration of the hyperelastic beam will become quasi-periodic or chaotic, which were rarely reported for the free vibration of linearly elastic beams. Also observed is the traveling wave feature of oscillating shapes of the hyperelastic beam, indicating that higher-order modes of the beam are excited even for free vibrations. All these new features in the nonlinear free vibrations of hyperelastic beams indicate that the material and geometric nonlinearities play a great role in the dynamic analysis of hyperelastic beams.

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Ansari, Mohd Zahid, Sang Kyo Lee, and Chong Du Cho. "Hyperelastic Muscle Simulation." Key Engineering Materials 345-346 (August 2007): 1241–44. http://dx.doi.org/10.4028/www.scientific.net/kem.345-346.1241.

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Biological soft tissues like muscles and cartilages are anisotropic, inhomogeneous, and nearly incompressible. The incompressible material behavior may lead to some difficulties in numerical simulation, such as volumetric locking and solution divergence. Mixed u-P formulations can be used to overcome incompressible material problems. The hyperelastic materials can be used to describe the biological skeletal muscle behavior. In this study, experiments are conducted to obtain the stress-strain behavior of a solid silicone rubber tube. It is used to emulate the skeletal muscle tensile behavior. The stress-strain behavior of silicone is compared with that of muscles. A commercial finite element analysis package ABAQUS is used to simulate the stress-strain behavior of silicone rubber. Results show that mixed u-P formulations with hyperelastic material model can be used to successfully simulate the muscle material behavior. Such an analysis can be used to simulate and analyze other soft tissues that show similar behavior.

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Wang, Hong, and Gen Yan Wang. "Mechanical Response of Ping-Pong Racket to Different Hyperelastic Surface Materials." Advanced Materials Research 941-944 (June 2014): 1566–69. http://dx.doi.org/10.4028/www.scientific.net/amr.941-944.1566.

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Synthetic rubber serving as the surface material of the ping-pong racket has good elasticity and anti-friction. Material parameters such as the hyperelastic constitutive model of the synthetic rubber are some of the critical parameters related to the competition achievement of Ping-Pong. Especially, the certain surface material of the ping-pong racket may be beneficial to the certain way of the racketting technique. The material parameters’ change may change the elasticity, plasticity, and anti-friction of the surface which would affect the playing level of the athletes. In order to access the relation between the hyperelastic ability and the racketting strength, it is necessary to predict the mechanical response of the ping-pong racket to the different hyperelastic surface materials. A two-dimensional finite element model is developed to predict the mechanical response between the hyperelastic ability and the racketting strength due to the material parameters’ change of the synthetic rubber. The Mooney-Rivlin model is considered as the hyperelastic material model using ANSYS soft in order to simulate the ping-pong racket’s surface material precisely. The different surface material parameters must affect the surface stress or strain of the racket which may change the athletes’ achievement. The special batting technique may acquire the special hyperelastic materials parameters. The rule will be obtained between the hyperelastic material parameters and the stress distribution of the racket surface materials. The ability accurately predicting the mechanical response of the ping-pong racket surface will greatly help the ping-pong racket designers in determining the suitable racket to the particular technology’s athletes.

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Thiagarajan, Ganesh, Yonggang Y. Huang, and K. Jimmy Hsia. "Fracture Simulation Using an Elasto-Viscoplastic Virtual Internal Bond Model With Finite Elements." Journal of Applied Mechanics 71, no. 6 (November 1, 2004): 796–804. http://dx.doi.org/10.1115/1.1796451.

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A virtual internal bond (VIB) model for isotropic materials has been recently proposed by Gao (Gao, H., 1997, “Elastic Waves in a Hyperelastic Solid Near its Plane Strain Equibiaxial Cohesive Limit,” Philos. Mag. Lett. 76, pp. 307–314) and Gao and Klein (Gao, H., and Klein, P., 1998, “Numerical Simulation of Crack Growth in an Isotropic Solid With Randomized Internal Cohesive Bonds,” J. Mech. Phys. Solids 46(2), pp. 187–218), in order to describe material deformation and fracture under both static and dynamic loading situations. This is made possible by incorporating a cohesive type law of interaction among particles at the atomistic level into a hyperelastic framework at the continuum level. The finite element implementation of the hyperelastic VIB model in an explicit integration framework has also been successfully described in an earlier work by the authors. This paper extends the isotropic hyperelastic VIB model to ductile materials by incorporating rate effects and hardening behavior of the material into a finite deformation framework. The hyperelastic VIB model is formulated in the intermediate configuration of the multiplicative decomposition of the deformation gradient framework. The results pertaining to the deformation, stress-strain behavior, loading rate effects, and the material hardening behavior are studied for a plate with a hole problem. Comparisons are also made with the corresponding hyperelastic VIB model behavior.

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Antunes, P. J., Gustavo R. Dias, A. T. Coelho, F. Rebelo, and T. Pereira. "Hyperelastic Modelling of Cork-Polyurethane Gel Composites: Non-Linear FEA Implementation in 3D Foot Model." Materials Science Forum 587-588 (June 2008): 700–705. http://dx.doi.org/10.4028/www.scientific.net/msf.587-588.700.

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The CPGC – Cork-Polyurethane Gel Composite is a material that is mechanically characterized by non-linear elastic behaviour at large deformations. The non-linear behaviour can be modelled by hyperelastic constitutive models based on strain energy functions enabling a structured phenomenological framework for CPGC material modelling. The CPGC is a promising material for human comfort enhancement and dynamic damping/control applications. This paper presents the experimental methodology used for the CPGC evaluation of material parameters used in the hyperelastic models and the finite element model build-up. A 3D foot FEA model is presented in order to evaluate the performance of the hyperelastic model in a real case situation and the mechanical performance of shoe insoles, namely, trough the monitoring of the contact pressure values at the insole/foot interface.

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Ciambella, J., and G. Saccomandi. "A continuum hyperelastic model for auxetic materials." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2163 (March 8, 2014): 20130691. http://dx.doi.org/10.1098/rspa.2013.0691.

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We propose a simple mathematical model to describe isotropic auxetic materials in the framework of the classical theory of nonlinear elasticity. The model is derived from the Blatz–Ko constitutive equation for compressible foams and makes use of a non-monotonic Poisson function. An application to the modelling of auxetic foams is considered and it is shown that the material behaviour is adequately described with only three constitutive parameters.

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Charmetant, Adrien, Emmanuelle Vidal-Sallé, and Philippe Boisse. "3D Hyperelastic Constitutive Model for Yarn Behaviour Description." Key Engineering Materials 504-506 (February 2012): 267–72. http://dx.doi.org/10.4028/www.scientific.net/kem.504-506.267.

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The preforming stage of the LCM composite manufacturing processes lead to fibrous reinforcement deformations which may be very large especially for double curvature shapes. Those deformations have significant influence on the second stage of the process, i.e. the injection of the resin. A way to predict accurately the spatial distribution of the permeability tensor consists in simulating for various configurations, the deformed shape of the reinforcement at the scale of the yarns. Mesoscopic scale analyses of textile reinforcements generally consider the yarns as a continuous material despite their fibrous nature. In order to have an accurate simulation tool, it is necessary to build up a constitutive law which accounts for the physical specificities linked to the microstructure of the yarns. Several models exist with reasonable accuracy. The present paper proposes a new approach in the hyperelasticity framework. The proposed model is based on the definition of mathematical invariants linked to the four main deformation modes of the yarn material: tension, compaction, longitudinal shear and transverse shear. The strain energy potential build up with those invariants is identified using classical fabric material tests: uni- and bi-axial tension and compression. The model has been validated on laboratory tests such as bias extension tests and gives promising results.

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Golbad, Sara, and Mohammad Haghpanahi. "Hyperelastic Model Selection of Tissue Mimicking Phantom Undergoing Large Deformation and Finite Element Modeling for Elastic and Hyperelastic Material Properties." Advanced Materials Research 415-417 (December 2011): 2116–20. http://dx.doi.org/10.4028/www.scientific.net/amr.415-417.2116.

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Pathologies in soft tissues are associated with changes in their elastic properties. Tumor tissues are usually stiffer than the fat tissues and other normal tissues and show the nonlinear behavior in large deformations. There have been a lot of researches about elastography (linear and nonlinear) as a new detecting technique based on mechanical behavior of tissue. In order to formulate the tissue’s nonlinear behavior, a strain energy function is required. For better estimation of nonlinear tissue parameters in elasticity imaging, non linear stress-strain curve of phantom is used. This work presents hyperelastic measurement results of tissue-mimicking phantom undergoing large deformation during uniaxial compression. For phantom samples, 8 hyperelastic models have been used. The results indicate that polynomial model with N=2 is the most accurate in terms of fitting experimental data. To compare the results between elastic and hyperelastic model, a 3-D finite element numerical model developed based on two different materials of elastic and hyperelastic material properties. The comparison confirm the approach of other recent studies about necessity of hyperelastic elastography and state that hyperelastic elastography should be used to formulate a technique for breast cancer diagnosis.

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Zanelli, L., A. Montanaro, E. L. Carniel, P. G. Pavan, and A. N. Natali. "The study of equivalent material parameters in a hyperelastic model." International Journal of Non-Linear Mechanics 89 (March 2017): 142–50. http://dx.doi.org/10.1016/j.ijnonlinmec.2016.12.014.

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Jemioło, S., and A. Franus. "A slightly compressible hyperelastic material model with the Mullins effect." IOP Conference Series: Materials Science and Engineering 1015, no. 1 (January 1, 2021): 012004. http://dx.doi.org/10.1088/1757-899x/1015/1/012004.

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Hesebeck, Olaf. "Transformation of Test Data for the Specification of a Viscoelastic Marlow Model." Solids 1, no. 1 (November 13, 2020): 2–15. http://dx.doi.org/10.3390/solids1010002.

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The combination of hyperelastic material models with viscoelasticity allows researchers to model the strain-rate-dependent large-strain response of elastomers. Model parameters can be identified using a uniaxial tensile test at a single strain rate and a relaxation test. They enable the prediction of the stress–strain behavior at different strain rates and other loadings like compression or shear. The Marlow model differs from most hyperelastic models by the concept not to use a small number of model parameters but a scalar function to define the mechanical properties. It can be defined conveniently by providing the stress–strain curve of a tensile test without need for parameter optimization. The uniaxial response of the model reproduces this curve exactly. The coupling of the Marlow model and viscoelasticity is an approach to create a strain-rate-dependent hyperelastic model which has good accuracy and is convenient to use. Unfortunately, in this combination, the Marlow model requires to specify the stress–strain curve for the instantaneous material response, while experimental data can be obtained only at finite strain rates. In this paper, a transformation of the finite strain rate data to the instantaneous material response is derived and numerically verified. Its implementation enables us to specify hyperelastic materials considering strain-rate dependence easily.

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Wrubleski, Eduardo Guilherme Mötke, and Rogério Marczak. "A new pseudo-energy function to simulate the Mullins effect." Journal of Elastomers & Plastics 50, no. 6 (December 5, 2017): 554–75. http://dx.doi.org/10.1177/0095244317741760.

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Several authors have proposed different parameters to include the softening effect in hyperelastic models; however, for a number of materials, softening parameters could be further improved. This article proposes a new softening parameter to include Mullins effect in hyperelastic material models. The methodology employed can be also used in cases with hysteresis or damage in a hyperelastic material, however this methodology modifies the behavior of the material differently from damage theories. Common hyperelastic constitutive models do not include dissipation effects and so the present work intends to fill this gap. Experimental data for silicone in uniaxial tensile test, equibiaxial, and pure shear tests were modeled in order to calibrate the models. The softening parameters essentially changes the constitutive law from the loading to the unloading path. Therefore, it is still necessary to use a hyperelastic model, and here Ogden and Hoss-Marczak material models were used. The obtained results show good agreement with experimental data even when simulating with a compressible finite element code and it can model isotropic Mullins effect.

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Karimzadeh, Atefeh, Majid Reza Ayatollahi, Seyed Saeid Rahimian Koloor, Abd Razak Bushroa, Mohd Yazid Yahya, and Mohd Nasir Tamin. "Assessment of Compressive Mechanical Behavior of Bis-GMA Polymer Using Hyperelastic Models." Polymers 11, no. 10 (September 27, 2019): 1571. http://dx.doi.org/10.3390/polym11101571.

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Despite wide industrial applications of Bis-GMA polymer, very few studies are available about the material classification, mechanical properties, and behavior of this material. In this study, the compressive behavior of Bis-GMA polymer was studied using different hyperelastic constitutive models through a hybrid experimental-computational process. Standard uniaxial compression tests were conducted to extract the mechanical behavior and structural response of the Bis-GMA polymer. A nano-indentation experiment was used to verify the compressive behavior of Bis-GMA polymer in the form of hyperelastic behavior. The finite element model and real-time simulation of the test incorporating different hyperelastic models were developed in comparison with the experimental finding to obtain the proper type of hyperelastic behavior of Bis-GMA polymer. The results indicate that a second-order polynomial hyperelastic model is the best fit to predict the behavior of Bis-GMA polymer. Next, the validated model was used to determine the true stress–strain curve of the Bis-GMA polymer.

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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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Liu, Yingfeng, Qiong Rao, Ming Chen, Xiongqi Peng, and Shaoqing Shi. "A Visco-Hyperelastic Constitutive Model for Multilayer Polymer Membranes and its Application in Packaging Air Cushion." International Journal of Applied Mechanics 08, no. 05 (July 2016): 1650062. http://dx.doi.org/10.1142/s1758825116500629.

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Air cushion is an important packaging material with admirable cushion property in protecting articles from damage. Polymer membrane in air cushion renders a highly nonlinear elastic and rate dependent mechanical behavior in experimental tensile test. A visco-hyperelastic constitutive model for a polymer membrane of an air cushion is developed by additively decomposing its mechanical response into a hyperelastic portion and a viscoelastic portion. Material parameters are consecutively obtained by matching experimental data of static and dynamic uni-axial tensile tests of the membrane, respectively. Compression test of a single air column of the air cushion is conducted as a means of validation on the proposed constitutive model. By comparing simulation results with experimental data, it is shown that the proposed visco-hyperelastic model can properly characterize the mechanical behavior of the air cushion packaging material. The model can be applied to evaluate cushion performance of air cushions and their optimum design.

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Fu, Xin Tao, Ze Peng Wang, and Lian Xiang Ma. "Numerical Mechanical Analysis of Filled Rubber under Different Deformation States Based on a New Hyperelastic Constitutive Model." Materials Science Forum 1032 (May 2021): 15–22. http://dx.doi.org/10.4028/www.scientific.net/msf.1032.15.

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The accuracy of the rubber constitutive model characterizing experiment data has a crucial influence on the mechanical analysis of rubber structures. In this paper, a new improved hyperelastic constitutive model is proposed, and the model is derived into the stress-strain forms of uniaxial tension, equibiaxial tension and pure shear. Based on the experimental data of filled rubber, the material parameters of each deformation state are obtained by using the newly proposed rubber hyperelastic constitutive model, and the uniaxial tensile (UT), Equibiaxial tension (ET) and Pure shear (PS) specimens are simulated and calculated in the finite element software. the stress state of each finite element specimen is analyzed and the obtained simulation data are compared with the experimental data. It is found that the new model can accurately characterize the hyperelastic mechanical properties of the experimental specimens in different deformation states. At the same time, the reasons for the deviation from the experimental data in the process of plane tensile simulation are analyzed and explained comprehensively. The reliability and accuracy of the classical rubber constitutive relations of polynomial models and eight-chain model are studied. the results show that different hyperelastic models have different ability to describe the hyperelastic behavior in different deformation states. the hyperelastic constitutive model proposed in this paper can be easily embedded into finite element software and has the advantages of accurate results, few material parameters and simple testing.

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Xiao, Yihua, Ziqiang Tang, and Xiangfu Hong. "Inverse Parameter Identification for Hyperelastic Model of a Polyurea." Polymers 13, no. 14 (July 9, 2021): 2253. http://dx.doi.org/10.3390/polym13142253.

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An inverse procedure was proposed to identify the material parameters of polyurea materials. In this procedure, a polynomial hyperelastic model was chosen as the constitutive model. Both uniaxial tension and compression tests were performed for a polyurea. An iterative inverse method was presented to identify parameters for the tensile performance of the polyurea. This method adjusts parameters iteratively to achieve a good agreement between tensile forces from the tension test and its finite element (FE) model. A response surface-based inverse method was presented to identify parameters for the compression performance of the polyurea. This method constructs a radial basis function (RBF)-based response surface model for the error between compressive forces from the compression test and its FE model, and it employs the genetic algorithm to minimize the error. With the use of the two inverse methods, two sets of parameters were obtained. Then, a complete identified uniaxial stress–strain curve for both tensile and compressive deformations was obtained with the two sets of parameters. Fitting this curve with the constitutive equation gave the final material parameters. The present inverse procedure can simplify experimental configurations and consider effects of friction in compression tests. Moreover, it produces material parameters that can appropriately characterize both tensile and compressive behaviors of the polyurea.

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Gajewski, Marcin, Radosław Szczerba, and Stanisław Jemioło. "Modelling of Elastomeric Bearings with Application of Yeoh Hyperelastic Material Model." Procedia Engineering 111 (2015): 220–27. http://dx.doi.org/10.1016/j.proeng.2015.07.080.

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Itskov, Mikhail. "A generalized orthotropic hyperelastic material model with application to incompressible shells." International Journal for Numerical Methods in Engineering 50, no. 8 (2001): 1777–99. http://dx.doi.org/10.1002/nme.86.

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YANG, ZHENGZHI, ZHIWEI DING, ZISHUN LIU, SOMSAK SWADDIWUDHIPONG, YI MIN TAN, and KEVIN LEE. "COMPARATIVE STUDY ON STRENGTH OF KNEE JOINT USING VARIOUS MATERIAL MODELS." International Journal of Computational Materials Science and Engineering 01, no. 02 (June 2012): 1250013. http://dx.doi.org/10.1142/s2047684112500133.

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In this study, we adopt different material models to study the strength and stiffness of menisci of the knee joint using finite element method. The three-dimensional (3-D) knee joint finite element model is constructed based on the Magnetic Resonance (MR) images of a human knee joint, and the strength of menisci is analyzed under a specific vertical loading case. In this paper we categorize and implement three types of appropriate material properties, namely isotropic linearly elastic, transversely isotropic elastic and isotropic hyperelastic for menisci of the knee joint. Different strain energy models are also studied and compared under hyperelastic category. The comparative study demonstrates that the hyperelastic model with Ogden form is more appropriate in modeling menisci of the knee joint. By referring to the test data of different material properties from earlier studies by various researchers, we hope to provide a comparative study leading to appropriate menisci material models and properties for finite element analyses of knee joint structures.

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Nam, Tran Huu. "Using FEM for large deformation analysis of inflated air-spring cylindrical shell made of rubber-textile cord composite." Vietnam Journal of Mechanics 28, no. 1 (April 17, 2006): 10–20. http://dx.doi.org/10.15625/0866-7136/28/1/5474.

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An orthotropic hyperelastic constitutive model is presented for large deformation analysis of the nonlinear anisotropic hyperelastic material of the cylindrical air-spring shell used in vibroisolation of driver's seat. Nonlinear hyperelastic constitutive equations of orthotropic composite material are incorporated into the finite strain analysis by finite element method (FEM). The results of deformation analysis of the inflated air-spring shell made of composite with rubber matrix reinforced by textile cords are given. Obtained numerical results of deformation corresponding to the experimentally measured deformation of the inflated cylindrical air-spring.

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Chanda, Arnab, Subhodip Chatterjee, and Vivek Gupta. "Soft composite based hyperelastic model for anisotropic tissue characterization." Journal of Composite Materials 54, no. 28 (June 23, 2020): 4525–34. http://dx.doi.org/10.1177/0021998320935560.

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Soft tissues are complex anisotropic composite systems comprising of multiple differently oriented layers of fiber embedded within a soft matrix. To date, soft tissues have been mainly characterized using simplified linear elastic material models, isotropic viscoelastic and hyperelastic models, and transversely isotropic models. In such models, the effect of fiber volume fraction (FVF), fiber orientation, and fiber-matrix interactions are missing, inhibiting accurate characterization of anisotropic tissue properties. The current work addresses this literature gap with the development of a novel soft composite based material framework to model tissue anisotropy. In this model, the fiber and matrix are considered as separate hyperelastic materials, and fiber-matrix interaction is modeled using multiplicative decomposition of the deformation gradient. The effect of the individual contribution of the fibers and matrix are introduced into the numerical framework for a single soft composite layer, and fiber orientation effects are incorporated into the strain energy functions. Also, strain energy formulations are developed for multiple soft composite layers with varying fiber orientations and contributions, describing the biomechanical behavior of an entire anisotropic tissue block. Stress-strain relationships were derived from the strain energy equations for a uniaxial mechanical test condition. To validate the model parameters, experimental models of soft composites tested under uniaxial tension were characterized using the novel anisotropic hyperelastic model (R2 = 0.983). To date, such a robust anisotropic hyperelastic composite framework has not been developed, which would be indispensable for experimental characterization of tissues and for improving the fidelity of computational biological models in future.

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Ozelo, R. R. M., P. Sollero, and A. L. A. Costa. "An Alternative Technique to Evaluate Crack Propagation Path in Hyperelastic Materials." Tire Science and Technology 40, no. 1 (March 1, 2012): 42–58. http://dx.doi.org/10.2346/1.3684484.

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Abstract REFERENCE: R. R. M. Ozelo, P. Sollero, and A. L. A. Costa, “An Alternative Technique to Evaluate Crack Propagation Path in Hyperelastic Materials,” Tire Science and Technology, TSTCA, Vol. 40, No. 1, January–March 2012, pp. 42–58. ABSTRACT: The analysis of crack propagation in tires aims to provide safety and reliable life prediction. Tire materials are usually nonlinear and present a hyperelastic behavior. Therefore, the use of nonlinear fracture mechanics theory and a hyperelastic material constitutive model are necessary. The material constitutive model used in this work is the Mooney–Rivlin. There are many techniques available to evaluate the crack propagation path in linear elastic materials and estimate the growth direction. However, most of these techniques are not applicable to hyperelastic materials. This paper presents an alternative technique for modeling crack propagation in hyperelastic materials, based in the J-Integral, to evaluate the crack path. The J-Integral is an energy-based parameter and is applicable to nonlinear materials. The technique was applied using abaqus software and compared to experimental tests.

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Mohd Yusop, Siti Hajar, Mohd Nor Azmi Ab Patar, Anwar P. P. Abdul Majeed, and Jamaluddin Mahmud. "A Parametric Investigation on the Neo-Hookean Material Constant." Advanced Materials Research 915-916 (April 2014): 853–57. http://dx.doi.org/10.4028/www.scientific.net/amr.915-916.853.

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This paper assesses the Neo-Hookean material parameters pertaining to deformation behaviour of hyperelastic material by means of numerical analysis. A mathematical model relating stress and stretch is derived based on Neo-Hookeans strain energy function to evaluate the contribution of the material constant, C1, in the constitutive equation by varying its value. A systematic parametric study was constructed and for that purpose, a Matlab programme was developed for execution. The results show that the parameter (C1) is significant in describing material properties behaviour. The results and findings of the current study further enhances the understanding of Neo-Hookean model and hyperelastic materials behaviour. The ultimate future aim of this study is to come up with an alternative constitutive equation that may describe skin behaviour accurately. This study is novel as no similar parametric study on Neo-Hookean model has been reported before.

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Fahimi, Shayan, Mostafa Baghani, Mohammad-Reza Zakerzadeh, and AmirHossein Eskandari. "Developing a visco-hyperelastic material model for 3D finite deformation of elastomers." Finite Elements in Analysis and Design 140 (February 2018): 1–10. http://dx.doi.org/10.1016/j.finel.2017.10.009.

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Chang, Mengzhou, Zhenqing Wang, and Wenyan Liang. "A visco-hyperelastic model characterizing the electromechanical behavior of nonhomogeneous soft material." AIP Advances 7, no. 9 (September 2017): 095119. http://dx.doi.org/10.1063/1.4990636.

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Pal, Sanjay, and Kinsuk Naskar. "Machine learning model predict stress-strain plot for Marlow hyperelastic material design." Materials Today Communications 27 (June 2021): 102213. http://dx.doi.org/10.1016/j.mtcomm.2021.102213.

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Cudny, Marcin, and Katarzyna Staszewska. "A hyperelastic model for soils with stress-induced and inherent anisotropy." Acta Geotechnica 16, no. 7 (March 5, 2021): 1983–2001. http://dx.doi.org/10.1007/s11440-021-01159-z.

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AbstractIn this paper, modelling of the superposition of stress-induced and inherent anisotropy of soil small strain stiffness is presented in the framework of hyperelasticity. A simple hyperelastic model, capable of reproducing variable stress-induced anisotropy of stiffness, is extended by replacement of the stress invariant with mixed stress–microstructure invariant to introduce constant inherent cross-anisotropic component. A convenient feature of the new model is low number of material constants directly related to the parameters commonly used in the literature. The proposed description can be incorporated as a small strain elastic core in the development of some more sophisticated hyperelastic-plastic models of overconsolidated soils. It can also be used as an independent model in analyses involving small strain problems, such as dynamic simulations of the elastic wave propagation. Various options and features of the proposed anisotropic hyperelastic model are investigated. The directional model response is compared with experimental data available in the literature.

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Markin, Alexey, Marina Sokolova, Dmitrii Khristich, and Yuri Astapov. "The Physically Nonlinear Model of an Elastic Material and Its Identification." International Journal of Applied Mechanics 11, no. 07 (August 2019): 1950064. http://dx.doi.org/10.1142/s1758825119500649.

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This work is devoted to the new variant of relations between the energetically conjugated Hencky strain tensor and corotational Kirchhoff stress tensor. The elastic energy is represented as a third-order polynomial of the Hencky tensor containing five material constants. Unlike the Almansi tensor in the Murnaghan model, the Hencky tensor allows assigning a clear physical meaning to material constants. Linear part of the constitutive relation represents the Hencky model and contains the bulk modulus and the shear modulus. The two extra constants express nonlinear effects at a purely volumetric strain and a purely isochoric strain, whereas the third constant takes into account the possible deviation from the similarity of the deviators of the Hencky stress and strain tensors. The resulting relations are naturally generalized for incompressible materials. In this case, the overall number of constants decreases from five to two. The designed test unit was used for a compression test of prismatic specimens made of incompressible material. The proposed version of the relations is in good agreement with the experimental data on the compression of rubber samples.

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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 (May 1, 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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Tabakci, Alican, and Erhan Ilhan Konukseven. "Mechanical Properties Identification of Viscoelastic/Hyperplastic Materials Using Haptic Device Based Experimental Setup." Key Engineering Materials 486 (July 2011): 115–18. http://dx.doi.org/10.4028/www.scientific.net/kem.486.115.

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Mechanical behavior simulation of viscoelastic materials is a difficult task. In order to obtain accurate simulations, material model should be well chosen and hyperelastic characteristics of the viscoelastic materials should also be incorporated in the model. Once the material model is selected the coefficients can be identified with the help of mechanical tests/experiments. The main goal of this study is to optimize material model’s coefficients by using the designed indenter test setup results and inverse finite element modeling. Indenter test setup was designed by using a haptic device, force sensor and data acquisition card to test the mechanical properties of the viscoelastic/hyperelastic materials. Inverse finite element modeling method is used in order to model the materials according to their material characteristics. The model obtained from the analysis was optimized by using the data obtained from indenter tests. The conformity of the chosen model and the tested materials is shown by inverse finite element modeling and the material model coefficients are proved to be identified correctly.

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Bartolomé, L., A. Aginagalde, A. B. Martínez, M. A. Urchegui, and W. Tato. "EXPERIMENTAL CHARACTERIZATION AND MODELLING OF LARGE-STRAIN VISCOELASTIC BEHAVIOR OF A THERMOPLASTIC POLYURETHANE ELASTOMER." Rubber Chemistry and Technology 86, no. 1 (March 1, 2013): 146–64. http://dx.doi.org/10.5254/rct.13.87998.

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ABSTRACT Thermoplastic polyurethane elastomers (TPUs) are a kind of elastomer that can be processed as thermoplastics. These elastomers exhibit a highly nonlinear behavior characterized by hyper-elastic deformability. Furthermore, the mechanical behavior of these elastomers is time-dependent, that is, they exhibit a viscoelastic behavior. We describe the material response of a TPU under moderate strains (ɛ < 1) by using an overlay visco-hyperelastic model assuming separation of time dependence from nonlinear stress–strain behavior. To achieve this goal, cyclic loading–unloading experimental tests are carried out for two homogeneous deformation states, uniaxial tension and pure shear, and the strain–stress data are then analyzed to fit a hyperelastic model. Conversely, a viscoelastic model is obtained from relaxation tests. Finally, the visco-hyperelastic model is implemented in a finite element calculation tool (ABAQUS), and the numerical results show a reasonable correlation with experimental data. As a result, a overlay visco-hyperelastic model depending on maximum strain is proposed.

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Karyakin, M. I., and L. P. Obrezkov. "STABILITY OF A CYLINDER FROM MURNAGHAN MATERIAL UNDER STRETCHING, COMPRESSION AND INFLATION." Problems of strenght and plasticity 81, no. 1 (2019): 30–39. http://dx.doi.org/10.32326/1814-9146-2019-81-1-30-39.

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The problem of equilibrium and stability of a hollow cylinder subjected to simultaneous uniaxial tension/compression and inflation is considered within the framework of the three-dimensional nonlinear theory of elasticity. To describe the mechanical properties of the material of the cylinder five-constant Murnaghan model is used. By the semi-inverse method the three-dimensional problem is reduced to the study of a nonlinear boundary value problem for an ordinary second-order differential equation. For most sets of material parameters known from the literature, the presence of a falling section in the stretching/inflation diagram, indicating the possible existence of instability zones even in the area of tensile stresses, has been found numerically. The stability analysis was carried out using a bifurcation approach based on linearization of the equilibrium equations in the neighborhood of the constructed solution by means of the method of imposing a small strain on a finite one. The value of a particular deformation characteristic, for which non-trivial solutions of a homogeneous boundary-value problem exist for the equations of neutral equilibrium obtained in the linearization process, was identified with the critical value of the loading parameter, i.e. value at which the system loses stability. As a rule, the coefficient of stretching/shortening of the cylinder and the coefficient of increase/decrease of its internal or external radius were chosen as such parameters. On the plane of the above-mentioned deformation characteristics the areas of stability under tension and compression, as well as under compression by external force and inflation by internal pressure, are constructed. The forms of possible of stability loss depending on the type of stress state are constructed, and the effect on the stability of material and geometric parameters is studied.

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Sebera, Václav, and Jan Tippner. "Possible use of the hyperelastic material models in numerical analysis of the wood-strand mat compression." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 57, no. 4 (2009): 83–94. http://dx.doi.org/10.11118/actaun200957040083.

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The main goal of the work was to evaluate a possibility of using various hyperelastic material models implemented into ANSYS computational system for the numerical analysis of wood-strand mat pressing or wood-based composites. Subsequently, the most suitable hyperelastic model was used as a material model in compression simulation. Pressing itself was modelled as a contact transient analysis with wood-strand mat being defined as a homogenous and isotropic continuum with the chosen material model. In the analysis only displacement degrees of freedom are considered. Output of the simulation is a contact pressure, which is necessary to apply to compress the mat on the required height. The analysis serves as a take-off platform for further research in wood-based composites pressing process.

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Khristich, D. V., Y. V. Astapov, E. V. Artyukh, and M. Y. Sokolova. "NONLINEAR MODEL OF DEFORMA TION OF COMPRESSIBLE SOILS." News of the Tula state university. Sciences of Earth 4, no. 1 (2019): 305–12. http://dx.doi.org/10.46689/2218-5194-2019-4-1-305-312.

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The possibility to apply a physically and geometrically non-linear model of a hyperelastic isotropic material to the description of strains of non-rocky soils is considered. The study examines the stability of the model, restrictions on the model constants, and the definition of the range of deformations within which the model is Drucker stable.

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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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Trivedi, A. R., and C. R. Siviour. "A Simple Rate–Temperature Dependent Hyperelastic Model Applied to Neoprene Rubber." Journal of Dynamic Behavior of Materials 6, no. 3 (June 29, 2020): 336–47. http://dx.doi.org/10.1007/s40870-020-00252-w.

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Abstract Rubber is widely used in engineering applications in which it may be subjected to impact loading leading to high strain rate deformation. This resulting deformation may occur at a variety of temperatures, notwithstanding the self-heating of the material. For this reason, it is necessary to study the mechanical behaviour of these materials over a range of loading conditions. The strong rate and temperature dependence of their properties provides a further motivation for this understanding. In this paper, the relationships between the response of a neoprene rubber at various strain rates and temperatures are investigated, and a simple model making use of the time–temperature superposition (TTS) principle proposed to describe the material behaviour. As it is challenging to obtain high rate data on rubbery materials using conventional apparatus, such as the split-Hopkinson pressure bar (SHPB), the simple two parameter hyperelastic model proposed here provides a useful complementary tool to interrogate the response.

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Mihai, L. Angela, Thomas E. Woolley, and Alain Goriely. "Stochastic isotropic hyperelastic materials: constitutive calibration and model selection." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2211 (March 2018): 20170858. http://dx.doi.org/10.1098/rspa.2017.0858.

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Biological and synthetic materials often exhibit intrinsic variability in their elastic responses under large strains, owing to microstructural inhomogeneity or when elastic data are extracted from viscoelastic mechanical tests. For these materials, although hyperelastic models calibrated to mean data are useful, stochastic representations accounting also for data dispersion carry extra information about the variability of material properties found in practical applications. We combine finite elasticity and information theories to construct homogeneous isotropic hyperelastic models with random field parameters calibrated to discrete mean values and standard deviations of either the stress–strain function or the nonlinear shear modulus, which is a function of the deformation, estimated from experimental tests. These quantities can take on different values, corresponding to possible outcomes of the experiments. As multiple models can be derived that adequately represent the observed phenomena, we apply Occam’s razor by providing an explicit criterion for model selection based on Bayesian statistics. We then employ this criterion to select a model among competing models calibrated to experimental data for rubber and brain tissue under single or multiaxial loads.

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Nam, Tran Huu. "Identification parameters of material model and large deformation analysis of inflated air-spring shell made of rubber-textile cord composite." Vietnam Journal of Mechanics 27, no. 2 (July 1, 2005): 118–28. http://dx.doi.org/10.15625/0866-7136/27/2/5721.

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In the paper an orthotropic hyperelastic constitutive model is presented which can be applied to numerical simulation for the response of biological soft tissue and of the nonlinear anisotropic hyperelastic material of the cylindrical air-spring shell used in vibroisolation of driver's seat. The parameters of strain energy function of the proposed constitutive model are fitted to the experimental results by the nonlinear least squares method. The deformation of the inflated cylindrical air-spring shell is calculated by solving the system of five first-order ordinary differential equations with the material constitutive law and proper boundary conditions. Numerical results of principal stretches and deformed profiles of the inflated cylindrical air-spring shell obtained by numerical deformation analysis are compared with experimental ones.

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Journal articles on the topic 'Murnaghan hyperelastic material model'

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