Modeling Payne effect on basis of linearization of a visco-hyperelastic model

The present work concerns the modeling of the Payne effect in nonlinear viscoelasticity. This effect is a characteristic property of filled elastomers. Indeed, under cyclic loading of increasing amplitude, a decrease is shown in the storage modulus and a peak in the loss modulus. In this study, the Payne effect is assumed to arise from a change of the material microstructure, i.e., the thixotropy. The so-called intrinsic time or shift time was inferred from solving a differential equation that represents the evolution of a material's microstructure. Then, the physical time is replaced by the shift time in the framework of a recent fractional visco-hyperelastic model, which was linearized in the neighborhood of a static pre-deformation. As a result, we have investigated the effects of static pre-deformation, frequency, and magnitude of dynamic strain on storage and loss moduli in the steady state. Thereafter, the same set of parameters identified from the complex Young's modulus was used to predict the stress in the pre-deformed configuration. Finally, it is demonstrated that the proposed model is reasonably accurate in predicting Payne effect.

Understanding regional mechanics of rat myocardia by fitting hyperelastic constitutive models

Background: Availability of biaxial mechanical data for heart myocardia remains high in demand for the development of accurate and detailed computational models. Lack of accurate mechanical data for myocardia may delay the understanding of heart diseases mechanisms. Therefore, the aim of this study is to develop understanding of the regional difference of wall mechanics using rat heart in the left ventricle (LV), septal wall (STW) and right ventricle (RV). This was achieved by conducting a biaxial test on three rat heart myocardia (i.e LV, RV and STW). To select the best hyperelastic model that may be utilised for the development of computational models of the heart, the Fung, Choi-Vito, Polynomial (Anisotropic), Four-Fiber family, Holzapfel (2000) and Holzapfel (2005) hyperelastic models were selected and fitted on the biaxial data of the LV, RV and STW. Results: The best hyperelastic model was selected based on evaluation index (EI) which utilises the Coefficient of Determination (R2). All the six hyperelastic constitutive models were then compared in all three rat heart myocardia. The results show that the Polynomial (Anisotropic) model outperforms the other five models in all myocardial tissues with EI’s above 90 %. The Four-fiber-family and the two Holzapfel models perform equally in the LV and STW myocardial tissue with EI of 50 and 70 %, respectively. Conclusions: The Fung and Choi-Vito models yielded poor goodness of fit in the LV and STW myocardial tissues. The results presented here will be useful for detailed development of accurate computational models studying mechanisms of cardiovascular diseases.

Biomechanical behaviour and hyperelastic model parameters identification of sheep omasum

The function of the omasum is incompletely understood; however, the omasum plays an important role in the transport of appropriately sized feed particles from the reticulorumen to the abomasum, oesophageal groove closure, fermentation of ingesta, and absorption of water, volatile fatty acids, and minerals. The aim of this study is to evaluate the suitable hyperelastic anisotropic model based on biomechanical properties of sheep omasum. The results show that all five (5) hyperelastic models may be suitable for the evaluation of sheep omasum. The average coefficient of determination (R2) of Fung, Polynomial (Anisotropic), Holzapfel (2000), Holzapfel (2005) and Four-Fiber-Family hyperelastic models were found to be 0.79 ± 0.19, 0.95 ± 0.05, 0.92 ± 0.07, 0.93 ± 0.05 and 0.94 ± 0.03, respectively. Also, it was found that the best hyperelastic model for fitting uniaxial data of the sheep omasum was Polynomial (Anisotropic) with EI of 100.0 followed by the Four-Fiber-Family model with EI of 96.18.

Understanding regional mechanics of rat myocardia by fitting hyperelatsic models

Availability of biaxial mechanical data for heart myocardia remains high in demand for the development of accurate and detailed computational models. The aim of this study is to study the regional difference of wall mechanics using rat heart in the left ventricle (LV), septal wall (STW) and right ventricle (RV). This was achieved by conducting a biaxial test on three rat heart myocardia (i.e LV, RV and STW). Fung, Choi-Vito, Polynomial (Anistropic), Four-Fiber family, Holzapfel (2000) and Holzapfel (2005) hyperelastic models were selected and fitted on the bixial data of the LV, RV and STW. The best hyperelastic model was the selected based on evaluation index (EI) determined from the coefficient of determination (R2). All the six models were then compared in all three rat heart myocardia. The results show that the Polynomial (Anisotropic) model outperforms the other five models in all myocardial tissues with EI’s above 90 % goodness of fit. The Four-fiber-family and the two Holzapfel models perform equally in the LV and STW myocardial tissue between 50 and 70 % goodness of fit. The Fung and Choi-Vito models yielded poor goodness of fit in the LV and STW myocardial tissues. Parameter fitting is useful method in advancing reliable data to be used in the development of accurate computational models.

The Effect of Catalysts Addition to Silicone Rubber as Pressure Transmitting Medium in the Pebble Fuel Production Process

Pebble Fuel is a spherical fuel for high temperature gas-cooled reactors (HTGR). This fuel must have a homogeneous density distribution. Hyperelastic material is used as a pressure transmitting medium (PTM) material in making Pebble fuel using the cold quasi-isostatic pressing method. PTM material properties and characteristics were predicted using the finite element analysis method. The problem is the type of material used and its suitable composition to make a pressure-transmitting medium that has the properties and characteristics of the material as predicted. This research discusses the manufacture of tensile specimens for pressure-emitting media using RTV-586 silicone rubber. The composition comprises three different variants with two major ingredients, namely RTV-586 silicone rubber and catalyst. The test results are then analyzed using the finite element method to determine the material composition that is appropriate or close to the predicted properties and characteristics of the PTM material. This initial study used the Mooney-Rivlin hyperelastic model. The Mooney-Rivlin model shows good similarity to the test result data. In future studies, it will make comparisons with other hyperelastic models to get a suitable PTM material constant.

Inverse Parameter Identification for Hyperelastic Model of a Polyurea

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.