Variations on Ogden’s model: close and distant relatives Ehret, A. E.; Stracuzzi, A.
Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences,
10/2022, Letnik:
380, Številka:
2234
Journal Article
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The power law in terms of stretch, the truncated series representation and the Valanis–Landel hypothesis are distinguished features of Ogden’s strain-energy density function. While they represent a ...set of special constitutive choices, they have also been shown recently to allow a particular molecular statistical interpretation of the model, where each of these ingredients can be associated with a step in the development of the strain-energy density of the polymer network from the statistical mechanics of long-chain molecules. The schematic of this perspective brings us into a position to vary these steps individually. By this means, Ogden’s theory can be embedded in a certain family of models within the large class of isotropic hyperelastic materials, whose members can be identified as close and distant ‘relatives’.
This article is part of the theme issue ‘The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity’.
Auxetic materials have gained increasing interest in the last decades, fostered by auspicious applications in various fields. While the design of new auxetics has largely focused on meta-materials ...with deterministic, periodically arranged structures, we show here by theoretical and numerical analysis that pronounced auxetic behaviour with negative Poisson's ratios of very large magnitude can occur in random fibre networks with slender, reasonably straight fibre segments that buckle and deflect. We further demonstrate in experiments that such auxetic fibre networks, which increase their thickness by an order of magnitude and more than quintuple their volume when moderately extended, can be produced by electrospinning. Our results thus augment the class of auxetics by a large group of straightforwardly fabricable meta-materials with stochastic microstructure.
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The development and application of nanofibres requires a thorough understanding of the mechanical properties on a single fibre level including respective modelling tools for precise ...fibre analysis. This work presents a mechanical and morphological study of poly-l-lactide nanofibres developed by needleless electrospinning. Atomic force microscopy (AFM) and micromechanical testing (MMT) were used to characterise the mechanical response of the fibres within a diameter range of 200–1400 nm. Young’s moduli E determined by means of both methods are in sound agreement and show a strong increase for thinner fibres below a critical diameter of 800 nm. Similar increasing trends for yield stress and hardening modulus were measured by MMT. Finite element analyses show that the common practice of modelling three-point bending tests with either double supported or double clamped beams is prone to significant bias in the determined elastic properties, and that the latter is a good approximation only for small diameters. Therefore, an analytical formula based on intermediate boundary conditions is proposed that is valid for the whole tested range of fibre diameters, providing a consistently low error in axial Young’s modulus below 10%. The analysis of fibre morphology by differential scanning calorimetry and 2D wide-angle X-ray scattering revealed increasing polymer chains alignment in the amorphous phase and higher crystallinity of fibres for decreasing diameter. The combination of these observations with the mechanical characterisation suggests a linear relationship between Young’s modulus and both crystallinity and molecular orientation in the amorphous phase.
Fibrous membranes have rapidly growing use in various applications, each of which comes with specific property requirements. However, the development and production of nanofibre membranes with dedicated mechanical properties is challenging, in particular with techniques suitable for industrial scales such as needleless electrospinning. It is therefore a key step to understand the mechanical and structural characteristics of single nanofibres developed in this process, and to this end, the present work presents changes of internal fibre structure and mechanical properties with diameter, based on dedicated models. Special attention was given to the commonly used models for analyzing Young’s modulus of single nanofibers in three-point bending tests, which are shown to be prone to large errors, and an improved robust approach is proposed.
In this contribution we create three-dimensional (3D) finite element models from a series of histological sections of porcine skeletal muscle tissue. Image registration is performed on the stained ...sections by affinely aligning them using auxiliary markers, followed by image segmentation to determine muscle fibres and the extracellular matrix in each section, with particular regard to the continuity of the fibres through the stack. With this information, 3D virtual tissue samples are reconstructed, discretised, and associated with appropriate non-linear elastic anisotropic material models. While the gross anatomy is directly obtained from the images, the local directions of anisotropy were determined by the use of an analogy with steady state diffusion. The influence of the number of histological sections considered for reconstruction on the numerically simulated mechanical response of the virtual tissue samples is then studied. The results show that muscle tissue is fairly heterogeneous along the fascicles, and that transverse isotropy is inadequate in describing their material symmetry at the typical length scale of a fascicle. Numerical simulations of different load cases suggest that ignoring the undulations of fibres and their non-uniform cross-sections only moderately affects the passive response of the tissue in tensile and compressive modes, but can become crucial when predicting the response to generic loads and activation.
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•3D finite element models of skeletal muscle tissue are developed from serial histological sections.•The effect of 3D structure on mechanical behaviour is studied in virtual experiments.•The 3D microstructure leads to heterogeneity and complex material symmetry.•The effect of ignoring the complex 3D structure in models can be very strong, but depends on the load case.
A systematic investigation of the factors affecting the suture retention test is performed. The specimen width w and the distance a of the suture bite from the specimen free edge emerge as the most ...influential geometrical parameters. A conservative approach for the quantification of suture retention strength is identified, based on the use of a camera to monitor the incipient failure and detect the instant of earliest crack propagation. The corresponding critical force, called break starting strength, is extremely robust against test parameter variations and its dependence on the specimen geometry becomes negligible when a≥ 2mm and w≥ 10mm. Comparison of suture retention and mode I crack opening tests reveals a linear correlation between break starting strength and tearing energy. This suggests that the defect created by the needle and the load applied by the suture thread lead to a fracture mechanics problem, which dominates the initiation of failure.
The commercial polydimethysiloxane elastomer Sylgard® 184 with mixing ratio 10:1 is in wide use for biomedical research or fundamental studies of mechanobiology. In this paper, a comprehensive study ...of the large strain mechanical behavior of this material under multiaxial monotonic and cyclic loads, and its change during the first 26 days after preparation is reported. The equibiaxial stress response studied in inflation experiments reveals a much stiffer and more nonlinear response compared to the uniaxial and pure shear characteristics. The polymer revealed remarkably elastic behavior, in particular, very little dependence on strain rates between 0.3%/s and 11%/s, and on the strain history in cyclic experiments. On the other hand, both the small-strain and large strain nonlinear mechanical characteristics of the elastomer are changing with sample age and the results suggest that this process has not ceased after 26 days. A recent re-interpretation of the well-known Ogden model for incompressible rubber-like materials was applied to rationalize the results and accurate agreement was obtained with the experimental data over all testing configurations and testing times. The change of a single parameter in this model is shown to govern the evolution of the nonlinear material characteristics with sample age, attributed to a continuation of the cross-linking process. Based on a kinetic relation to account for this process over time, the model provided successful predictions of the material behavior even after more than one year.
New chromophores were explored for use in dye-sensitized solar cells. The attachment of various di-carboxylated cyanine dyes to nanocrystalline TiO2 was examined spectroscopically and through their ...performance in a sensitized solar cell. It was found that aggregated forms of these cyanine dyes sensitized with an efficiency equal to that of the monomer form and that combinations of cyanine dyes could be used to sensitize solar cells over the entire visible spectrum. With the high extinction coefficients of the organic dyes, short circuit photocurrents for these cyanine-sensitized systems was maximized at a 4 μm thickness of the nanocrystalline TiO2. Short circuit photocurrents for these 4 μm solar cells were found to exceed that of ruthenium coordination complexes.
The results of a comprehensive mechanical analysis of five silicone-based elastomers are presented. Large strain monotonic tests were performed under uniaxial, strip biaxial and equi-biaxial stress ...states. Based on the multiaxial experimental data, hyperelastic constitutive models were determined for each material. The small strain elastic modulus ranges from 49 kPa to 1.5 MPa, and the materials show different degrees of non-linearity of their stress-strain response. Data on the time and history dependence allow determining the deviation from the behavior predicted using a non-dissipative hyperelastic constitutive model. Next to representing a guideline for a comprehensive characterization of highly deformable materials, the present results provide data which can be used for the selection of an appropriate material, depending on the specific application. The corresponding models can be used to simulate the performance of each elastomer in applications involving large strains and multiaxial loading states.
•The strong effect of clamping conditions on the tearing energy is demonstrated.•A post hoc correction for imperfect clamping is proposed and validated.•An improved clamping design preventing ...slippage is presented.
A typical measure for the toughness of highly stretchable materials is the energy for tearing, determined in mode I fracture tests on wide specimens with a lateral cut. In the present paper we show that, when slippage occurs in the grips that hold the specimens, the classical analysis of this test leads to an overestimation of the tearing energy, if sample stretches are determined from the grip displacements. Unlike for elastic properties, the use of local strain data retrieved by an optical measurement system does not remedy this issue but, vice versa, underpredicts the tearing energy. Here we propose a simple post hoc correction of the measured tearing energy, and an improved clamp design to prevent slippage. Applied to a commercial acrylic elastomer, the corrected tearing energy was independent of the occurrence of slippage and consistent with the result obtained with the new clamping system as well as values reported in literature.
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