Small Strain Range Research Articles

Optical flow method for measuring deformation of soil specimen subjected to torsional shearing

In this study optical flow method was used for soil small deformation measurement in laboratory tests. The main objective was to observe how the deformation distributes along the whole height of cylindrical soil specimen subjected to torsional shearing (TS test). The experiments were conducted on dry non-cohesive soil specimens under two values of isotropic pressure. Specimens were loaded with low-amplitude cyclic torque to analyze the deformation within the small strain range (0.001–0.01%). Optical flow method variant by Ce Liu (2009) was used for motion estimation from series of images. This algorithm uses scale-invariant feature transform (SIFT) for image feature extraction and coarse-to-fine matching scheme for faster calculations. The results were validated with the Particle Image Velocimetry (PIV). The results show that the displacement distribution deviates from commonly assumed linearity. Moreover, the observed deformation mechanisms analysis suggest that the shear modulus G commonly determined through TS tests can be considerably overestimated.

Optimizing modified triaxial testing for small strain zone using local displacement transducers and bender element for cement-treated soft soil

The settlement behavior is a common problem on the railway structure that can be optimized by applying cement-treated soil as ground restoration. However, the application of a high cement mixing content needs a proper estimation that can be achieved by adjusting the element testing. The strain measurement devices can estimate the deformation characteristics, such as secant modulus, Poisson ratio, and shear modulus that can describe the settlement behavior and stiffness of cement-treated soil. This research is focused on a static analysis of triaxial consolidated undrained (CU¯) testing that is improved by the axial and radial local displacement transducer (LDT) and bender element to increase the accuracy of measurement results. Furthermore, the secant modulus and shear modulus is more accurate when the combination of radial and axial LDT is used due to a small strain range. Lastly, the shear modulus measurement is improved by using a filler in the cement-treated soil for the bender element test. To conclude, this system of testing for the static condition can be utilized for the dynamic condition, because the measurement shows a reliable result for a small strain range which is the parameter of the dynamics condition.

Flexible hierarchical helical yarn with broad strain range for self-powered motion signal monitoring and human-machine interactive

To realize broad strain range and highly flexible self-sustainable intelligent wearable electronics, an ideal solution is integrating the structural diversity of flexible textiles with rapidly evolving energy harvesting technologies. Herein, a highly stretchable, flexible yarn with broad strain response range up to 120% is reported based on a multi-gradient hierarchical helical structure. The flexible hierarchical helical yarn (HHY) was obtained via coiling the conductive electrodes around a highly stretchable PU (the first helix layer) and super flexible silicon rubber (the second helix layer), respectively. The optimized HHY can operate within the strain range of 60%–120% and in the low-frequency scope of less than 2 Hz that matches human movement, the response ability of as-designed HHY to small strain range was also verified via harvesting the energy generated by body movement. Simultaneously, the generation of different current signals shows its distinct advantage in distinguishing joint-bending related human motion. Significantly, it was discovered that the harvested bioenergy can be directly applied to wirelessly control household devices without amplifying the signal. Furthermore, the HHY can be successfully served as a trigger switch to drive the electric piano and robotic arm synchronously when incorporating in a human-machine interactive system, indicating that the HHY has superior responsiveness to multiple synergy action mode. The paper shows that our HHY with a wide deformation range is a promising candidate for self-powered sensing and intelligent interaction.

Predicting tensile properties of monolayer white graphene involving edge effect

Elastic properties of monolayer h-BN nanosheet, also known as white graphene, involving edge effect are systematically studied by the atomic finite element method. By carrying out a uniaxial tensile test along zigzag and armchair directions, respectively, the corresponding stress–strain curves of various types of h-BN nanosheets can be obtained by the first-order derivative of potential with respect to the strain. Consequently, zigzag and armchair Young’s moduli of h-BN nanosheets can be extracted from stress to strain curves in the small strain range which mainly follows a linear relationship. The results demonstrate that zigzag edge can always bear a slightly larger stress than armchair edge. As the size increases, both zigzag and armchair Young’s moduli decrease and get close to each other. This phenomenon indicates an isotropy material of h-BN nanosheets which is also verified by an analytical model. From a systemic study of various h-BN nanosheets, it is found that zigzag edge atoms have a distinctly increasing effect on elastic properties while armchair edge atom show a slight decreasing effect.

A Creep Model of Asphalt Mixture Based on Variable Order Fractional Derivative

In order to quantitatively describe the time-varying mechanical properties of asphalt mixture during creep process, a nonlinear viscoelastoplastic creep model was proposed, by using variable-order fractional calculus. The differential order of the variable-order fractional element of the model is no longer constant, but a variable that changes with time, which reflects the changes of the mechanical properties of the material during the creep process. Whereas the tertiary creep phase is modeled by the viscoplastic element with time-varying viscosity, which is attributed to damage evolution. The uniaxial creep compression tests of AC-13C asphalt mixture under different stress levels (0.7 MPa, 0.9 MPa, 1.1 MPa, 1.3 MPa, 1.5 MPa, 1.7 MPa) were carried out with MTS-809 testing machine at 25 °C, and the test results were analyzed by the model using Levenberg–Marquardt optimization algorithm. It is shown that creep damage occurs when the applied stress exceeds a certain critical value, and the damage incubation time depends on the applied stress level. The higher stress decreases the damage incubation time. The model is in good agreement with the experimental results, and is applicable to describe the entire creep process, which consists of primary, steady and tertiary stages. Moreover, the variation of the model parameter can describe the change of viscoelastic properties of the material during the creep process. The differential order of the variable-order fractional element is constant during the primary creep stage, indicating that the creep behavior of the asphalt mixture is linear viscoelastic in small strain range. For the same stress level, the fractional order of the steady creep stage is greater than that of the primary creep stage, and it increases with the increasing stress level, which shows that the viscous behavior in the steady creep is more remarkable than that in the primary creep, and the higher the stress level, the more prominent the viscous performance exhibits.

Change in mechanical behaviour of gap-graded soil subjected to internal erosion observed in triaxial compression and torsional shear

Internal erosion can be a cause of failure in hydraulic structures such as levees, dikes and embankment dams. Suffusion is a type of internal erosion in which the fine particles migrate through the voids between the coarse particles under seepage flow, leaving behind the coarse skeleton. In this study the impacts of suffusion on the mechanical properties of soil in triaxial compression and torsional shear were investigated using a gap-graded soil mix of Silica sand No.5 and non-plastic silt. It was found that the erosion process varied depending on the initial density of the soil and higher density specimens showed relatively lower rates of erosion, degree of erosion, and compressive straining during erosion as compared with loose specimens. Effects on the mechanical behaviour​ of the soil were also dependent on the initial density of the specimen, with changes in the small strain stiffness, secant stiffness degradation, yield loci, small strain peak strength and medium strain strength in both drained and undrained conditions. In triaxial loading, force chains of coarse particles’ skeleton reinforced by fines developed in the suffusion process in the direction of major principal stress, then the stiffness at small strain increased. On the other hand, in torsional shear testing, the reinforced soil skeleton established by the erosion did not resist against shear loading. Increase in stiffness at small strain range was not observed.

Strain engineering the behaviors of small molecules over defective MoS2 monolayers in the 2H and 1T′ phases

The influence of strain on the behaviors of gas molecules over surface is always limited by the relative weak gas adsorption, the small range of elastic strain of adsorbents and the uniform response of surface sites. However, the latter two factors may be overcome in two-dimensional (2D) materials with defects. In this work, we employ first-principles calculations to investigate the behavior of a series of common gas molecules (CO, CO2, NH3, SO2, NO, NO2 and O2) on defective (S vacancies and non-metal C/N/O doped) MoS2 monolayers in both the 2H and 1T′ phases under biaxial strain (± 5%). When defects are introduced, strain can cause the gas molecules around the defects to physically/chemically adsorb, desorb, dissociate or even react with dopant. Meanwhile, the mechanical energy consumed to generate strain can be effectively transferred to change the energy of adsorption/desorption/reaction of adsorbates with an efficiency of at least 15% (if only adsorption strength is altered) up to 200% (if reaction is triggered). Subsequently, a number of interesting phenomena can be observed. For example, the doping-and-undoping cycle (e.g., the C doping of 2H-MoS2 and N doping of 1T′-MoS2 monolayers) can be dynamically controlled by pumping relevant gases and applying proper strain. Reversible adsorption and desorption of NH3 on defective MoS2 monolayers in both phases can be achieved within ± 3% strain. NO or NO2 and CO can be converted into non-toxic N2O and CO2 over the N-doped (3% strain) and O-doped (− 3% strain) 1T′-MoS2 monolayers. In essence, defective 2D materials can serve as ideal multi-purpose platforms for strain engineering the behaviors of adsorbates.

Refinement of the Hardening Soil model within the small strain range

The popularity of the elasto-plastic Hardening Soil (HS) model is based on simple parameter identification from standard testing and empirical formulas. The HS model is implemented in many commercial FE codes designed to analyse geotechnical problems. In its basic version, the stress–strain behaviour within the elastic range is subject to the hypoelastic power law, which assures the barotropy of the elastic stiffness. However, a proper modelling within the small strain range, i.e. strain-induced stiffness degradation and correct reproduction of the hysteretic behaviour, was one of the most important drawbacks in the HS formulation. The first small strain stiffness extension to the HS model was proposed by Benz (Small strain stiffness of soils and its numerical consequences, 2007), and the new model was called Hardening Soil Small (HSS). Despite the simple isotropic formulation, its applicability was proved in various numerical simulations in geotechnics. However, the HSS formulation exhibits a serious fault known in the literature as overshooting, i.e. uncontrolled reset of the loading memory after tiny unloading–reloading cycles. The authors' main aim was to retain the set of material parameters for the HSS formulation and to propose a new small strain extension to the HS model without overshooting. The new proposal is based on the Brick model which represents the concept of nested yield surfaces in strain space. The implementation aspects of the new HS-Brick model are described, and its performance is presented in some element tests and selected boundary value problems by comparisons with the HSS formulation.

Application of adaptive neuro-fuzzy inference system for numerical interpretation of soil torsional shear test results

The aim of this study is to replace the stress-strain constitutive relation within a finite element method (FEM) implementation with an adaptive neuro-fuzzy inference system (ANFIS). The computation is supported by the Compute Unified Device Architecture (CUDA) technology available on modern Nvidia graphics processing units (GPUs). The multi-threaded multiple input / multiple output (MIMO) CUDA-ANFIS model is compared with experimental results of torsional shear (TS) tests. The cylindrical non-cohesive soil samples were tested within the small strain range (0.001–0.1%). Particular attention was paid to a good reflection of the results of laboratory tests in numerical simulations based on FEM with embedded ANFIS. The obtained results confirm the possibility of replacing explicit constitutive relations with a neuro-fuzzy inference system and using this model to determine the soil mechanical properties in engineering practice. The most important finding is that the decrease in the discretization mesh density as well as the decrease in the number of linguistic labels result in better overall system performance. In addition, the created ANFIS algorithm adapted to the GK110 graphics processor architecture speeds up calculations 27 times compared to single-threaded implementation. The presented approach can be used to construct implicit constitutive models based on the numerical interpretation of the results obtained from laboratory and/or field tests.

A homogenization equation for the small strain stiffness of gap-graded granular materials

Sandstone usually disintegrates into gap-graded granular materials with a matrix-sustained structure due to weathering factors. This paper presents an investigation on the small strain stiffness of this type of granular materials based on Discrete Element Method (DEM) simulations. Our numerical results indicate the percentage of sliding contact is negligibly small within the small strain range, and the small strain stiffness of fines is well consistent with the widely recognized Hardin’s equation. Both findings confirm the validity of DEM simulations on the study of small strain response of granular materials. The simulation results are further analyzed based on mixture theory. A structure variable is introduced to correlate with the evolution of inter-aggregates structure. This variable is found to increase with the volume fraction of coarse aggregates but is rather independent of the confining stress and the initial void ratio of the fine matrix. Based on the insights drawn from DEM simulations, a homogenization equation is proposed for the small strain stiffness of gap-graded granular soils to reproduce the small strain stiffness of gap-gaped materials observed in our numerical simulations and is further validated by laboratory test data from the literature. The equation can be conveniently incorporated into classical elastoplastic models to model gap-graded granular materials.

Acoustic Emission Behavior of Tropical Residual Soil

emission technique has extensively been used for a wide variety of engineering materials, but less attention has yet been paid on the application of this non-destructive technique to investigate the fundamental behaviors of geomaterial. In the present study, acoustic emission method was adopted in conjunction with the conventional stress-strain-time measurement to investigate the mechanical behaviors of a selected tropical residual soil. A systematic acoustic emission instrumentation setup, which was devised in a monotonic triaxial shear apparatus, was evidenced to provide reasonable experimental results. From the isotropic consolidation results, it was realized that the Kaiser’s effect was observable and the pre-stressed level as induced by compaction could be determined through acoustic emission. In undrained shearing, the acoustic emission response was found to be corresponding with the axial strain measurement. Initial soil yielding, which was mobilized at small strain range, was also able to be determined. The acoustic emission response of the studied tropical residual soil also showed good similarity with the reported soils constituting considerable fines content.

An enhanced François distortional yield model: Theoretical framework and experimental validation

A distorted yield surface with a higher curvature in the preloading direction and a rather flat curve in the reverse direction has been observed in numerous materials that experience a preloading process. To describe such distorted yield surfaces, a novel distortional yield model was proposed. The model involves the distorted stress extended from the original version defined by François, and can be theoretically applied to any quadratic or nonquadratic yield functions. The original Hill48 and Barlat91 yield criteria were adopted as representatives in this work, for describing the behavior of different steel and aluminum sheets in a two-stage loading experiment. The experimental outcomes obtained from previous publications were employed for the validation of the model. A case of application in a deliberately designed two-stage loading experiment with annealed 6061 aluminum sheet was presented as well. Distinct yield surface distortion has been observed in the second loading stage at small deformation levels with the prestrained sheet metals, and the surface distortion gradually recovers and stabilizes within a small range of strain thereafter. Additionally, initial distortion is positively correlated with the prestrain level. Associated with a novel evolution rule of back stress, the distorted yield surface, as well as the transient phenomena including the Bauschinger effect, orthogonal softening and permanent softening effects in the second loading stage, was successfully described by the proposed model.

Intergranular Clay Films Control Inelastic Deformation in the Groningen Gas Reservoir: Evidence From Split‐Cylinder Deformation Tests

AbstractProduction of oil and gas from sandstone reservoirs leads to small elastic and inelastic strains in the reservoir, which may induce surface subsidence and seismicity. While the elastic component is easily described, the inelastic component, and any rate‐sensitivity thereof remain poorly understood in the relevant small strain range (≤1.0%). To address this, we performed a sequence of five stress/strain‐cycling plus strain‐marker‐imaging experiments on a single split‐cylinder sample (porosity 20.4%) of Slochteren sandstone from the seismogenic Groningen gas field. The tests were performed under in situ conditions of effective confining pressure (40 MPa) and temperature (100 °C), exploring increasingly large differential stresses (up to 75 MPa) and/or axial strains (up to 4.8%) in consecutive runs. At the small strains relevant to producing reservoirs (≤1.0%), inelastic deformation was largely accommodated by deformation of clay‐filled grain contacts. High axial strains (>1.4%) led to pervasive intragranular cracking plus intergranular slip within localized, conjugate bands. Using a simplified sandstone model, we show that the magnitude of inelastic deformation produced in our experiments at small strains (≤1.0%) and stresses relevant to the Groningen reservoir can indeed be roughly accounted for by clay film deformation. Thus, inelastic compaction of the Groningen reservoir is expected to be largely governed by clay film deformation. Compaction by this mechanism is shown to be rate insensitive on production timescales and is anticipated to halt when gas production stops. However, creep by other processes cannot be eliminated. Similar, clay‐bearing sandstone reservoirs occur widespread globally, implying a wide relevance of our results.

Dynamic performance of a full-scale micropile group: Relevance of nonlinear behaviour of the soil adjacent to micropiles

An extensive experimental in-situ campaign of dynamic tests carried out on a full-scale 2 × 2 group of inclined injected micropiles in alluvial soils is described in this paper. The campaign includes ambient vibration and impact load tests to investigate the dynamic behaviour of the soil-micropile system in the small strain range, and forced vibration tests to investigate the performance of the system in the nonlinear field. Accelerometers and geophones are adopted to acquire the dynamic response on the cap and the soil nerby the cap, while strain gauges are installed along the shaft of one micropile to capture the local curvatures and deflections. The influence of the micropile inclination on the translational and rotational behaviour of the group is evaluated. Moreover, the evolution of degradation phenomena such as the gap opening and slippage at the soil-micropile interface and the radial cracking of soil surrounding micropiles, are recognized, critically commenting the relevant effects on the fundamental frequencies and damping ratios of the system.

Micromechanical and microstructure analysis of strain-induced phenomena in ultrasonic additively-manufactured Al-6061 alloy

This work investigates the anisotropic mechanical behavior (both macro and micro) of Al6061 alloy samples manufactured using ultrasonic additive manufacturing. Samples from both sonotrode travel and vibration directions (TD and VD, respectively) were investigated in the as-built and aged (8 h at 180 °C under Argon gas) conditions. The aged VD-specimens showed appearance and propagation of Luders-like band, which did not exist in the TD-specimens, deformed at the same strain rate. X-ray diffraction, x-ray computed tomography, scanning electron microscopy, laser flash technique and in-situ loading with neutron diffraction were used to characterize the material and its hardening behavior during straining. Aging was mainly found to lead to relaxation of stresses, induced by the build process, some decrease in yield stress, and potential secondary phase reprecipitation. Stress partitioning, revealed via in situ neutron diffraction, showed that one of grain families, (110) || tensile axis, revealed strain softening at small strain range. This texture component, (110) || tensile axis, dominated the structure of VD-specimens, and was one of key factors stimulating band appearance and propagation.

The effect of reduced temperatures on microstructure development in tensile tested high-manganese steel

The current research is part of a project covering several grades of high-manganese steels (20–26 wt% Mn) with different chemical compositions, which were deformed at room and reduced temperatures. In the present paper, the microstructure development is analyzed at the onset of plastic deformation in Fe–Mn–Al–Si steel containing 21.2 wt% Mn. The examination was conducted under conditions of lowering the deformation temperature and aimed to show the influence of reduced temperatures on the occurrence of strain induced phase (martensitic) transformation.The steel samples were subjected to uniaxial deformation in a tensile test at gradually reduced temperatures, starting from 20 °C and then applying the temperatures 0 °C, −50 °C and −150 °C. The present paper includes the analysis of microstructure development and orientation relationships as well as determination of operating deformation mechanisms for samples after 10% of tensile strain. The main part of the research was carried out by means of scanning electron microscopy (SEM), using the method of electron back-scatter diffraction (EBSD).The carried out analysis indicates that within the range of small strains the mechanism controlling deformation behavior of high-manganese steel Fe–21Mn–3Al–3Si was slip of partial dislocations. This was immediately followed by the occurrence of strain induced phase transformation γ (fcc) → ε (hcp) and then locally ε (hcp) → α' (bcc). With decreasing deformation temperature a noticeable increase of the volume fraction of the martensitic phases was observed, first of all the ε-phase and to a much lesser extent α′-martensite. The ε-martensite appeared on the background of a deformed austenite initially in the form of relatively narrow bands. The α′-martensite was formed predominantly at the intersections of the ε-bands. An interesting result, however, is the fact that numerous places were also found where α′-martensite was formed in single set of parallel ε-phase bands. The preferential crystallographic orientation relations (ORs) between the γ-austenite and the strain induced ε- and α′- phases were successively followed, showing first of all the appearance of Shoji-Nishiyama (S–N) and Kurdjumov-Sachs (K–S) ORs respectively.

Experimental study on mechanical properties of the ventral and the dorsal tissues of porcine descending aorta

The mechanical properties of the aorta tissue is not only important for maintaining the cardiovascular health, but also is closely related to the development of cardiovascular diseases. There are obvious differences between the ventral and dorsal tissues of the descending aorta. However, the cause of the difference is still unclear. In this study, a biaxial tensile approach was used to determine the parameters of porcine descending aorta by analyzing the stress-strain curves. The strain energy functions Gasser-Ogden-Holzapfel was adopted to characterize the orthotropic parameters of mechanical properties. Elastic Van Gieson (EVG) and Sirius red stain were used to observe the microarchitecture of elastic and collagen fibers, respectively. Our results showed that the tissue of descending aorta had more orthotropic and higher elastic modulus in the dorsal region compared to the ventral region in the circumferential direction. No significant difference was found in hyperelastic constitutive parameters between the dorsal and ventral regions, but the angle of collagen fiber was smaller than 0.785 rad (45°) in both dorsal and ventral regions. The arrangement of fiber was inclined to be circumferential. EVG and Sirius red stain showed that in outer-middle membrane of the descending aorta, the density of elastic fibrous layer of the ventral region was higher than that of the dorsal region; the amount of collagen fibers in dorsal region was more than that of the ventral region. The results suggested that the difference of mechanical properties between the dorsal and ventral tissues in the descending aorta was related to the microstructure of the outer membrane of the aorta. In the relatively small strain range, the difference in mechanical properties between the ventral and dorsal tissues of the descending aorta can be ignored; when the strain is higher, it needs to be treated differently. The results of this study provide data for the etiology of arterial disease (such as arterial dissection) and the design of artificial blood vessel.

Cyclic and postcyclic behaviour of silts and silty sands from the Indo Gangetic Plain

The Indo Gangetic Plain (IGP) that lies on the verge of subduction zone of Indian and Eurasian plate is a seismically active, densely populated region with deep soil deposits. A number of critical structures such as rail and highway bridges and nuclear power plants are being built in the region to cater to the large population of the region, and hence the characterization of deep soil deposits in this region are important. In the present study undisturbed soil samples (UDS) from a site in the IGP plane are examined for static, cyclic, and post-cyclic behaviour. The soils tested have fines content varying from about 20% to 80%, and the fines are non-plastic in nature. The modulus reduction and damping ratio of soil at small, medium and large strain range is examined with the UDS by carrying out bender element, resonant column, and cyclic triaxial tests, respectively. Post cyclic behaviour of non-plastic silty soils is also examined with single stage and multistage cyclic triaxial testing. It is observed that the post-cyclic shear strength increases with increase in the non-plastic fines in the soil. The history of cyclic loading preceding the post cyclic tests is found to influence the tangent modulus observed in post cyclic tests. A site specific calibration parameter is proposed to predict pore pressure response using the energy based Green Mitchel Polito (GMP) pore pressure model.

Electromechanical Decoupling by Porous Aerogel Conducting Polymer

In the field of biointerface electronics, electromechanical decoupling—electrical performance independent of mechanical deformation—can ensure reliability of measured signals, which is critical in stable electrode. Herein, Chen et al. report such a decoupled and stretchable conductive polymer foam.

Evaluation and modeling of mechanical behaviors of thermosetting polymer under monotonic and cyclic tensile tests

A nonlinear elastic-inelastic model for a thermosetting polymer is proposed based on the molecular chain network theory. In the proposed model, the bond of the polymer chain is divided into physical and chemical bonds, and the physical bond is allowed to separate and recombine during the deformation. The decrease in the rigidity and increase in the inelastic strain are related to the development of the physical bond density to represent the characteristic deformation behavior of the polymer. A rate-form large deformation constitutive equation is then formulated based on the updated Lagrangian method. Additionally, deformation behaviors of the epoxy under monotonic and cyclic tensile tests were evaluated by experimental and computational studies. The experimental results of the monotonic tensile test displayed a gradual transition from elastic to inelastic deformation, strain softening behavior after the macroscopic yielding stress, and an increase in the initial slope and the macroscopic yielding stresses with an increasing strain rate. The computational model can represent such characteristics by controlling the development of the physical bond density. In a cyclic test, a decrease in the rigidity and an increase in the residual strain with increasing cycles were observed even in a small strain range. Such inelastic deformation depended on the strain rate and the given upper stress in the cyclic test. Further, the proposed model successfully reproduced such nonlinear behavior in the cyclic test.