Tangent Modulus Research Articles

Analysis of Undrained Shear Characteristics and Structural Damage of Granite Residual Soil

Three-dimensional consolidation testing, scanning electron microscopy, and undrained triaxial testing of granite residual soil (GRS) in Shenzhen, China, were conducted. The effect of the structural strength of GRS was quantitatively analyzed using the method of comprehensive structure potential parameter description. The failure strength ratio of the soil decreases with increasing confining pressure, and it is approximately 1 when the confining pressure is higher than the yield stress (σs). The undrained shear strength (Su) of the undisturbed soil varies in stages with confining pressure σ3. The relationship between Su and σ3 for the reconstituted soil is approximated as a straight line through the origin. The soil's comprehensive structure potential parameters (the structural contribution rates of the tangential shear modulus, mE, and the deviatoric stress, md) decrease linearly with increasing σ3. The mE and md sample values are similar under the same confining pressure. It is reasonable to use structure potential parameters to quantitatively evaluate the structure contribution rate of GRS. The microstructure is constantly adjusted, and the soil microstructure form for different confining pressures strongly correlates with its shear characteristics.

Corneal Biomechanical Properties Demonstrate Anisotropy and Correlate With Axial Length in Myopic Eyes.

The purpose of this study was to investigate the ex vivo and in vivo biomechanical characteristic of cornea in myopic eyes. Fifty-one corneal stromal lenticules were obtained from myopic eyes during the SMILE procedure and were tested by a biaxial tensile system within 24 hours postoperatively. The material properties of the lenticules were described using stress-strain curves and were compared among axial length (AL) <26 mm and AL ≥ 26 mm group. Pre-operative stress-strain index (SSI) parameters were used to evaluate the biomechanical properties of the cornea in vivo. Compared with AL < 26 mm, the tangent modulus significantly decreased in horizontal and vertical directions when AL ≥ 26 mm (P < 0.05); SSI also significantly decreased when AL ≥ 26 mm (P < 0.05). Anisotropic parameter is positively correlated with AL (r = 0.307, P < 0.05). Compared with AL < 26 mm, anisotropic parameter significantly increased when AL ≥ 26 mm (P < 0.05). SSI was negatively correlated with AL (r = -0.380, P < 0.05) in the AL < 26 mm group but not in the AL ≥ 26 mm group (P > 0.05). Compared with 26 mm ≤ AL < 27 mm group, the tangent modulus significantly decreased in the horizontal direction (P < 0.05) but not in the vertical direction when 27 mm ≤ AL < 28 mm (P > 0.05). The biomechanical properties of cornea decreased with the increase of AL. Tangent modulus significantly decreased in the horizontal direction compared with vertical direction. AL should be taken into account during calculation of corneal biomechanical parameters in order to improve validity.

Prediction of CO2 and ethylene produced in‐packaged apricot under cold plasma treatment by machine learning approach

AbstractIn this study, the fresh and in‐packaged apricots were treated with dielectric barrier discharge (DBD) cold plasma for 5, 10, and 15 min and then stored at 21°C for 12 days to simulate the shelf life of the apricot. The effects of DBD treatment on the main quality attributes of apricot such as physicochemical traits (mass loss, pH, soluble solid content, titratable acidity, and skin color), mechanical properties (Young's modulus, tangent modulus, and bioyield stress), in‐package gas composition and ethylene production were investigated during the storage time. In addition, the bruise susceptibility (BS) of control and treated samples at the microscale was evaluated by using pendulum test and scanning electron microscopy. The results of the mass loss, pH, soluble solid content, titratable acidity, skin color, and bioyield stress have been applied for input parameters of the developed artificial neural network (ANN) and support vector regression (SVR) models to predict the CO2 and ethylene production. The statistical data showed the performance of the developed ANN to predict the CO2 (R2 = 0.983, root mean square error [RMSE] = 0.486) and ethylene production (R2 = 0.933, RMSE = 5.376) was superior to SVR (CO2: R2 = 0.894, RMSE = 6.077 and ethylene: R2 = 0.759, RMSE = 14.117). These results indicated that intelligent methods are effective and robust tools for predicting the quality parameters of fresh fruits in the postharvest process.Practical ApplicationsAdvancement of technology and artificial intelligence leads to the tendency of many food industry engineers and researchers in the R&amp;D department to use this technology to classify and predict various food industry processes. In the process of packaging products, there are challenges such as the amount of produced carbon dioxide and ethylene inside the package, which affects the shelf life of fresh agricultural products. In this research, artificial neural networks and support vector machine methods have been used to predict the two mentioned parameters. This approach can be used for the digitalization of the packaging process of agricultural and horticultural products and reduce the number of experimental activities. In addition, it is possible to improve the digitalization process by the fusion of smart sensors with machine learning methods.

A new approach to the stability design of Ramberg–Osgood material struts

An energy formulation employing total potential energy principles is presented to derive a governing equation for strength predictions of struts made from materials following the Ramberg–Osgood constitutive law such as stainless steel, cold-formed steel, and aluminium alloys. The formula is generic and applicable to arbitrary cross-sections and all strut slendernesses for which flexural buckling is critical. Extensive comparisons against experimental data on square and rectangular hollow section struts as well as finite element simulations demonstrate the accuracy of the developed formula, while the effect of varying material parameters is examined through comprehensive parametric studies. Owing to its simplicity and its derivation based on mechanical principles, arbitrary configurations of material parameters and cross-sections can be analysed, making the formula suitable for use in design practice, representing effectively a non-iterative alternative to the widely accepted design load employing the tangent modulus. With the aid of the formula, new column buckling design provisions are developed, which show excellent agreement with experimental data and meet the reliability requirements specified within the structural Eurocodes.

Stability Calculation of the Plane Steel Frame Structures Using Tangent Modulus Theory

This paper considers the phenomenon of the instability of steel plane frame structures in the elastic–plastic domain. The numerical analysis uses finite element method, where the corresponding stiffness matrices are based upon the trigonometric and hyperbolic interpolation functions of normal forces. The tangent modulus concept is applied when buckling occurs in the plastic range. Thus, the stiffness matrices for nonlinear material behavior are also derived. The procedure for determining effective length factors of compressed columns, which implies a global stability analysis of entire frames, is established too. It means that the proposed approach is based on the assumption that the collapse of the structure occurs when the most loaded columns reach their stability limit. So, the presented procedure enables the calculation of the real critical load of plane frame structures in the elastic–plastic domain and determines the corresponding effective length factors.

Mechanical responses of anchoring structure under triaxial cyclic loading

Dynamic load on anchoring structures (AS) within deep roadways can result in cumulative damage and failure. This study develops an experimental device designed to test AS under triaxial loads. The device enables the investigation of the mechanical response, failure mode, instability assessment criteria, and anchorage effect of AS subjected to combined cyclic dynamic-static triaxial stress paths. The results show that the peak bearing strength is positively correlated with the anchoring matrix strength, anchorage length, and edgewise compressive strength. The bearing capacity decreases significantly when the anchorage direction is severely inclined. The free face failure modes are typically transverse cracking, concave fracturing, V-shaped slipping and detachment, and spallation detachment. Besides, when the anchoring matrix strength and the anchorage length decrease while the edgewise compressive strength, loading rate, and anchorage inclination angle increase, the failure intensity rises. Instability is determined by a negative tangent modulus of the displacement-strength curve or the continued deformation increase against the general downward trend. Under cyclic loads, the driving force that breaks the rock mass along the normal vector and the rigidity of the AS are the two factors that determine roadway stability. Finally, a control measure for surrounding rock stability is proposed to reduce the internal driving force via a pressure relief method and improve the rigidity of the AS by full-length anchorage and grouting modification.

Broadband dielectric behaviour and structural characterization of PVDF/PMMA/OMMT polymer nanocomposites for promising performance nanodielectrics in flexible technology advances

Characterization of broadband dielectric behaviour of polymer nanocomposites (PNCs) is vital for the exploration of efficient nanodielectrics as energy storage, flexible dielectric substrates, and insulators in a wide range of advanced electronic device technologies. Accordingly, herein, PNC films based on poly(vinylidene fluoride) (PVDF)/ poly(methyl methacrylate) (PMMA) blend matrix (80/20 wt/wt%) dispersed with 0, 2.5, 5, and 10 wt% organo-modified montmorillonite (OMMT) nanoclay are developed by state-of-the-art homogenized solution casting method. These PVDF/PMMA/OMMT compositions based flexible PNC films are characterized in detail by employing a scanning electron microscope (SEM) equipped with energy dispersive x-ray (EDX) device, x-ray diffractometer (XRD), Fourier transform infrared (FTIR) spectrometer, differential scanning calorimeter (DSC), inductance-capacitance-resistance (LCR) meter, and impedance/material analyzer (IMA). The SEM microimages, XRD traces, and FTIR spectra evidenced appreciable homogeneity and surface morphology, intercalated and exfoliated OMMT structures, and the α, β and γ-phase crystallites of the PVDF in these complex semicrystalline PNCs. The DSC thermograms confirmed a significant alteration in the melting temperature and degree of crystallinity of the PVDF crystallites with the increased amount of OMMT in the 80PVDF/20PMMA blend host matrix. The broadband dielectric dispersion spectra over the frequency range of 20 Hz−1 GHz explained the contribution of interfacial polarization in the complex dielectric permittivity at lower experimental frequencies, whereas at higher frequencies permittivity is ruled by dipolar polarization in these composites at 27 °C. The dielectric loss angle tangent and electric modulus spectra revealed an intense structural dynamics relaxation process in the upper radio frequency region. The influence of OMMT concentration on the dielectric permittivity and electrical conductivity is explored. The detailed dielectric and electrical characterization of these innovative semicrystalline composites with important structural and thermal properties revealed their immense potential as high-performance nanodielectrics for highlighting current applications of broadband frequency range electrical and electronic device technologies.

Structural analysis of shield machine cutting monopile using p-y curve based finite element method

In this study, the structural response of piles during shield machine cutting is analyzed using p-y curves based on the finite element method (FEM). In the FEM program, the tangent stiffness matrix of the nonlinear soil-pile spring is derived from the tangent modulus of the p-y curve. The nonlinear finite element equation is solved using the Newton-Raphson iterative method. The program can consider the influence of the shield thrust force, the soil reinforcement, and the cross-sectional area decrease during shield cutting. The program output comprises the lateral displacement, internal force, and bending moment of the laterally loaded monopile. The correctness and accuracy of this method are validated with both field test data and commercial finite difference method (FDM) program. The results show that shield thrust force is the main factor affecting the lateral displacement and bending moment of the pile; as the cutting section area of the pile is decreasing, the maximum negative moment increases while the maximum positive moment decreases; soil reinforcement has a negligible effect on the internal force but can effectively reduce the lateral displacement of the pile head.

Nonlinear bending–twisting coupling in electromechanical finite deformation of fiber-reinforced tubular dielectric elastomer for soft actuators

Previous studies have revealed that fiber-reinforced tubular dielectric elastomer actuators (TDEAs) exhibit unique characteristics, such as coupled deformation. Therefore, the present study focuses on the electromechanical behavior of fiber-reinforced TDEAs and analyzes induced coupled bending–twisting deformation analytically and numerically. An analytical framework is derived from the Helmholtz free energy of the system and, using the variation method, leads to equilibrium equations. Despite the limitation of homogeneous deformation, the results indicate relevant facts about the electromechanical behavior and stability of the considered TDEA. On the other hand, a numerical method is devised based on the nonlinear continuum, electro-elasticity, and large deformation theory. The resultant model and presented tangent modulus are validated using experimental data. The model makes it possible to develop a FEM algorithm and explore the behavior of the TDEA under various loading and boundary conditions. For example, the current paper presents the final deformation of a fiber-reinforced TDEA under internal pressure, axial force, and torque. It also explores the bending deformation of a designed tubular bending actuator using numerical analysis and the developed model. Analytical and numerical results share similar trends in longitudinal, radial, and torsional deformations before instability. It is also evident that for voltages higher than the critical voltage, when instability is detected, fiber orientation may cause more significant effects. Analytical and numerical findings confirm coupled deformations in different directions.

Buckling in inelastic regime of a uniform console with symmetrical cross section: computer modeling using Maple 18

The method of numerical integration of Euler problem of buckling of a homogeneous console with symmetrical cross section in regime of plastic deformation using Maple18 is presented. The ordinary differential equation for a transversal coordinate \(y\) was deduced which takes into consideration higher geometrical momenta of cross section area. As an argument in the equation a dimensionless console slope \(p=tg \theta\) is used which is linked in mutually unique manner with all other linear displacements. Real strain-stress diagram of metals (steel, titan) and PTFE polymers were modelled via the Maple nonlinear regression with cubic polynomial to provide a conditional yield point (\(t\),\(\sigma_f\)). The console parameters (free length \(l_0\), \(m\), cross section area \(S\) and minimal gyration moment \(J_x\)) were chosen so that a critical buckling forces \(F_\text{cr}\) corresponded to the stresses \(\sigma\) close to the yield strength \(\sigma_f\). To find the key dependence of the final slope \(p_f\) vs load \(F\) needed for the shape determination the equality for restored console length was applied. The dependences \(p_f(F)\) and shapes \(y(z)\), \(z\) being a longitudinal coordinate, were determined within these three approaches: plastic regime with cubic strain-stress diagram, tangent modulus \(E_\text{tang}\) approximations and Hook’s law. It was found that critical buckling load \(F_\text{cr}\) in plastic range nearly two times less of that for an ideal Hook’s law. A quasi-identity of calculated console shapes was found for the same final slope \(p_f\) within the three approaches especially for the metals.

Simplified Phenomenological Model for Ferroelectric Micro-Actuator.

As smart structures are becoming increasingly ubiquitous in our daily life, the need for efficient modeling electromechanical coupling devices is also rapidly advancing. Smart structures are often made of piezoelectric materials such as lead zirconate titanate (PZT), which exhibits strong nonlinear behavior known as hysteresis effect under a large applied electric field. There have been numerous modeling techniques that are able to capture such an effect; some techniques are suitable for obtaining physical insights into the micro-structure of the material, while other techniques are better-suited to practical structural analyses. In this paper, we aim to achieve the latter. We propose a simplified phenomenological macroscopic model of a nonlinear ferroelectric actuator. The assumption is based on the direct relation between the irreversible strain and irreversible electric field, and the consequently irreversible polarization. The proposed model is then implemented in a finite element framework, in which the main features such as local return mapping and the tangent moduli are derived. The outcomes of the model are compared and validated with experimental data. Therefore, the development presented in this paper can be a useful tool for the modeling of nonlinear ferroelectric actuators.

Particle shape effects on dynamic properties of granular soils: A DEM study

Particle shape is an essential aspect of granular soils that affects their mechanical properties. It is challenging to isolate the effect of particle shape from other mechanical properties such as inter-particle friction coefficient and particle shear modulus in laboratory tests. The discrete element method (DEM) makes it feasible to investigate the effect of macroscopic and mesoscopic particle morphologies including sphericity and roundness. This study provides a systematical DEM investigation of the particle shape effect on the dynamic properties of granular soils by simulating cyclic undrained triaxial tests at various initial confining pressures and void ratios. The results indicate that specimen consisting of angular particles generally exhibit a higher secant shear modulus G than that of rounded particles. Additionally, particle shape has no significant effect on modulus ratio G/G0 but a noticeable impact on damping ratio D at relatively large strains due to dilatancy. A weighted coordination number CN' was proposed to reveal the microscopic effect of particle shape on G0. Contact sliding was found to be the main cause of modulus degradation and damping increase with increasing shear strain. The tangential shear modulus ratio Gtan/G0 is inversely correlated to the weighted contact sliding ratio fs'.

A simplified finite strain plasticity model for metallic applications

In this work, a finite strain elastoplastic model is proposed within a total Lagrangian framework based on multiplicative decomposition of the deformation gradient, with several simplifications aimed at facilitating more concise code implementation and enhancing computational efficiency. Pre- and post-processors are utilised for conversion between different stress and strain measures, sandwiching the core plastic flow algorithm which preserves the small strain form. Simplifications focus on the pre- and post-processor components by substituting certain arithmetic operations associated with high computational demands with simpler ones without compromising accuracy. These modifications are based on assumptions, which are valid for most metals, that the elastic strains are small compared to plastic strains, and that the incremental plastic deformations are small for each step. In addition, the consistent tangent modulus matrix is derived in a reduced form, both for the general full model and the new simplified model, facilitating more straightforward computations in both cases. The models are verified against two classical numerical examples where favourable comparisons are achieved. Overall, the simplified model is shown to provide a significant reduction in computational demand for the two considered numerical problems, with negligible deviation in the results compared to the full model, subject to fulfilling the underlying assumptions with the adoption of a sufficiently small step size.

Study of Natural Fiber over Strength and Density of Cement Stabilized Rammed Earth Blocks.

The promotion of sustainable materials is needed in the construction industry; in this study demolishing waste (DW) is used to replace natural sand. Initially, the test blocks were cast with the local soil and DW stabilized with 8% of cement at optimum moisture content. The blocks were prepared and tested; the required density of blocks was achieved through dynamic compaction and cured in a Gunny bag for 28 days. The effects of different compositions and different mix ratios between soil, DW, and FA (5–20%) and curtailing cement by 1% of the total mix. To improve the strength and durability of the material three different natural fibers i.e. wheat straw, jute, and coconut coir (0–2%) are randomly added by total weight.The density, tangent modulus (Ei) and wet strengthl of the geo material are investigated. The density of the block is reduced from 17.012 to 15.845kN/m3 with the addition in FA. The density of the mix increases considerably up to 10% FA and 1.5% of all fibers. Further addition of FA and fibers decreases the wet density and eventually the strength. The thermal conductivity of wheat straw is better but the wet cube compressive strength of blocks with coconut coir is 5.735 MPa around 40 to 45 % more than wheat straw at 1.5% fiber of total mix. Referring to the above study higher the density higher the strength and stiffness. It is observed from the above study that the range of Ei values is in between 5.5 to 9.75 MPa in moist conditions. The material developed in the study can be used as an energy-efficient, non-toxic and sustainable alternative to burnt bricks for load-bearing walls of low-rise buildings.

Non-iterative stress projection method for anisotropic hardening

In this paper, a fully explicit non-iterative stress projection method for the instant stress integration of advanced plasticity models that account for the history-dependent deformation is proposed. In this non-iterative stress projection method, the stress increment is directly determined based on the elastoplastic constitutive law. Generalized formulations of the elastoplastic tangent moduli for anisotropic hardening models are discussed considering the morphological yield surface changes in the context. Precise integrations of the stress tensor, effective plastic strain, and other state variables are accomplished for kinematic- and distortional hardening models. The implemented plasticity hardening models are validated through a series of non-proportional loadings and a sheet metal forming simulation to check the fidelity, numerical robustness, and computational efficiency of the suggested non-iterative stress projection method. Consequently, the computation cost for a large-scale metal forming simulation is reduced up to 50%.

Simulations of multivariant Si I to Si II phase transformation in polycrystalline silicon with finite-strain scale-free phase-field approach

Scale-free phase-field approach and corresponding finite element method simulations for multivariant martensitic phase transformation from cubic Si I to tetragonal Si II in a polycrystalline aggregate are presented. Important features of the model are large and very anisotropic transformation strain tensor ɛt={0.1753;0.1753;−0.447} and stress-tensor dependent athermal dissipative threshold for transformation, which produce essential challenges for computations. 3D polycrystals with stochastically oriented grains are subjected to uniaxial strain- and stress-controlled loadings under periodic boundary conditions and zero averaged lateral strains. Coupled evolution of discrete martensitic microstructure, volume fractions of martensitic variants and Si II, stress and transformation strain tensors, and texture are presented and analyzed. Macroscopic variables effectively representing multivariant transformational behavior are introduced. Macroscopic stress–strain and transformational behavior for 55 and 910 grains are close. Large transformation strains and grain boundaries lead to huge internal stresses of tens GPa, which affect microstructure evolution and macroscopic behavior. In contrast to a single crystal, the local mechanical instabilities due to phase transformation and negative local tangent modulus are stabilized at the macroscale by arresting/slowing the growth of Si II regions by the grain boundaries. This leads to increasing stress during transformation. The developed methodology can be used for studying similar phase transformations with large transformation strains and for further development by including plastic strain and strain-induced transformations.

Approach for the simulation of the load-deformation behaviour of hyperelastic bonded joints using strain and strain rate dependent tangent moduli

In structural glass, Structural Sealant Glazing (SSG) systems are often used to realise facades with maximum transparency. The used silicone adhesives are currently designed in accordance to the European Technical Approval Guideline 002 (ETAG 002) by a simplified two-dimensional stress calculation concept. For a more precise calculation of the adhesive stresses and deformations, finite element analyses are used. The quality of the results, however, strongly depends on the calculation concept and material model used. In this paper, a practice-oriented viscoelastic approach using strain and strain rate dependent tangent moduli within FEA is presented. Required material parameters can be determined with a simple uniaxial tension test only. The proposed model is validated with numerous FE calculations of reality-based adhesively bonded component tests with different geometric ratios that include complex multiaxial stress states. The proposed approach allows a precise prediction of the strain state- and time-dependent stress behaviour of hyperelastic silicone bonds. The prediction quality is significantly more accurate than often used linear-elastic material models or commonly available hyperelastic models.

Determining the Soil Modulus for Use in Soil–Pipe Interaction Modeling

Research and engineering practice for the earthquake, landslide, or tunneling response of underground pipelines has focused on large ground deformation (LGD) effects, recognizing that LGD often causes the most serious local damage in buried pipelines. The adjacent soil reaction that develops as the pipe moves, i.e., soil–pipe interaction, is of key importance in the response of underground pipelines subject to LGD. A finite-element elastoplastic model can be used to analyze the soil–pipe interaction, and the model requires a soil modulus to simulate the force versus displacement behavior. In the simulation of soil–pipe interaction, a secant modulus associated with high stress and strain should be used in the finite-element model rather than an initial tangent modulus. This research provides a strain-compatible secant modulus that can be used in a finite-element analysis (FEA) of soil–pipe interaction for lateral, upward, downward, and oblique pipe movements. The favorable comparison between the experimental data and the FEA using the strain-compatible secant modulus implies that the proposed approach is suitable to predict soil–pipe behavior under large ground deformation.

Influence of volume compression on the unloading deformation behavior of red sandstone under damage-controlled cyclic triaxial loading

A reasonable evaluation of unloading deformation characteristics is of great significance for the effective analysis of deformation and stability of surrounding rocks after underground excavation. In this study, the damage-controlled cyclic triaxial loading tests were conducted to investigate the pore compaction mechanism and its influences on the unloading deformation behavior of red sandstone, including Young's modulus, Poisson's ratio, volumetric strain, and irreversible strain. The experimental results show that the increases of volumetric and irreversible strains of rocks can be attributed to the compaction mechanism, which almost dominates the entire pre-peak deformation process. The unloading deformation consists of the reversible linear and nonlinear strains, and the irreversible strain under the influence of the porous grain structure. The pre-peak Young's modulus tends to increase and then decrease due to the influence of the unloading irreversible strain. However, it hardly changes with the increasing volumetric strain compaction under the influence of reversible nonlinear strain. Instead, the initial unloading tangent modulus is highly related to the volumetric strain, and clearly reflects the compaction state of red sandstone. Furthermore, both the reversible nonlinear and irreversible unloading deformations are independent of confining pressure. This study is beneficial for the theoretical modeling and prediction of cyclic unloading deformation behavior of red sandstone.

基于单轴压缩物理试验和虚拟仿真的钙果力学模型构建

The mechanical parameters of Cerasus humilis are the basic data for subsequent studies on fruit deformation, damage, and movement characteristics during harvesting and transportation, but these parameters are rarely reported. Relevant mechanical parameters of whole fruit compression are calculated by comparing physical tests and virtual simulations. The orthogonal rotating combined experimental design was used to arrange the simulation tests, with the elastic modulus (E), yield limit (Ey), and tangent modulus (Et) as the influence factors and compression force as the result. Response surface optimization was employed to find the closest test point to the force–deformation curve of the physical test. The parameters of the pulp test point are as follows: E = 0.923 MPa, Ey = 0.0897 MPa, and Et = 0.478 MPa. Results show that the step on the force–deformation curve was not the beginning of the pulp yield, which was substantially earlier than the strain rate at the simulation step. The region of increased stress in the pulp first appeared at the junction with the core due to stress concentration. Combining virtual and physical tests to solve the mechanical parameters of fruits is more suitable than testing the standard pulp sample.