Equibiaxial Strain Research Articles

Graphene flakes under controlled biaxial deformation.

Thin membranes, such as monolayer graphene of monoatomic thickness, are bound to exhibit lateral buckling under uniaxial tensile loading that impairs its mechanical behaviour. In this work, we have developed an experimental device to subject 2D materials to controlled equibiaxial strain on supported beams that can be flexed up or down to subject the material to either compression or tension, respectively. Using strain gauges in tandem with Raman spectroscopy measurements, we monitor the G and 2D phonon properties of graphene under biaxial strain and thus extract important information about the uptake of stress under these conditions. The experimental shift over strain for the G and 2D Raman peaks were found to be in the range of 62.3 ± 5 cm–1/%, and 148.2 ± 6 cm–1/%, respectively, for monolayer but also bilayer graphenes. The corresponding Grüneisen parameters for the G and 2D peaks were found to be between 1.97 ± 0.15 and 2.86 ± 0.12, respectively. These values agree reasonably well with those obtained from small-strain bubble-type experiments. The results presented are also backed up by classical and ab initio molecular dynamics simulations and excellent agreement of Γ-E2g shifts with strains and the Grüneisen parameter was observed.

The Biaxial Moduli of Cubic Materials Subjected to an Equi-biaxial Elastic Strain

This is the final version of the article. It was first available from Springer via http://dx.doi.org/10.1007/s10659-015-9558-x

Design of a Novel Equi-Biaxial Stretcher for Live Cellular and Subcellular Imaging.

Cells in the body experience various mechanical stimuli that are often essential to proper cell function. In order to study the effects of mechanical stretch on cell function, several devices have been built to deliver cyclic stretch to cells; however, they are generally not practical for live cell imaging. We introduce a novel device that allows for live cell imaging, using either an upright or inverted microscope, during the delivery of cyclic stretch, which can vary in amplitude and frequency. The device delivers equi-biaxial strain to cells seeded on an elastic membrane via indentation of the membrane. Membrane area strain was calibrated to indenter depth and the device showed repeatable and accurate delivery of strain at the scale of individual cells. At the whole cell level, changes in intracellular calcium were measured at different membrane area strains, and showed an amplitude-dependent response. At the subcellular level, the mitochondrial network was imaged at increasing membrane area strains to demonstrate that stretch can lead to mitochondrial fission in lung fibroblasts. The device is a useful tool for studying transient as well as long-term mechanotransduction as it allows for simultaneous stretching and imaging of live cells in the presence of various chemical stimuli.

Dielectric Elastomer Based "Grippers" for Soft Robotics.

The use of few stiff fibers to control the deformation of dielectric elastomer actuators, in particular to break the symmetry of equi-biaxial lateral strain in the absence of prestretch, is demonstrated. Actuators with patterned fibers are shown to evolve into unique shapes upon electrical actuation, enabling novel designs of gripping actuators for soft robotics.

Microscopically crumpled indium-tin-oxide thin films as compliant electrodes with tunable transmittance

Indium-tin-oxide (ITO) thin films are perceived to be stiff and brittle. This letter reports that crumpled ITO thin films on adhesive poly-acrylate dielectric elastomer can make compliant electrodes, sustaining compression of up to 25% × 25% equi-biaxial strain and unfolding. Its optical transmittance reduces with crumpling, but restored with unfolding. A dielectric elastomer actuator (DEA) using the 14.2% × 14.2% initially crumpled ITO thin-film electrodes is electrically activated to produce a 37% areal strain. Such electric unfolding turns the translucent DEA to be transparent, with transmittance increased from 39.14% to 52.08%. This transmittance tunability promises to make a low-cost smart privacy window.

Biaxial stress relaxation of semilunar heart valve leaflets during simulated collagen catabolism: Effects of collagenase concentration and equibiaxial strain state.

Heart valve leaflet collagen turnover and remodeling are innate to physiological homeostasis; valvular interstitial cells routinely catabolize damaged collagen and affect repair. Moreover, evidence indicates that leaflets can adapt to altered physiological (e.g. pregnancy) and pathological (e.g. hypertension) mechanical load states, tuning collagen structure and composition to changes in pressure and flow. However, while valvular interstitial cell-secreted matrix metalloproteinases are considered the primary effectors of collagen catabolism, the mechanisms by which damaged collagen fibers are selectively degraded remain unclear. Growing evidence suggests that the collagen fiber strain state plays a key role, with the strain-dependent configuration of the collagen molecules either masking or presenting proteolytic sites, thereby protecting or accelerating collagen proteolysis. In this study, the effects of equibiaxial strain state on collagen catabolism were investigated in porcine aortic valve and pulmonary valve tissues. Bacterial collagenase (0.2 and 0.5 mg/mL) was utilized to simulate endogenous matrix metalloproteinases, and biaxial stress relaxation and biochemical collagen concentration served as functional and compositional measures of collagen catabolism, respectively. At a collagenase concentration of 0.5 mg/mL, increasing the equibiaxial strain imposed during stress relaxation (0%, 37.5%, and 50%) yielded significantly lower median collagen concentrations in the aortic valve (p = 0.0231) and pulmonary valve (p = 0.0183), suggesting that relatively large strain magnitudes may enhance collagen catabolism. Collagen concentration decreases were paralleled by trends of accelerated normalized stress relaxation rate with equibiaxial strain in aortic valve tissues. Collectively, these in vitro results indicate that biaxial strain state is capable of affecting the susceptibility of valvular collagens to catabolism, providing a basis for further investigation of how such phenomena may manifest at different strain magnitudes or in vivo.

Improving the electromechanical performance of dielectric elastomers using silicone rubber and dopamine coated barium titanate

Abstract In this work, a new soft dielectric elastomer (DE) was fabricated from dopamine coated barium titanate particles and silicone rubber (SR). The results showed that the barium titanate (BaTiO 3 , BT) was coated by dopamine and the coated particles were highly compatible with SR. In order to achieve a maximum voltage-induced deformation, the minimum secant moduli of DEs were obtained in experimentation at a stretch ratio of approximately 1.6 by applying equi-biaxial tensile strain using the bubble inflation method. Additionally, it was found that the addition of DP-BT into SR led to an increased dielectric constant and decreased dielectric loss tangent for the matrix by comparison with SR/BT composites. Furthermore, the electromechanical properties of the SR/DP-BT composites were greatly improved in terms of voltage-induced deformation ( s a ), electromechanical energy density ( e ) and coupling efficiency ( K 2 ). A maximum actuated area strain of approximately 78%, which was 30% larger than that of the SR/BT composites, was achieved for the sample having a DP-BT content of 20 wt.%. This strain corresponded to a low dielectric strength of around 53 V/μm, the composite exhibited a maximum energy density of 0.07 MJ/m 3 and coupling efficiency of 0.68.

Investigation of forming limit diagram for tube hydroforming considering effect of changing strain path

The forming limit diagram (FLD) has been widely used as a measure of the maximum formability of a material in tube hydroforming (THF). The geometric shape of the FLD varies owing to the influences of many factors, especially the strain path. Therefore, discussing the change rule of FLDs under various strain paths has practical significance. In the present study, strain paths generated from THF are classified as simple or complex ones. The FLDs for THF are established based on Swift’s diffused necking criterion and Hill’s localised necking criterion along both simple and complex strain paths. Through a comparison of the FLDs obtained from various strain paths, the influences of changing strain path are revealed. Some THF experiments under various strain paths are performed to verify the theoretical analysis. The theoretical analysis and experimental results prove that the position of the FLD changes with different strain paths. Compared with the FLD position established along a simple strain path, the FLD position under a two-stage linear strain path moves in the upper left direction with an initial uniaxial tensile strain path and in the lower right direction with an initial equibiaxial tensile strain path.

Characterization of the Shear Stress State Under Non-Proportional Strain Paths Realized by Biaxial Stretching in the Marciniak Test

Complex parts with sharp corners are on the rise to satisfy increasing customer demands on the design. To realize these parts in single or multistage forming processes the information of the material behavior under linear and non-linear strain paths is essential. As Bauschinger already showed for the material behavior under cyclic loading, a reduction of the subsequent beginning of plastic yielding can be observed. Different research works studied the Bauschinger effect under cyclic proportional loading or non-proportional strain paths mostly with uniaxial pre-straining of the material. In this paper the material behavior under shearing after previous biaxial stretching in the Marciniak test is analyzed for the aluminum alloy AA5182 and the advanced high strength steel DP600. The Marciniak test is suited for biaxial pre-straining due to an almost almost equibiaxial strain state and a homogeneous strain distribution in-plane on the bottom of the specimen up to higher strains than in a biaxial tensile test. The subsequent shear test is realized with a modified shear test specimen according to the ASTM standard. Finally, the influence of biaxal pre-straining on the beginning of plastic yielding under shear condition, the hardening behavior and the maximum reachable shear strain is investigated for a better understanding of the material behavior under non-proportional loading paths.

A medium throughput device to study the effects of combinations of surface strains and fluid-flow shear stresses on cells.

We report a medium throughput device to study the effects of combinations of two mechanical stimuli - surface strains and fluid flow shear stresses, on cells. The first generation prototype can screen combinations of five strain and five shear stress levels. Computational modeling and empirical measurements were used to determine the generated strains and flows. Uniform equibiaxial strains up to 20% and shear stresses up to 0.3 Pa can be generated. Compatibility of the device with cell culture and end point fixation, staining and imaging is shown using C2C12 mouse myoblast cells.

Three-dimensional development of tensile pre-strained annulus fibrosus cells for tissue regeneration: An in-vitro study

Prior research has investigated the immediate response after application of tensile strain on annulus fibrosus (AF) cells for the past decade. Although mechanical strain can produce either catabolic or anabolic consequences to the cell monolayer, little is known on how to translate these findings into further tissue engineering applications. Till to date, the application and effect of tensile pre-strained cells to construct a three-dimensional (3D) AF tissue remains unknown. This study aims to investigate the effect of tensile pre-strained exposure of 1 to 24h on the development of AF pellet culture for 3 weeks. Equibiaxial cyclic tensile strain was applied on AF monolayer cells over a period of 24h, which was subsequently developed into a cell pellet. Investigation on cellular proliferation, phenotypic gene expression, and histological changes revealed that tensile pre-strain for 24h had significant and lasting effect on the AF tissue development, with enhanced cell proliferation, and up-regulation of collagen type I, II, and aggrecan expression. Our results demonstrated the regenerative ability of AF cell pellets subjected to 24h tensile pre-straining. Knowledge on the effects of tensile pre-strain exposure is necessary to optimize AF development for tissue reconstruction. Moreover, the tensile pre-strained cells may further be utilized in either cell therapy to treat mild disc degeneration disease, or the development of a disc construct for total disc replacement.

Regulation of thrombomodulin expression and release in human aortic endothelial cells by cyclic strain.

Background and ObjectivesThrombomodulin (TM), an integral membrane glycoprotein expressed on the lumenal surface of vascular endothelial cells, promotes anti-coagulant and anti-inflammatory properties. Release of functional TM from the endothelium surface into plasma has also been reported. Much is still unknown however about how endothelial TM is regulated by physiologic hemodynamic forces (and particularly cyclic strain) intrinsic to endothelial-mediated vascular homeostasis.MethodsThis study employed human aortic endothelial cells (HAECs) to investigate the effects of equibiaxial cyclic strain (7.5%, 60 cycles/min, 24 hrs), and to a lesser extent, laminar shear stress (10 dynes/cm2, 24 hrs), on TM expression and release. Time-, dose- and frequency-dependency studies were performed.ResultsOur initial studies demonstrated that cyclic strain strongly downregulated TM expression in a p38- and receptor tyrosine kinase-dependent manner. This was in contrast to the upregulatory effect of shear stress. Moreover, both forces significantly upregulated TM release over a 48 hr period. With continuing focus on the cyclic strain-induced TM release, we noted both dose (0–7.5%) and frequency (0.5–2.0 Hz) dependency, with no attenuation of strain-induced TM release observed following inhibition of MAP kinases (p38, ERK-1/2), receptor tyrosine kinase, or eNOS. The concerted impact of cyclic strain and inflammatory mediators on TM release from HAECs was also investigated. In this respect, both TNFα (100 ng/ml) and ox-LDL (10–50 µg/ml) appeared to potentiate strain-induced TM release. Finally, inhibition of neither MMPs (GM6001) nor rhomboids (3,4-dichloroisocoumarin) had any effect on strain-induced TM release. However, significantly elevated levels (2.1 fold) of TM were observed in isolated microparticle fractions following 7.5% strain for 24 hrs.ConclusionsA preliminary in vitro investigation into the effects of cyclic strain on TM in HAECs is presented. Physiologic cyclic strain was observed to downregulate TM expression, whilst upregulating in a time-, dose- and frequency-dependent manner the release of TM.

Wrinkle-to-fold transition in soft layers under equi-biaxial strain: A weakly nonlinear analysis

Soft materials can experience a mechanical instability when subjected to a finite compression, developing wrinkles which may eventually evolve into folds or creases. The possibility to control the wrinkling network morphology has recently found several applications in many developing fields, such as scaffolds for biomaterials, stretchable electronics and surface micro-fabrication. Albeit much is known of the pattern initiation at the linear stability order, the nonlinear effects driving the pattern selection in soft materials are still unknown. This work aims at investigating the nature of the elastic bifurcation undertaken by a growing soft layer subjected to a equi-biaxial strain. Considering a skin effect at the free surface, the instability thresholds are found to be controlled by a characteristic length, defined by the ratio between capillary energy and bulk elasticity. For the first time, a weakly nonlinear analysis of the wrinkling instability is performed here using the multiple-scale perturbation method applied to the incremental theory in finite elasticity. The Ginzburg–Landau equations are derived for different superposing linear modes. This study proves that a subcritical pitchfork bifurcation drives the observed wrinkle-to-fold transition in swelling gels experiments, favoring the emergence of hexagonal creased patterns, albeit quasi-hexagonal patterns might later emerge because of an expected symmetry break. Moreover, if the surface energy is somewhat comparable to the bulk elastic energy, it has the same stabilizing effect as for fluid instabilities, driving the formation of stable wrinkles, as observed in elastic bi-layered materials.

Biomechanical strain as a trigger for pore formation in Schlemm's canal endothelial cells

The bulk of aqueous humor passing through the conventional outflow pathway must cross the inner wall endothelium of Schlemm's canal (SC), likely through micron-sized transendothelial pores. SC pore density is reduced in glaucoma, possibly contributing to obstructed aqueous humor outflow and elevated intraocular pressure (IOP). Little is known about the mechanisms of pore formation; however, pores are often observed near dome-like cellular outpouchings known as giant vacuoles (GVs) where significant biomechanical strain acts on SC cells. We hypothesize that biomechanical strain triggers pore formation in SC cells. To test this hypothesis, primary human SC cells were isolated from three non-glaucomatous donors (aged 34, 44 and 68), and seeded on collagen-coated elastic membranes held within a membrane stretching device. Membranes were then exposed to 0%, 10% or 20% equibiaxial strain, and the cells were aldehyde-fixed 5 min after the onset of strain. Each membrane contained 3-4 separate monolayers of SC cells as replicates (N = 34 total monolayers), and pores were assessed by scanning electron microscopy in 12 randomly selected regions (∼65,000 μm2 per monolayer). Pores were identified and counted by four independent masked observers. Pore density increased with strain in all three cell lines (p < 0.010), increasing from 87 ± 36 pores/mm2 at 0% strain to 342 ± 71 at 10% strain; two of the three cell lines showed no additional increase in pore density beyond 10% strain. Transcellular “I-pores” and paracellular “B-pores” both increased with strain (p < 0.038), however B-pores represented the majority (76%) of pores. Pore diameter, in contrast, appeared unaffected by strain (p = 0.25), having a mean diameter of 0.40 μm for I-pores (N = 79 pores) and 0.67 μm for B-pores (N = 350 pores). Pore formation appears to be a mechanosensitive process that is triggered by biomechanical strain, suggesting that SC cells have the ability to modulate local pore density and filtration characteristics of the inner wall endothelium based on local biomechanical cues. The molecular mechanisms of pore formation and how they become altered in glaucoma may be studied in vitro using stretched SC cells.

Hysteresis in electroactive polymers

Abstract In this paper we present a model for the description of rate-independent hysteresis in Electroactive Polymers (EAPs). Our analysis is based on a model proposed by the authors for the description of damage and healing effects in polymeric materials and on a variational formulation for the resulting electromechanical equilibrium problem. The analysis of the class of equibiaxial strain, relevant for many actuation and energy harvesting devices, evidences that the model is effective and computationally efficient. The model shows a significant agreement with important experimental phenomena observed in EAP devices.

Effect of friction in stretch forming and its influence on the forming limit curve

Formability is an important property requirement in sheet metal forming and mostly useful to automobile and aerospace industries. Every product design starts with finite element simulation before the die design and material selection stage. The forming limit curve along with finite element results acts as tool to investigate whether the design is feasible. Hence, it is of utmost importance that the forming limit curve is accurate over a wide range of strain path. Generally, a forming limit curve is derived from discrete failure strain points corresponding to different strain ratios by fitting a smooth curve. It has been observed from many studies that the generated forming limit curves are devoid of any failure points corresponding to equibiaxial strain path. This is found to be true even when the test conditions are supposed to produce biaxial state of strain. To understand the reason behind this observation, a set of forming limit diagram experiments and finite element analyses were carried out for high-strength interstitial free steel and interstitial free galvannealed steel with three different friction conditions. It was observed that friction plays an important role in right-hand side of the forming limit curve. Finite element results and experimental validation suggest that failure strain points for biaxial strain paths can be obtained only if the tests are conducted with proper lubrication system.

Strain-assisted structural transformation and band gap tuning in BeO, MgTe, CdS and 2H-SiC: A hybrid density functional study

Structural transformations and electronic structures of (0001) BeO, MgTe, CdS and 2H-SiC films under equibiaxial in-plane strains are studied using the HSE06 range-separated hybrid functionals. The main results are summarized as follows: I) The structural transition from the polar wurtzite to the nonpolar graphite-like phase is predicted for BeO, MgTe and CdS but not for 2H-SiC, which is more covalent in nature. II) Either a direct or an indirect band structure is displayed in wurtzite BeO and 2H-SiC based on the values of strain, while only a direct band gap is displayed in wurtzite MgTe and CdS. At large tensile strains, the band gaps of graphite-like BeO and CdS are always indirect, whereas the graphite-like MgTe undergoes a direct-to-indirect band gap transition. Furthermore, the decrease in band gap is observed for both types of strain, thereby enabling a number of important technological applications.

Mechanosensitive release of adenosine 5'-triphosphate through pannexin channels and mechanosensitive upregulation of pannexin channels in optic nerve head astrocytes: a mechanism for purinergic involvement in chronic strain.

As adenosine 5'-triphosphate (ATP) released from astrocytes can modulate many neural signaling systems, the triggers and pathways for this ATP release are important. Here, the ability of mechanical strain to trigger ATP release through pannexin channels and the effects of sustained strain on pannexin expression were examined in rat optic nerve head astrocytes. Astrocytes released ATP when subjected to 5% of equibiaxial strain or to hypotonic swelling. Although astrocytes expressed mRNA for pannexins 1-3, connexin 43, and VNUT, pharmacological analysis suggested a predominant role for pannexins in mechanosensitive ATP release, with Rho kinase contribution. Astrocytes from panx1(-/-) mice had reduced baseline and stimulated levels of extracellular ATP, confirming the role for pannexins. Swelling astrocytes triggered a regulatory volume decrease that was inhibited by apyrase or probenecid. The swelling-induced rise in calcium was inhibited by P2X7 receptor antagonists A438079 and AZ10606120, in addition to apyrase and carbenoxolone. Extended stretch of astrocytes in vitro upregulated expression of panx1 and panx2 mRNA. A similar upregulation was observed in vivo in optic nerve head tissue from the Tg-MYOC(Y437H) mouse model of chronic glaucoma; genes for panx1, panx2, and panx3 were increased, whereas immunohistochemistry confirmed increased expression of pannexin 1 protein. In summary, astrocytes released ATP in response to mechanical strain, with pannexin 1 the predominant efflux pathway. Sustained strain upregulated pannexins in vitro and in vivo. Together, these findings provide a mechanism by which extracellular ATP remains elevated under chronic mechanical strain, as found in the optic nerve head of patients with glaucoma.

Cyclic strain alters the expression and release of angiogenic factors by human tendon cells.

Angiogenesis is associated with the tissue changes underlying chronic overuse tendinopathy. We hypothesized that repetitive, cyclic loading of human tendon cells would lead to increased expression and activity of angiogenic factors. We subjected isolated human tendon cells to overuse tensile loading using an in vitro model (1 Hz, 10% equibiaxial strain). We found that mechanically stimulated human tendon cells released factors that promoted in vitro proliferation and tube formation by human umbilical vein endothelial cells (HUVEC). In response to cyclic strain, there was a transient increase in the expression of several angiogenic genes including ANGPTL4, FGF-2, COX-2, SPHK1, TGF-alpha, VEGF-A and VEGF-C, with no change in anti-angiogenic genes (BAI1, SERPINF1, THBS1 and 2, TIMP1-3). Cyclic strain also resulted in the extracellular release of ANGPTL4 protein by tendon cells. Our study is the first report demonstrating the induction of ANGPTL4 mRNA and release of ANGPTL4 protein in response to cyclic strain. Tenocytes may contribute to the upregulation of angiogenesis during the development of overuse tendinopathy.

Tuning magnetism of monolayer MoS2 by doping vacancy and applying strain

In view of important role of inducing and manipulating the magnetism in two-dimensional materials for the development of low-dimensional spintronic devices, the influences of strain on electronic structure and magnetic properties of commonly observed vacancies doped monolayer MoS2 are investigated using first-principles calculations. It is shown that unstrained VS, VS2, and VMoS3 doped monolayer MoS2 systems are nonmagnetic, while the ground state of unstrained VMoS6 doped system is magnetic and the magnetic moment is contributed mainly by six Mo atoms around VMoS6. In particular, tensile strain can induce magnetic moments in VS, VS2, and VMoS3 doped monolayer MoS2 due to the breaking of Mo–Mo metallic bonds around the vacancies, while the magnetization induced by VMoS6 can be effectively manipulated by equibiaxial strain due to the change of Mo–Mo metallic bonds around VMoS6 under strains.