In this research, the nonlinear elastic behavior of human extensor apparatus was investigated. To this goal, firstly the best material parameters of hyperelastic strain energy density functions ...consisting of the Mooney–Rivlin, Ogden, invariants, and general exponential models were derived for the simple tension experimental data. Due to the significance of stress response in other deformation modes of nonlinear models, the calculated parameters were used to study the pure shear and balance biaxial tension behavior of the extensor apparatus. The results indicated that the Mooney–Rivlin model predicts an unstable behavior in the balance biaxial deformation of the extensor apparatus, while the Ogden order 1 represents a stable behavior, although the fitting of experimental data and theoretical model was not satisfactory. However, the Ogden order 6 model was unstable in the simple tension mode and the Ogden order 5 and general exponential models presented accurate and stable results. In order to reduce the material parameters, the invariants model with four material parameters was investigated and this model presented the minimum error and stable behavior in all deformation modes. The ABAQUS Explicit solver was coupled with the VUMAT subroutine code of the invariants model to simulate the mechanical behavior of the central and terminal slips of the extensor apparatus during the passive finger flexion, which is important in the prediction of boutonniere deformity and chronic mallet finger injuries, respectively. Also, to evaluate the adequacy of constitutive models in simulations, the results of the Ogden order 5 were presented. The difference between the predictions was attributed to the better fittings of the invariants model compared with the Ogden model.
In this study, the hyperelastic models of demineralized and deproteinized bovine cortical femur bone were investigated and appropriate models were developed. Using uniaxial compression test data, the ...strain energy versus stretch was calculated and the appropriate hyperelastic strain energy functions were fitted on data in order to calculate the material parameters. To obtain the mechanical behavior in other loading conditions, the hyperelastic strain energy equations were investigated for pure shear and equi-biaxial tension loadings. The results showed the Mooney–Rivlin and Ogden models cannot predict the mechanical response of demineralized and deproteinized bovine cortical femur bone accurately, while the general exponential–exponential and general exponential-power law models have a good agreement with the experimental results. To investigate the sensitivity of the hyperelastic models, a variation of 10% in material parameters was performed and the results indicated an acceptable stability for the general exponential–exponential and general exponential–power law models. Finally, the uniaxial tension and compression of cortical femur bone were studied using the finite element method in VUMAT user subroutine of ABAQUS software and the computed stress–stretch curves were shown a good agreement with the experimental data.
The asymptotic homogenization technique is involved to derive the effective elastic response of biological membranes viewed as repetitive beam networks. Thereby, a systematic methodology is ...established, allowing the prediction of the overall mechanical properties of biological membranes in the nonlinear regime, reflecting the influence of the geometrical and mechanical micro-parameters of the network structure on the overall response of the equivalent continuum. Biomembranes networks are classified based on nodal connectivity, so that we analyze in this work 3, 4 and 6-connectivity networks, which are representative of most biological networks. The individual filaments of the network are described as undulated beams prone to entropic elasticity, with tensile moduli determined from their persistence length. The effective micropolar continuum evaluated as a continuum substitute of the biological network has a kinematics reflecting the discrete network deformation modes, involving a nodal displacement and a microrotation. The statics involves the classical Cauchy stress and internal moments encapsulated into couple stresses, which develop internal work in duality to microcurvatures reflecting local network undulations. The relative ratio of the characteristic bending length of the effective micropolar continuum to the unit cell size determines the relevant choice of the equivalent medium. In most cases, the Cauchy continuum is sufficient to model biomembranes. The peptidoglycan network may exhibit a re-entrant hexagonal configuration due to thermal or pressure fluctuations, for which micropolar effects become important. The homogenized responses are in good agreement with FE simulations performed over the whole network. The predictive nature of the employed homogenization technique allows the identification of a strain energy density of a hyperelastic model, for the purpose of performing structural calculations of the shape evolutions of biomembranes.
The main aim of this paper is to automate the implementation of finite strain anisotropic hyperelastic models into a general finite element framework. The automation presented in this paper enables ...the end-user to implement a hyperelastic model by programming its Helmholtz free energy function alone. The automation is achieved by employing hyper-dual number system to evaluate analytical quality derivatives. New perturbation techniques are introduced and are employed to extend the hyper-dual numbers system to evaluate tensor derivatives. The capability of the proposed automation scheme is demonstrated by implementing five finite strain anisotropic hyperelastic models. The merits and demerits of the proposed automation scheme are compared to an automation scheme based on the central difference method.
High performance Fluorosilicone rubber (FS)/organoclay (OC) nanocomposites have been prepared by a melt compounding process. The results of mechanical investigation revealed that Young’s modulus and ...hardness of FS rubber are improved with introduction of OCs while an inverse trend was observed for elongation at break and tensile strength. Eight constitutive models, Yeoh, Arruda-Boyce, Mooney-Rivilen, Neo-Hookean, Marlow, polynomial, Van der Waals, and Odgen were studied to investigate the stress-strain behavior of FS/OC nanocomposites. It was concluded that the ability of these models to predict the true behavior of the FS/OC samples directly depends on the amount of OC. Two modified Halpin-Tsai and inverse rule of mixtures theories were applied to evaluate the dependence of Young modulus of nanocomposites on volume fraction of OCs. The experimental data were employed for determining modified models parameters as well as for validating models. It was shown that, OCs can also play a fundamental role in controlling volume shrinkage of FS after cure. FS was proved that still retain its specific properties as well as the fuel and thermal resistance after introduction of OCs. Combination of these results verifies that incorporation of OCs can provide tailored mechanical properties without sacrificing fuel and thermal resistance of FS elastomers.
The purpose of this study was to determine biomechanical properties of linea alba subjected to transverse planar tension and to compare its behavior at different locations of the abdominal wall. ...Samples of linea alba from five different porcine abdominal walls were tested in planar tension. During these tests, strain maps were measured for the first time ever using the stereo-digital image correlation (S-DIC) technique. The strain maps were used to derive the properties of different hyperelastic material models. It was shown that the Ogden model and the Holzapfel–Gasser–Ogden model are appropriate to reproduce the response in planar tension. The linea alba located above the umbilicus was significantly more compliant than below the umbilicus. This difference which is reported for the first time here is consistent with the tissue microstructure and it is discussed within the perspective of clinically-relevant numerical simulations.
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The arterial wall is a complex fiber-reinforced composite. Pathological conditions, such as aneurysms, significantly alter the mechanical response of the arterial wall, resulting in a loss of ...elasticity, enhanced anisotropy, and increased chances of mechanical failure. Invariant-based models of the healthy and aneurysmal abdominal aorta were constructed based on first principles and published experimental data with implementations for several numerical cases, as well as comparisons to current healthy and aneurysmal tissue data. Inherent limitations of a traditional invariant-based methodology are also discussed and compared to the models' ability to accurately reproduce experimental trends. The models capture the nonlinear and anisotropic mechanical responses of the two arterial sections and make reasonable predictions regarding the effects of alterations in healthy and diseased tissue histology. Additionally, the new models exhibit convex and anisotropic monotonically increasing energy contours (suggesting numerical stability) but have potentially the inherent limitations of a covariant theoretical framework. Although the traditional invariant framework exhibits significant covariance, the invariant terms utilized in the new models exhibited limited covariance and are able to accurately reproduce experimental trends. A streamlined implementation is also possible for future numerical investigations of fluid-structure interactions in abdominal aortic aneurysms.
An analysis is conducted of application of the Hertz model for measuring the cardiac myocytes' mechanical properties. Atomic force microscopy (AFM) was used, which characterises the cellular ...mechanical properties at a nanoscale precision. The Hertz model, the most common model in contact mechanics, was applied to the experimental data and an elastic modulus was determined by analysing the relationship between the AFM indentation force and the depth. To determine the Hertz model appropriateness accurately, the contribution of the viscous properties, the cell adherence and the elastic modulus extracting method were examined. The elastic moduli were 48.08 ± 2.26 kPa and 55.67 ± 2.56 kPa, respectively, with two different evaluation approaches. The cardiac myocyte exhibited a nonlinear elastic behaviour since the elastic modulus determined by the Hertz model was not constant in the different indentation depths. Furthermore, the viscous dissipation was negligible; therefore the mechanical behaviour of this cell type can be well described by appropriate hyperelastic models.
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