scholarly journals A new concept for the representative directions method: Directionalisation of first and second invariant based hyperelastic models

2021 ◽  
Vol 222-223 ◽  
pp. 111017
Author(s):  
A.B. Aydogdu ◽  
K. Loos ◽  
M. Johlitz ◽  
A. Lion
Keyword(s):  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.


2021 ◽  
Vol 2 (108) ◽  
pp. 75-85
Author(s):  
Q.H. Jebur ◽  
M.J. Jweeg ◽  
M. Al-Waily ◽  
H.Y. Ahmad ◽  
K.K. Resan

Purpose: Rubber is widely used in tires, mechanical parts, and user goods where elasticity is necessary. Some essential features persist unsolved, primarily if they function in excessive mechanical properties. It is required to study elastomeric Rubber's performance, which is operational in high-level dynamic pressure and high tensile strength. These elastomeric aims to increase stress breaking and preserve highly pressurised tensile strength. Design/methodology/approach: The effects of carbon black polymer matrix on the tensile feature of different Rubber have been numerically investigated in this research. Rubber's material characteristics properties were measured using three different percentages (80%, 90%and 100%) of carbon black filler parts per Hundreds Rubber (pphr). Findings: This study found that the tensile strength and elongation are strengthened as the carbon black filler proportion increases by 30%. Practical implications: This research study experimental tests for Rubber within four hyperelastic models: Ogden's Model, Mooney-Rivlin Model, Neo Hooke Model, Arruda- Boyce Model obtain the parameters for the simulation of the material response using the finite element method (FEM) for comparison purposes. These four models have been extensively used in research within Rubber. The hyperelastic models have been utilised to predict the tensile test curves—the accurate description and prediction of elastomer rubber models. For four models, elastomeric material tensile data were used in the FEA package of Abaqus. The relative percentage error was calculated when predicting fitness in selecting the appropriate model—the accurate description and prediction of elastomer rubber models. For four models, elastomeric material tensile data were used in the FEA package of Abaqus. The relative percentage error was calculated when predicting fitness in selecting the appropriate model. Numerical Ogden model results have shown that the relative fitness error was the case with large strains are from 1% to 2.04%. Originality/value: In contrast, other models estimate parameters with fitting errors from 2.3% to 49.45%. The four hyperelastic models were tensile test simulations conducted to verify the efficacy of the tensile test. The results show that experimental data for the uniaxial test hyperelastic behaviour can be regenerated effectively as experiments. Ultimately, it was found that Ogden's Model demonstrates better alignment with the test data than other models.


2021 ◽  
Author(s):  
M. M. Matygov ◽  
I. A. Magomedov ◽  
I. M. Daudov

Author(s):  
Mathieu Nierenberger ◽  
Yves Rémond ◽  
Saïd Ahzi

Medical surgery is currently rapidly improving and requires modeling faithfully the mechanical behavior of soft tissues. Various models exist in literature; some of them created for the study of biological materials, and others coming from the field of rubber mechanics. Indeed biological tissues show a mechanical behavior close to the one of rubbers. But while building a model, one has to keep in mind that its parameters should be loading independent and that the model should be able to predict the behavior under complex loading conditions. In addition, keeping physical parameters seems interesting since it allows a bottom up approach taking into account the microstructure of the material. In this study, the authors consider different existing hyperelastic models based on strain energy functions and identify their coefficients successively on single loading stress-stretch curves. The experimental data used, come from a paper by Zemanek dated 2009 and concerning uniaxial, equibiaxial and plane tension tests on porcine arterial walls taken in identical experimental conditions. To achieve identification, the strain energy function of each model is derived differently to provide an expression of the Cauchy stress associated to each loading case. Firstly the parameters of each model are identified on the uniaxial tension curve using a least squares method. Then, keeping the obtained parameters, predictions are made for the two other loading cases (equibiaxial and plane tension) using the associated expressions of stresses. A comparison of these predictions with experimental data is done and allows evaluating the predictive capabilities of each model for the different loading cases. A similar approach is used after swapping the loading types. Since the predictive capabilities of the models are really dependent on the loading chosen to determine their parameters, another type of identification procedure is set up. It consists in adding the residues over the three loading cases during identification. This alternative identification method allows a better agreement between each model and the various types of experiments. This study evaluated the ability of some classical hyperelastic models to be used for a predictive scope after being identified on a specific loading type. Besides it brought to light some existing models which can describe at best the mechanical behavior of biological tissues submitted to various loadings.


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