Uniaxial Extension Research Articles

Isomorphism Continuum Stored Energy Functional for Finite Thermoelastic Deformation

Continuum mechanics for isotropic finite thermoelastic deformations have been reviewed. Thermal effects on mechanical responses of rubbers have been captured by the isomorphism continuum stored energy (CSE) functional with the multiplicative decomposition of deformation gradient while preserving the structure of symmetry for finite structural deformation. The CSE finite thermoelastic model fits and predicts experimental data of SR and NR-C60 rubbers at different external temperatures. For internal temperature effects of both NR and NR-SIC rubbers, the CSE finite thermoelastic model of stored energy and entropy, along with the newly developed CTE and CI models, fits both nominal stress-stretch and temperature change-stretch experimental data in uniaxial extension tests.

Exact large strain analysis for the Poynting effect of freely twisted thin-walled tubes made of highly elastic soft materials

Toward handling nonlinear coupling effects at large elastic deformations, a decoupled form of the multi-axial elastic potential for highly elastic soft materials is first constructed based on Hencky’s logarithmic strain, and this new potential is then used to obtain analytic results for the uniaxial extension and compression of a bar, the equi-biaxial extension of a plate, the plane-strain extension of a strip and, in particular, the large torsion of a thin-walled tube with free ends. Novelties are included in the following three respects: (a) Experimental data for responses of the uniaxial extension, equi-biaxial extension (uniaxial compression) and plane-strain extension (simple shear) may be accurately matched up to large strain with strain-stiffening effects; (b) exact responses for the Poynting effect of freely twisted thin-walled tubes may be derived for changes in the axial length and the wall thickness as well as the averaged radius; and (c) the coupling nonlinear complexities involved in all such responses may be worked out in a decoupled sense.

Stress concentration around a circular rigid inclusion in incompressible nonlinearly elastic transversely isotropic and orthotropic thin sheets under uniaxial extension

In this paper, we study the stress concentration around a circular rigid inclusion in an incompressible anisotropic homogeneous nonlinearly elastic thin sheet subjected to in-plane finite deformation uniaxial extension. Two classes of material symmetry are considered: transverse isotropy and orthotropy. For the case of transverse isotropy, a three-parameter constitutive relation that under infinitesimal deformations reduces appropriately to the classical incompressible linearized elastic transversely isotropic constitutive relation is studied. Similarly, a six-parameter constitutive relation is considered for the case of orthotropic material symmetry. These constitutive relations may be suitable to describe the response of transversely isotropic and orthotropic bodies subjected to moderate deformations.

Stochastic modeling of inhomogeneities in the aortic wall and uncertainty quantification using a Bayesian encoder–decoder surrogate

Inhomogeneities in the aortic wall can lead to localized stress accumulations, possibly initiating dissection. In many cases, a dissection results from pathological changes such as fragmentation or loss of elastic fibers. But it has been shown that even the healthy aortic wall has an inherent heterogeneous microstructure. Some parts of the aorta are particularly susceptible to the development of inhomogeneities due to pathological changes, however, the distribution in the aortic wall and the spatial extent, such as size, shape and type, are difficult to predict. Motivated by this observation, we describe the heterogeneous distribution of elastic fiber degradation in the dissected aortic wall using a stochastic constitutive model. For this purpose, random field realizations, which model the stochastic distribution of degraded elastic fibers, are generated over a non-equidistant grid. The random field then serves as input for a uniaxial extension test of the pathological aortic wall, solved with the finite element method. To include the microstructure of the dissected aortic wall, a constitutive model developed in a previous study is applied, which also includes an approach to model the degradation of interlamellar elastic fibers. To then assess the uncertainty in the output stress distribution due to the proposed stochastic constitutive model, a convolutional neural network, specifically a Bayesian encoder–decoder, was used as a surrogate model that maps the random input fields to the output stress distribution obtained from the finite element analysis. The results show that the neural network is able to predict the stress distribution of the finite element analysis while also significantly reducing the computational time. In addition, this provides the probability for exceeding certain rupture stresses within the aortic wall, which could allow for the prediction of delamination or fatal rupture.

Evolution of Force Chains Explains the Onset of Strain Stiffening in Fiber Networks

Abstract Fiber networks are the primary structural components of many biological structures, including the cell cytoskeleton and the extracellular matrix. These materials exhibit global nonlinearities, such as stiffening in extension and shear, during which the fibers bend and align with the direction of applied loading. Precise details of deformations at the scale of the fibers during strain stiffening are still lacking, however, as prior work has studied fiber alignment primarily from a qualitative perspective, which leaves incomplete the understanding of how the local microstructural evolution leads to the global mechanical behavior. To fill this gap, we studied how axial forces are transmitted inside the fiber network along paths called force chains, which continuously evolve during the course of deformation. We performed numerical simulations on two-dimensional networks of random fibers under uniaxial extension and shear, modeling the fibers using beam elements in finite element software. To quantify the force chains, we identified all chains of connected fibers for which the axial force was larger than a preset threshold and computed the total length of all such chains. To study the evolution of force chains during loading, we computed the derivative of the total length of all force chains with respect to the applied engineering strain. Results showed that the highest rate of evolution of force chains coincided with the global critical strain for strain stiffening of the fiber network. Therefore, force chains are an important factor connecting understanding of the local kinematics and force transmission to the macroscale stiffness of the fiber network.

A specialized protocol for mechanical testing of isolated networks of type II collagen

The mechanical responses of most soft biological tissues rely heavily on networks of collagen fibers, thus quantifying the mechanics of both individual collagen fibers and networks of these fibers advances understanding of biological tissues in health and disease. The mechanics of type I collagen are well-studied and quantified. Yet no data exist on the tensile mechanical responses of individual type II collagen fibers nor of isolated networks comprised of type II collagen. We aimed to establish methods to facilitate studies of networked and individual type II collagen fibers within the native networked structure, specifically to establish best practices for isolating and mechanically testing type II collagen networks in tension. We systematically investigated mechanical tests of networks of type II collagen undergoing uniaxial extension, and quantified ranges for each of the important variables to help ensure that the experiment itself does not affect the measured mechanical parameters. Specifically we determined both the specimen (establishing networks of isolated collagen, the footprint and thickness of the specimen) and the mechanical test (both the device and the strain rate) to establish a repeatable and practical protocol. Mechanical testing of isolated networks of type II collagen fibers leveraging this protocol will lead to better understanding of the mechanics both of these networks and of the individual fibers. Such understanding may aid in developing and testing therapeutics, understanding inter-constituent interactions (and their roles in bulk-tissue biomechanics), investigating mechanical/biochemical modifications to networked type II collagen, and proposing, calibrating, and validating constitutive models for finite element analyses.

Biomechanical Characterization of Human Corneal Lenticules

Abstract In surgical refractive interventions over-correction or under-correction still occur in 10-15 % of cases. Improved outcomes could be achieved by incorporating patient-specific corneal biomechanics into surgical planning. As a first step, this study mechanically characterizes and numerically simulates corneal lenticules harvested during a refractive intervention called Corneal Lenticule Extraction for Advanced Refractive Correction (CLEAR). These human corneal lenticules were mechanically tested in uniaxial extension in nasal-temporal and 45 deg orientations. An HGO material model that accounts for the unique collagen arrangement of the human cornea was developed and used to identify the material parameters using a finite element model of the experimental setup. The material parameters that best represent the experimental force/displacement were obtained by parameter estimation using Bayesian optimization. The uniaxial experiments performed on 3 patients did not show distinctive differences in orientation. The estimated material parameters fit well with the experimental data, representing a promising material model. In the future, Brillouin measurements will be performed on the CLEAR patients before lenticule extraction so that material parameters can be estimated in vivo, providing the surgeon with a patient specific-surgical planning tool.

Simulation of Mechanical Behaviour of Woven Fabrics at the Scale of Yarns under Multi-Loading

The mechanical behaviour of textile structures is one of their most important characteristics as far as their end use is concerned. Textile structures, fabrics, or yarns are often considered as continuous mediums apart from the fact that they are composed of some discrete elements, individual fibres composing yarns and yarns composing fabrics. This is known as the transition scale, a very important lock to be considered, to evaluate the real structure behaviour. In this context, this work presents some simulations of the mechanical behaviour of a fabric where the yarn is a continuum material. Particular attention was paid to simultaneous loading in uniaxial or biaxial extension and shear loadings. The results of numerical simulations, which show the deformed fabric unit cell under multi-load conditions, are coherent with experimental observations and encourage the authors to continue the present work with parametrical and inverse case studies.

Two-Dimensional Finite Element Method for Modeling Edge Effects in Cross-Ply Laminates

A 2-dimensional finite element (FE) method, based on an approximate analytical solution, is developed to define accurately stress fields and boundary layer width in symmetrically laminated composites. A better insight into the edge effect and delamination failure of cross-ply laminates is attained through a physical explanation of the mathematical FE solution. While some other solutions failed, the present FE solution obtains accurate results using a limited number of elements, and therefore reduces computer storage and computation time. A perturbation technique is employed to derive shape functions for the free edge boundary region, which properly describes the physics of sudden exponential growth of stress field in the vicinity of the edge. An original and comprehensive FE computer program is developed, using these specific shape functions, special numerical integration, and mesh generation algorithms. Results for bidirectional laminates under uniaxial extension are presented and compared with finite difference, FE, and approximate analytical solution.
 HIGHLIGHTS
 
 Defining accurately stress field in free edge region is the main challenge
 Shape functions based on perturbation solution yield accurate results
 Boundary layer width is proportional to geometric ratio of laminates
 Finer mesh in boundary region is required for small geometric ratio laminates
 A huge number of finite elements are needed to determine narrow boundary width
 
 GRAPHICAL ABSTRACT

Model droplet formation in extensional filament stretching within a Filament Extension Atomizer

Further innovation in the field of selective laser sintering (SLS) is strongly connected to the availability of new materials since the market is dominated by polyamide 12 (>90%). The aim of this publication is to develop a descriptive model for the droplet formation process in a Filament Extension Atomizer to predict the applicability to exploit further polymers for the SLS process. The feasibility was tested, investigated and characterized using a “Dripping out of a nozzle” setup for uniaxial extension. The droplet formation process was then observed via high-speed camera imaging and classified for certain parameters. The experiments were carried out using semi-diluted polyethylene oxide (600–4000 kg/mol), glycerol and water solutions as model fluids. Driven by the Plateau-Rayleigh instability, different types of spherical droplets were observed and various droplet formation mechanisms demonstrated and analyzed. Based on the experimental results, a predictive model is derived to describe various essential parameters.

Extensional rheology and flow-induced crystal alignment in polypropylene ionomers

The nonlinear response to the uniaxial extension of a series of isotactic polypropylene (iPP) ionomers is studied by melt rheology and ex situ small and wide-angle x-ray scattering measurements. These ionomers bear iPP backbones decorated with pendant aluminum carboxylate groups. Minuscule amounts of ion groups (<0.1 mol. %) are sufficient to produce remarkably high extensional strain hardening ratios of up to 200 and maximum stretch ratios (before breakage) of up to 50. Small and wide-angle scattering measurements from an iPP ionomer sample quenched during an extensional flow reveal monotonic correlations between Hencky strain, crystallinity, and crystal alignment. These results indicate a direct correlation between extensional stress and the chain alignment in the ionomer melt. Intriguingly, the ion clusters in the ionomer show no alignment induced by extensional deformation, suggesting undetermined rearrangements involving cluster dissociation and reassociation that occur during the flow. Slow stress relaxation, after flow cessation, was measured in the ionomers, in sharp contrast to much faster relaxation typically observed in the iPP homopolymer. Stress relaxation is not concomitant with a decrease in crystal alignment, which indicates that chain recoiling is not the stress relaxation mechanism in iPP ionomers.

Understanding the Dynamics of Cellulose Dissolved in an Ionic Liquid Solvent Under Shear and Extensional Flows.

Ionic liquids (ILs) hold great potential as solvents to dissolve, recycle, and regenerate cellulosic fabrics, but the dissolved cellulose material system requires greater study in conditions relevant to fiber spinning processes, especially characterization of nonlinear shear and extensional flows. To address this gap, we aimed to disentangle the effects of the temperature, cellulose concentration, and degree of polymerization (DOP) on the shear and extensional flows of cellulose dissolved in an IL. We have studied the behavior of cellulose from two sources, fabric and filter paper, dissolved in 1-ethyl-3-methylimidazolium acetate ([C2C1Im][OAc]) over a range of temperatures (25 to 80 °C) and concentrations (up to 4%) that cover both semidilute and entangled regimes. The linear viscoelastic (LVE) response was measured using small-amplitude oscillatory shear techniques, and the results were unified by reducing the temperature, concentration, and DOP onto a single master curve using time superposition techniques. The shear rheological data were further fitted to a fractional Maxwell liquid (FML) model and were found to satisfy the Cox-Merz rule within the measurement range. Meanwhile, the material response in the non-LVE (NLVE) regime at large strains and strain rates has special relevance for spinning processes. We quantified the NLVE behavior using steady shear flow tests alongside uniaxial extension using a customized capillary breakup extensional rheometer. The results for both shear and extensional NLVE responses were described by the Rolie-Poly model to account for flow-dependent relaxation times and nonmonotonic viscosity evolution with strain rates in an extensional flow, which primarily arise from complex polymer interactions at high concentrations. The physically interpretable model fitting parameters were further compared to describe differences in material response to different flow types at varying temperatures, concentrations, and DOP. Finally, the fitting parameters from the FML and Rolie-Poly models were connected under the same superposition framework to provide a comprehensive description within the wide measured parameter window for the flow and handling of cellulose in [C2C1Im][OAc] in both linear and nonlinear regimes.

Polymer-turbulence interactions in a complex flow and implications for the drag reduction phenomenon

We present direct numerical simulation data for turbulent duct flow of a finite-extensibility non-linear elastic dumbbell model with the Peterlin approximation (FENE-P) fluid in the high drag reduction regime. While the secondary flow pattern is qualitatively similar to that in a Newtonian fluid, its magnitude is significantly reduced, resulting in a less uniformly distributed velocity profile and hence smaller gradients at the wall. The Reynolds stress tensor in the polymer-laden flow was found to be increasingly anisotropic with most of the turbulent kinetic energy retained in the streamwise component, u′u′¯. We introduce a novel approach for investigating polymer stretching using the anisotropy invariant map of the polymer stress tensor and observe the persistence of both uniaxial and biaxial extension. Analysis of the transport equation for the mean kinetic energy indicates that polymer stretching and relaxation is a highly dissipative process; hence, the introduction of an additional channel for dissipation in a flow is key to drag reduction.

Carbon deposition and argon post-treatment of polyurethane surface: Structural-mechanical and fracture properties

Modification of polymeric surface by plasma ions has perspectives in creating flexible functional materials; their deformation behavior is one of the most important properties, as poor fracture resistance cancels all advantages. Carbon ions were deposited on the surface of elastic polyurethane with subsequent argon treatment. Created carbon-containing nanolayer has increased wettability and nonuniform local mechanical properties. Uniaxial extension to strains >100% induces discontinuous microcracks of carbon-modified surfaces but their propagation is constrained by inhomogeneities of the modified layer. Argon post-treatment improves wettability further but makes local mechanical properties uniform that decreases the fracture resistance. Multi-cycle uniaxial loading to 50% doesn't damage the surface but forms in the modified layer weakened domains – precursors of failure; this improves crack resistance at strains >100% a mesh of disordered microcracks appears preventing propagation of long cracks.

A reappraisal of active tectonics along the Fethiye–Burdur trend, southwestern Turkey

SUMMARYWe investigate active tectonics in southwestern Turkey along the trend between Fethiye, near the eastern end of the Hellenic subduction zone, and Burdur, on the Anatolian plateau. Previously, regional GNSS velocities have been used to propose either (1) a NE-trending zone of strike-slip faulting coined the Fethiye–Burdur Fault Zone, or (2) a mix of uniaxial and radial extension accommodated by normal faults with diverse orientations. We test these models against the available earthquake data, updated in light of recent earthquakes at Arıcılar (24 November 2017, Mw 5.3), Acıpayam (20 March 2019, Mw 5.6) and Bozkurt (8 August 2019, Mw 5.9), the largest in this region in the last two decades. Using Sentinel-1 InSAR and seismic waveforms and arrival times, we show that the Arıcılar, Acıpayam and Bozkurt earthquakes were partially or fully buried ruptures on pure normal faults with subtle or indistinct topographic expressions. By exploiting ray paths shared with these well-recorded modern events, we relocate earlier instrumental seismicity throughout southwestern Turkey and incorporate these improved hypocentres in an updated focal mechanism compilation. The southwestern Fethiye–Burdur trend is dominated by ESE–WNW trending normal faulting, even though most faults evident in the topography strike NE–SW. This hints at a recent change in regional strain, perhaps related to eastward propagation of the Gökova graben into the area or to rapid subsidence of the Rhodes basin. The northeastern Fethiye–Burdur trend is characterized by orthogonal normal faulting, consistent with radial extension and likely responsible for the distinct physiography of Turkey’s Lake District. We find that the 1971 Mw 6.0 Burdur earthquake likely ruptured a NW-dipping normal fault in an area of indistinct geomorphology near Salda Lake, contradicting earlier studies that place it on well-expressed faults bounding the Burdur basin, and further highlighting how damaging earthquakes are possible on faults that would prove difficult to identify beforehand. Overall, our results support GNSS-derived kinematic models that depict a mix of uniaxial and radial extension throughout southwestern Turkey, with no evidence from focal mechanisms for major, active strike-slip faults anywhere along the Fethiye–Burdur trend. Normal faulting orientations are consistent with a stress field driven primarily by contrasts in gravitational potential energy between the elevated Anatolian plateau and the low-lying Rhodes and Antalya basins.

Noninvasive Assessment of In Vivo Passive Skeletal Muscle Mechanics as a Composite Material Using Biomedical Ultrasound.

This study develops a biomedical ultrasound imaging method to infer microstructural information (i.e., tissue level) from imaging mechanical behavior of skeletal muscle (i.e., organ level). We first reviewed the constitutive model of skeletal muscle by regarding it as a transversely isotropic (TI) hyperelastic composite material, for which a theoretical formula was established among shear wave speed, deformation, and material parameters (MPs) using the acoustoelasticity theory. The formula was evaluated by finite element (FE) simulations and experimentally examined using ultrasound shear wave imaging (SWI) and strain imaging (SI) on in vivo passive biceps brachii muscles of two healthy volunteers. The imaging sequence included 1) generation of SW in multiple propagation directions while resting the muscle at an elbow angle of 90°; 2) generation of SW propagating along the myofiber direction during continuous uniaxial muscle extension by passively changing the elbow angle from 90° to 120°. Ultrasound-quantified SW speeds and muscle deformations were fitted by the theoretical formula to estimate MPs of in vivo passive muscle. Estimated myofiber stiffness, stiffness ratio of myofiber to extracellular matrix (ECM), and ECM volume ratio all agreed with literature findings. The proposed mathematical formula together with our in-house ultrasound imaging method enabled assessment of microstructural material properties of in vivo passive skeletal muscle from organ-level mechanical behavior in an entirely noninvasive way. Noninvasive assessment of both micro and macro properties of in vivo skeletal muscle will advance our understanding of complex muscle dynamics and facilitate treatment and rehabilitation planning.

Experimental Investigation of the Anisotropic Mechanical Response of the Porcine Thoracic Aorta.

Knowledge of the mechanical properties of blood vessels and determining appropriate constitutive relations are essential in developing methodologies for accurate prognosis of vascular diseases. We examine the directional variation of the mechanical properties of the porcine thoracic aorta by performing uniaxial extension tests on dumbbell-shaped specimens cut at five different orientations with respect to the circumferential direction of the aorta. Specimens in all the orientations considered exhibit a nonlinear constitutive response that is typical of collagenous soft tissues. Shear strain under uniaxial extension demonstrates clearly discernible anisotropy of the mechanical response of the porcine aorta, and samples oriented at 45[Formula: see text] and 60[Formula: see text] with respect to the circumferential direction show a peculiar crescent-shaped shear strain-nominal stretch response not displayed by axial and circumferential specimens. Failure stress indicates decreasing tensile strength of the porcine aortic wall from the circumferential direction to the longitudinal direction. Furthermore, we determine the material parameters for the four-fiber-family and Gasser-Holzapfel-Ogden models from the mechanical response data of the circumferential and longitudinal specimens. It is shown how the material parameters derived from the uniaxial tests on circumferential and longitudinal specimens are insufficient to characterize the response of off-axis specimens.

Quantifying bond rupture during indentation fracture of soft polymer networks using molecular mechanophores

Understanding the resistance of soft materials to puncture bears relevance to many fields. However, the complex mechanics during deep indentation make it difficult to disentangle how the different dissipation processes contribute to the fracture energy and how this depends on the molecular structure of the material. To investigate this, we perform deep indentation experiments with a flat-ended cylindrical probe on polymer networks containing the covalently incorporated mechanoluminescent bond rupture sensor 1,2-dioxetane. By carrying out the experiments inside an integrating sphere, we are able to quantify the number of ruptured bonds during puncture nucleation and propagation. We find that puncture is associated with significant diffuse damage, both prior to nucleation of the main crack and during crack propagation. Moreover, in agreement with earlier results for uniaxial extension, we show that puncture of double networks leads to strongly enhanced rupture in the prestretched sacrificial network, while fracture of the matrix network is much more localized. Finally, we complement the experiments with MD simulations that allow us to link the rupture processes to the distribution of tension in the networks.

Rheology, crystallization, and enhanced mechanical properties of uniaxially oriented ethylene–octene copolymer/polyolefin elastomer blends

The application of polyethylene in artificial turf promotes research on the processing and properties of uniaxial extension modified polyethylene materials. The effects of comonomer (octene/butene) structure on the properties of pre-stretched linear low density polyethylene (LLDPE)/polyolefin elastomer (POE) blends are investigated. The melt tensile stress and melt stretch ratio of LLDPE ethylene‒octene copolymer (EOC)/POE reach 4.0 × 105 Pa and 12.8, respectively. At the pre-stretching ratio λ = 5, the tensile strength of EOC/POEλ5 reaches 62.5 MPa, the critical length is 5.7 mm, and the strain hardening degree increases. Differential scanning calorimetry, Raman spectroscopy and X-ray diffraction show the crystallinity of EOC/POEλ5 is higher than that of LLDPE ethylene‒butene copolymer (EBC)/POEλ5. Large short-chain branch length EOC is demonstrated to rebuild the “physical crosslinking point” after pre-stretched, thereby enhancing the interaction between molecular chains in EOC/POEλ5. This research provides a new clue for the development of artificial turf materials.

Impact of oleuropein on rheology and breadmaking performance of wheat doughs, and functional features of bread

SummaryOleuropein (OP) is a polyphenol present in drupes and leaves of olive tree with health benefits and, as antioxidant, potentiality to alter gluten functionality. Effects of OP inclusion to wheat flour (0.01% and 0.02% on flour weight basis) on dough rheology and breadmaking performance, and bread features were investigated. Farinograph, uniaxial extension and shear rheometry (oscillatory and creep‐recovery) were applied. Doughs containing OP were stronger, more elastic, and less sticky indicating the ability of OP to act as flour improver. The strengthening effect of OP on gluten led to the increase in bread volume and softer crumb compared to control. A lower crumb density of bread with the addition of OP was related to a higher in vitro glycaemic response. An increase in the antioxidant capacity of bread made with the phenolic compound was also found.