Strain Regime Research Articles

Flexible electrically resistive-type strain sensors based on reduced graphene oxide-decorated electrospun polymer fibrous mats for human motion monitoring

In this work, a novel flexible electrically resistive-type strain sensor with special three-dimensional conductive network was developed based on reduced graphene oxide (RGO)-decorated flexible thermoplastic polyurethane (TPU) electrospun fibrous mats. Scanning electron microscopy results indicated that RGO was localized on surfaces of the TPU fibers uniformly and formed conductive paths. The interaction between electrospun TPU fibers and RGO was investigated by using Fourier transform infrared spectra and X-ray diffraction. These fibers conductive paths connected with each other and constructed an excellent three-dimensional conductive network. The special hierarchical conductive network endowed our RGO/TPU strain sensors with a desirable integration of good stretchability and high sensitivity (gage factor (GF) of 11 in strain of 10% and 79 in strain of 100% in reversible strain regime), good durability and stability (stretch/release test of 6000 cycles) and a fast response speed. The mechanism of the evolution of residual resistance and residual strain of RGO/TPU strain sensors under cyclic loading were investigated in detail. RGO/TPU strain sensors were attached on skin or clothes to monitor various human motions. The results demonstrate that our flexible strain sensors have wide application prospects in smart wearable device.

On the characterisation of polar fibrous composites when fibres resist bending

This study aims to initiate research for the invention of methods appropriate for characterisation of fibre-reinforced materials that exhibit polar material behaviour due to fibre bending resistance. It thus focuses interest in the small strain regime, where there are examples of particular deformations for which non-polar linear elasticity fails to distinguish clearly the nature of a fibrous composite or even to account for the presence of fibres. Particular attention is accordingly given to the solution of the polar material version of the pure bending problem of transverse isotropic or special orthotropic plates with embedded fibres resistant in bending. It is seen that pure bending deformation enables polar fibre-reinforced materials to generate constant couple stress-field which, in turn, endorses uniqueness of the solution of the corresponding boundary value problem. In this context, by appropriately extending the validity of Clapeyron's theorem within the regime of polar linear elasticity for fibre-reinforced materials, it is shown that the solution of well-posed linear elasticity boundary value problems that generate a constant couple-stress field is unique. The well-known uniqueness of solution of conventional, non-polar linear elasticity boundary value problems is, in fact, a particular case in which the generated constant value of the couple-stress field is zero.

A curvilinear high order finite element framework for electromechanics: From linearised electro-elasticity to massively deformable dielectric elastomers

This paper presents a high order finite element implementation of the convex multi-variable electro-elasticity for large deformations large electric fields analyses and its particularisation to the case of small strains through a staggered scheme. With an emphasis on accurate geometrical representation, a high performance curvilinear finite element framework based on an a posteriori mesh deformation technique is developed to accurately discretise the underlying displacement-potential variational formulation. The performance of the method under near incompressibility and bending actuation scenarios is analysed with extremely thin and highly stretched components and compared to the performance of mixed variational principles recently reported by Gil and Ortigosa (2016) and Ortigosa and Gil (2016). Although convex multi-variable constitutive models are elliptic hence, materially stable for the entire range of deformations and electric fields, other forms of physical instabilities are not precluded in these models. In particular, physical instabilities present in dielectric elastomers such as pull-in instability, snap-through and the formation, propagation and nucleation of wrinkles and folds are numerically studied with a detailed precision in this paper, verifying experimental findings. For the case of small strains, the essence of the approach taken lies in guaranteeing the objectivity of the resulting work conjugates, by starting from the underlying convex multi-variable internal energy, whence avoiding the need for further symmetrisation of the resulting Maxwell and Minkowski-type stresses at small strain regime. In this context, the nonlinearity with respect to electrostatic counterparts such as electric displacements is still retained, hence resulting in a formulation similar but more competitive with the existing linearised electro-elasticity approaches. Virtual prototyping of many application-oriented dielectric elastomers are carried out with an eye on pattern forming in soft robotics and other potential medical applications.

How to Realize Volume Conservation During Finite Plastic Deformation

Volume conservation during plastic deformation is the most important feature and should be realized in elastoplastic theories. However, it is found in this paper that an elastoplastic theory is not volume conserved if it improperly sets an arbitrary plastic strain rate tensor to be deviatoric. We discuss how to rigorously realize volume conservation in finite strain regime, especially when the unloading stress free configuration is not adopted in the elastoplastic theories. An accurate condition of volume conservation is first clarified and used in this paper that the density of a volume element after the applied loads are completely removed should be identical to that of the initial stress free states. For the elastoplastic theories that adopt the unloading stress free configuration (i.e., the intermediate configuration), the accurate condition of volume conservation is satisfied only if specific definitions of the plastic strain rate are used among many other different definitions. For the elastoplastic theories that do not adopt the unloading stress free configuration, it is even more difficult to realize volume conservation as the information of the stress free configuration lacks. To find a universal approach of realizing volume conservation for elastoplastic theories whether or not adopt the unloading stress free configuration, we propose a single assumption that the density of material only depends on the trace of the Cauchy stress by using their objectivities. Two strategies are further discussed to satisfy the accurate condition of volume conservation: directly and slightly revising the tangential stiffness tensor or using a properly chosen stress/strain measure and elastic compliance tensor. They are implemented into existing elastoplastic theories, and the volume conservation is demonstrated by both theoretical proof and numerical examples. The potential application of the proposed theories is a better simulation of manufacture process such as metal forming.

High strain rate deformation of ARMOX 500T and effects on texture development using neutron diffraction techniques and SHPB testing

The authors evaluated the crystallographic texture, defined as the distribution of orientation of crystals (or grains), to gauge the deformation and microstructural evolution of ARMOX 500T armour plates at elevated strain rates. Using neutron diffraction, the authors examined a number of specimens deformed at room temperature and high strain rates and contrasted these with equivalent samples deformed quasi-statically. Since crystallographic texture can play a part in the armour's ballistic response the authors were able to observe a rate dependent textural development, with the strengthening of the rolling α-fibre. The hot rolling process used in the manufacture of these steels leads to a through thickness texture variation that leads to an asymmetric transitional texture in the strain regime (1–2%) but with increased strain a symmetric texture develops irrespective of the strain rate, albeit with different intensities. By extending the testing program the authors were also able to deduce the strength parameters for the Johnson-Cook model through split Hopkinson pressure bar testing at high strain rates (1000–3000s−1) and elevated temperatures (20–600°C). The results, when compared with existing literature, show deviations in the strain rate sensitives of the tested specimens and, subsequently, variations in the computed flow stress parameters.

A note on the linearization of the constitutive relations of non-linear elastic bodies

Within the context of the non-linear theory of Cauchy elastic bodies (hence Green elastic bodies which are a sub-set of Cauchy elastic bodies wherein the stress is derivable from a potential), linearization with regard to the gradient of displacement, in the sense that the squares of the norms of the gradient of displacement can be neglected in comparison tothe norm of the gradient of displacement, leads inexorably to the classical linearized elastic model. It is however common, especially in work related to inelastic bodies, to see expressions for the Cauchy stress as a nonlinear function of the linearized strain. Even though such models are outside the purview of purely elastic response, the nonlinear relationship between the stress and the linearized strain is also often assumed to hold in the elastic range also. While the linearized strain being a nonlinear function of the stress has no basis within the context of the classical Cauchy elasticity theory, we show that a proper justification can be provided for such models within the context of the new class of constitutive relations that have been developed to describe the response of elastic bodies by Rajagopal [19], and these models can be generalized to also describe the inelastic response in the small strain regime.

Effects of hot/cold deformation on the microstructures and mechanical properties of ultra-low carbon medium manganese quenching-partitioning-tempering steels

The mechanical properties and designed microstructure evolution have been investigated in ultra-low carbon medium Mn steels for enhanced strength, plasticity and toughness, after an innovative quenching-partitioning-tempering (QPT) treatment with different initial conditions, cold rolling (CR) and hot rolling (HR). The transmission electron microscopy (TEM) combined with 3D atom probe tomography (APT) observed plenty of block austenite (30%) with dispersed precipitation in CR-QPT steels, while less amounts of film austenite (18%) with a higher density of nanoprecipitates were found in HR-QPT steels. The controlled multiphase microstructure evolution strongly depends on the Mn diffusion and segregation process. The overall strength-ductility combinations of two QPT-steels from the contribution of combined nanoprecipitation hardening and transformation-induced plasticity (TRIP) effects, are strongly influenced by the varying austenite mechanical stability connected with the volume fraction, grain size, morphologh and dislocation density of CR and HR-QPT samples. The unloading-reloading tests reveal the respective roles of precipitation hardening and TRIP effect in the overall mechanical properties according to the Baushinger effect (BE): the nanoprecipitation results in a higher back stress strengthening, while the deformation-induced martensite transformation in a wide strain regime degrades the large stress concentration in grain boundaries (GB), leading to a back stress softening but effective stress hardening in the later deformation stage. In addition, CR-QPT samples show a significant higher value of impact toughness than HR-QPT samples. The QPT treatment of CR-QPT steels can not only eliminate the susceptible prior austenite grain boundaries, but also drive Mn enrichment at the phase boundaries diffusing into the pre-existing austenite interior due to a low migration rate of austenite/ferrite interfaces impeded by the nanoprecipitations in ferrite, contributing to a homogeneous Mn distribution and removing the grain boundary embrittlement.

DEFORMATION HISTORY AND CORRELATION OF PAIKON AND TZENA TERRANES (AXIOS ZONE, CENTRAL MACEDONIA, GREECE)

Paikon and Tzena terranes are situated in the centre part of Axios zone, between Almopia and Paionia ophiolitic belts. Tectonostratigraphic data reveal that both have been affected by the same polyphase deformation and metamorphism, as well that they have the same lithostratigraphic column. The first deformation phase took place during the Middle to Late Jurassic and is associated with ophiolite obduction, nappe- stacking, terrane accretion and crustal thickening (D1). Metamorphism does not exceed greenschist facies (M1). Relict HP-LT metamorphic assemblages predating M1 metamorphism are possibly developed during subduction processes and overloading of the obducted ophiolites on the continental margin, characterized the initial stages of deformation. Compressional tectonics and intense thrusting with the same kinematics continued in Lower Cretaceous time, affected all pre-Upper Cretaceous units and the obducted ophiolites (D2). This phase is associated with low-greenschist metamorphism (M2). The first main extensional event occurs in the Late Cretaceous, related to basin formation and sedimentation (D3). During Paleocene to Eocene, D4 intense imbrication of all tectonic units towards mainly SW takes place again. Nappes collapse and finally crustal exhumation taken place during Oligocene to Miocene, associated with low - angle normal faults, with a main top to the SW sense of movement (D5). In Miocene to recent times, high - angle normal and strike-slip faults are formed in an extensional to transtensional strain regime (D6), associated with Neogene to Quaternary basin formation and terrane dispersion. The basement rocks of both terranes are of Pelagonian origin, exhumed as a multiple tectonic window.

Single-Nanowire strain sensors fabricated by nanoskiving

This article describes the fabrication of single-nanowire strain sensors by thin sectioning of gold films with an ultramicrotome—i.e., “nanoskiving.” The nanowire sensors are transferred to various substrates from the water bath on which they float after sectioning. The electrical response of these single nanowires to mechanical strain is investigated, with the lowest detectable strain determined to be 1.6 × 10−5 with a repeatable response to strains as high as 7 × 10−4. The sensors are shown to have an enhanced sensitivity with a gauge factor of 3.1 on average, but as high as 9.5 in the low strain regime (ε ∼ 1 × 10−5). Conventional thin films of gold of the same height as the nanowires are used as controls, and exhibit inferior sensitivity. The practicality of this sensor is investigated by transferring a single nanowire to polyimide tape, and placing the sensor on the wrist to monitor the pulse pressure waveform from the radial artery. The nanowires are fabricated with simple tools and require no lithography. Moreover, the sensors can be “manufactured” efficiently, as each consecutive section of the film is a quasi copy of the previous nanowire. The simple fabrication of these nanowires, along with the compatibility with flexible substrates, offers possibilities in developing new kinds of devices for biomedical applications and structural health monitoring.

A robust hyper-elastic beam model under bi-axial normal-shear loadings

In this paper, a simple and robust constitutive model is proposed to simulate mechanical behaviors of hyper-elastic materials under bi-axial normal-shear loadings in the finite strain regime. The Mooney–Rivlin strain energy function is adopted to develop a two-dimensional (2D) normal-shear constitutive model within the framework of continuum mechanics. A motion field is first proposed for combined normal and shear deformations. The deformation gradient of the proposed field is calculated and then substituted into right Cauchy–Green deformation tensor. Constitutive equations are then derived for normal and shear deformations. They are two explicit coupled equations with high-level polynomial non-linearity. In order to examine capabilities of the developed hyper-elastic model, uniaxial tensile responses and non-linear stability behaviors of moderately thick straight and curved beams undergoing normal axial and transverse shear deformations are simulated and compared with experiments. Fused deposition modeling technique as a 3D printing technology is implemented to fabricate hyper-elastic beam structures from soft poly-lactic acid filaments. The printed specimens are tested under tensile/compressive in-plane and compressive out-of-plane forces. A finite element formulation along with the Newton–Raphson and Riks techniques is also developed to trace non-linear equilibrium path of beam structures in large defamation regimes. It is shown that the model is capable of predicting non-linear equilibrium characteristics of hyper-elastic straight and curved beams. It is found that the modeling of shear deformation and finite strain is essential toward an accurate prediction of the non-linear equilibrium responses of moderately thick hyper-elastic beams. Due to simplicity and accuracy, the model can serve in the future studies dealing with the analysis of hyper-elastic structures in which two normal and shear stress components are dominant.

Effect of second hardening on floor response spectrum of a base-isolated nuclear power plant

The floor response spectra are calculated by constructing a numerical model (APR1400) equipped with base isolators of a bilinear material and a Bouc-Wen material, respectively, in order to investigate the effect of the second hardening. The variations of the earthquakes are incorporated to the loads, and two different properties of the isolator materials are modeled. The second hardening behavior increases the stiffness of the isolator in the high strain regime and suppresses the displacement of the isolator. Therefore, the role of the base isolation device isolating the superstructure from the ground motion does not perform properly, which causes amplification of the floor response of the superstructure. In practice, the second hardening of the isolator material might need to be taken into account for designing the base isolation system.

Eclogite inclusions from subducted metaigneous continental crust (Malpica‐Tui Allochthonous Complex, NW Spain): Petrofabric, geochronology, and calculated seismic properties

AbstractThis study describes the strain geometry, crystal‐plastic deformational features, isotopic age of metamorphism, and calculated seismic properties of two medium‐temperature eclogite types from the Malpica‐Tui Allochthonous Complex of Variscan NW Iberia. The eclogite types are eclogites with coronitic garnets and eclogites with a planolinear fabric. Both of them were buried, deformed and recrystallized under maximum pressure and temperature of 2.6 GPa and 610–640°C, and subsequently exhumed in a late Devonian subduction channel. The metamorphic peak of the subduction‐exhumation cycle occurred ~375 Ma ago. Omphacite petrofabric ties eclogites with coronitic garnet to noncoaxial constrictional strain and eclogites with planolinear fabrics to noncoaxial flattening strain and stretching along the lineation. We also used omphacite crystallographic preferred orientations to calculate and constrain the seismic properties of the eclogites. The slight variations in petrophysical properties observed are interpreted to result from variations in the strain regime recorded by pristine eclogites, or from variations in the modal proportions of the constituent high‐pressure minerals. We foresee that eclogite in subduction metamorphic complexes might be either seismically undetectable or detected as planar features with high impedance contrasts relative to their host rocks.

A fractional transient model for the viscoplastic response of polymers based on a micro-mechanism of free volume distribution

In the present work, the nonlinear viscoelastic/viscoplastic response of polymeric materials is described by introducing essential modifications on a model developed in previous works. A constitutive equation of viscoelasticity, based on the transient network theory, is introduced in a more generalized form, which takes into account volume changes during deformation. This time-dependent equation accounts for the nonlinearity and viscoplasticity at small elastic and finite plastic strain regime. The present description was proved to be more flexible, given that it contains a relaxation function that has been derived by considering instead of first order kinetics a fractional derivative that controls the rate of molecular chain detachment from their junctions. Therefore, the new equation has a more global character, appropriate for cases where heavy tails are expected. On the basis of the distributed nature of free volume, a new functional form of the rate of plastic deformation is developed, which is combined with a proper kinematic formulation and leads to the separation of the total strain into the elastic and plastic part. A three-dimensional constitutive equation is then derived for an isotropic, compressible medium. This analysis was proved to be capable of capturing the main aspects of inelastic response as well as the instability stage taking place at the tertiary creep, related to the creep failure.

Static and Dynamic Large Strain Properties of Methyl Cellulose Hydrogels

Methyl cellulose (MC) hydrogels display thermoreversible gelation upon heating. These hydrogels are abundantly employed in a variety of applications, rendering study of their mechanical properties relevant and important. Here we report on their basic elastic properties, based on ultrasonic measurements, and focusing on the heated solid gel, their mechanical properties in the quasi-static and dynamic (impact) large strain regimes are characterized. Unlike most other solids which soften upon heating, we find that methyl cellulose gels toughen increasingly on heating beyond the gelation point. Flow stress curves reveal polymer concentration dependent hardening. Contrary to most other soft materials, MC hydrogels do not present strain-rate sensitivity in the quasi-static range. Nevertheless, a dramatic change is observed in the dynamic regime, where at strain rates of ∼1500 s–1 a 10–20-fold increase in flow strength is observed relative to the quasi-static regime. The results of this investigation complement ...

New insights on the tectonics of the Lampedusa Plateau from the integration of offshore, onland and space geodetic data

Joint analysis of multichannel seismic reflection profiles calibrated with well-logs across the northern part of the Lampedusa Plateau (central sector of the Pelagian Block, Sicily Channel), of structural data collected on Lampedusa island, and of GNSS geodetic velocities of sites on the islands and on the northern shore of the Channel, suggests that this part of the plateau forms an anticlinorium (Lampedusa Plateau Anticlinorium, LPA). The LPA developed during Paleogene to Early Miocene intraplate contraction followed by Miocene to current strike-slip deformation. It is formed by WNW-ESE striking highs and lows, which have an ~20 km average wavelength and culminate at the Lampione-Lampedusa High. These broad folds are bounded by high-angle faults with a reverse component of displacement, which cut Eocene to Lower Pliocene strata offshore, and Late Miocene strata on Lampedusa. Extensional faults, that have a bathymetric expression and are responsible for marked stratal tilting due to their listric geometry, are only found to the NE of the island and are associated to the rifting that affected the central part of the Sicily Channel in the Pliocene-Quaternary. Seismic reflection profiles show that normal fault activity peaked during the middle part of the Pliocene and strongly diminished afterward. Appraisal of recent plate motion reconstructions and of published and new structural data offshore and on-land suggest that the main growth phase of the LPA occurred during (Late Cretaceous?) Paleocene-Early Miocene ~N-S convergence between Nubia and Eurasia and associated intraplate shortening. Starting from Early Miocene, likely in response to a CCW rotation of the plate convergence direction, strike-slip deformation occurred with a ~NW-SE shortening axis and ~NE-SW extension axis. During this time span the previous contractional structures were locally reactivated in transpression. The two different strain regimes, extensional and transpressional that established since Miocene NE and W to NW of Lampedusa, respectively, still persist today as documented by geodetic velocities.

Mechanical Stability and Deformation-Induced Transformation of Retained Austenite in TRIP Steels at Low Temperatures

The tensile properties and the stability of retained austenite in TRIP steels with different volume fraction of retained austenite have been studied at low temperature. The steels showed a good valance of strength and ductility at 193 K. Their work-hardening rates were decreased linearly and kept a high value in the high strain regime at 193 K. The retained austenite was mostly transformed into martensite less than 10% strain at 193 K.

The interplay between subduction and lateral extrusion: A case study for the European Eastern Alps based on analogue models

A series of analogue experiments simulating intra-continental subduction contemporaneous with lateral extrusion of the upper plate are performed to study the interference between these two processes at crustal levels and in the lithospheric mantle. The models demonstrate that intra-continental subduction and coeval lateral extrusion of the upper plate are compatible processes leading to similar deformation structures within the extruding region as compared to the classical setup, lithosphere-scale indentation. Strong coupling across the subduction boundary allows for the transfer of stresses to the upper plate, where strain regimes are characterized by crustal thickening near a confined margin and dominated by lateral displacement of material near a weak lateral confinement. The strain regimes propagate laterally during ongoing convergence creating an area of overlap characterized by transpression. When subduction is oblique to the convergence direction, the upper plate is less deformed and as a consequence the amount of lateral extrusion decreases. In addition, strain is partitioned along the oblique plate boundary resulting in less subduction in expense of right lateral displacement close to the weak lateral confinement. Both oblique and orthogonal subduction models have a strong resemblance to lateral extrusion tectonics of the Eastern Alps (Europe), where subduction of the adjacent Adriatic plate beneath the Eastern Alps is debated. Our results imply that subduction of Adria is a valid mechanisms to induce extrusion-type deformation within the Eastern Alps lithosphere. Furthermore, our findings suggest that the Oligocene to Late Miocene structural evolution of the Eastern Alps reflects a phase of oblique subduction followed by a later stage of orthogonal subduction conform a Miocene shift in the plate motion of Adria. Oblique subduction also provides a viable mechanism to explain the rapid decrease in slab length of the Adriatic plate beneath the Eastern Alps towards the Pannonian Basin.

3D full-field quantification of cell-induced large deformations in fibrillar biomaterials by combining non-rigid image registration with label-free second harmonic generation.

To advance our current understanding of cell-matrix mechanics and its importance for biomaterials development, advanced three-dimensional (3D) measurement techniques are necessary. Cell-induced deformations of the surrounding matrix are commonly derived from the displacement of embedded fiducial markers, as part of traction force microscopy (TFM) procedures. However, these fluorescent markers may alter the mechanical properties of the matrix or can be taken up by the embedded cells, and therefore influence cellular behavior and fate. In addition, the currently developed methods for calculating cell-induced deformations are generally limited to relatively small deformations, with displacement magnitudes and strains typically of the order of a few microns and less than 10% respectively. Yet, large, complex deformation fields can be expected from cells exerting tractions in fibrillar biomaterials, like collagen. To circumvent these hurdles, we present a technique for the 3D full-field quantification of large cell-generated deformations in collagen, without the need of fiducial markers. We applied non-rigid, Free Form Deformation (FFD)-based image registration to compute full-field displacements induced by MRC-5 human lung fibroblasts in a collagen type I hydrogel by solely relying on second harmonic generation (SHG) from the collagen fibrils. By executing comparative experiments, we show that comparable displacement fields can be derived from both fibrils and fluorescent beads. SHG-based fibril imaging can circumvent all described disadvantages of using fiducial markers. This approach allows measuring 3D full-field deformations under large displacement (of the order of 10μm) and strain regimes (up to 40%). As such, it holds great promise for the study of large cell-induced deformations as an inherent component of cell-biomaterial interactions and cell-mediated biomaterial remodeling.

Crack‐Free, Soft Wrinkles Enable Switchable Anisotropic Wetting

AbstractSoft skin layers on elastomeric substrates are demonstrated to support mechano‐responsive wrinkle patterns that do not exhibit cracking under applied strain. Soft fluoropolymer skin layers on pre‐strained poly(dimethylsiloxane) slabs achieved crack‐free surface wrinkling at high strain regimes not possible by using conventional stiff skin layers. A side‐by‐side comparison between the soft and hard skin layers after multiple cycles of stretching and releasing revealed that the soft skin layer enabled dynamic control over wrinkle topography without cracks or delamination. We systematically characterized the evolution of wrinkle wavelength, amplitude, and orientation as a function of tensile strain to resolve the crack‐free structural transformation. We demonstrated that wrinkled surfaces can guide water spreading along wrinkle orientation, and hence switchable, anisotropic wetting was realized.

Crack-Free, Soft Wrinkles Enable Switchable Anisotropic Wetting.

Soft skin layers on elastomeric substrates are demonstrated to support mechano-responsive wrinkle patterns that do not exhibit cracking under applied strain. Soft fluoropolymer skin layers on pre-strained poly(dimethylsiloxane) slabs achieved crack-free surface wrinkling at high strain regimes not possible by using conventional stiff skin layers. A side-by-side comparison between the soft and hard skin layers after multiple cycles of stretching and releasing revealed that the soft skin layer enabled dynamic control over wrinkle topography without cracks or delamination. We systematically characterized the evolution of wrinkle wavelength, amplitude, and orientation as a function of tensile strain to resolve the crack-free structural transformation. We demonstrated that wrinkled surfaces can guide water spreading along wrinkle orientation, and hence switchable, anisotropic wetting was realized.