Effective Modulus Research Articles

Equivalent numerical method and sensitivity analysis of microparameters for micropore compression stage of cemented tailings backfill

The discrete element method has been widely used to study the mechanical properties of rock and cemented tailings backfill (CTB). The high matching degree of mechanical properties between numerical simulation and experiment is the precondition of accurate numerical simulation research. However, as the discrete element method’s particle system cannot characterize pore structure of rock and CTB, it cannot simulate the micropore compression stage (MPCS) of laboratory test. Therefore, the traditional discrete element method cannot accurately simulate the whole process of stress − strain curve of rock and CTB. To solve this problem, in this study, the variation law of the porosity and pore radius of CTB samples’ MPCS were first explored using nuclear magnetic resonance and computed tomography scanning tests. Based on the findings, the equivalent cell model of CTB is proposed. The relative deformation of cells can equivalently characterize the compressive deformation of pores in CTBs. Thus, the initial effective modulus, E0, the progressive coefficient of the effective modulus, k, and cycle steps, b, were introduced to improve the soft-bond model (SBM) in a particle flow code (PFC). This improvement changes the contact structure between particles and makes the contact deformation between particles more consistent with the deformation behavior of micropores in laboratory test. A numerical method for the nonlinear deformation of MPCS is established in PFC. Finally, the parameter sensitivity of the softening factor, softening tensile strength factor, friction coefficient, E0, k, and b in the improved SBM was analyzed. The variation law of samples’ macromechanical parameters with different microparameters is obtained. The results provide a basis for a more accurate study of the mechanical behavior of rock and CTB based on the discrete element method.

Ageing-induced shrinkage of intervessel pit membranes in xylem of Clematis vitalba modifies its mechanical properties as revealed by atomic force microscopy.

Bordered pit membranes of angiosperm xylem are anisotropic, mesoporous media between neighbouring conduits, with a key role in long distance water transport. Yet, their mechanical properties are poorly understood. Here, we aim to quantify the stiffness of intervessel pit membranes over various growing seasons. By applying an AFM-based indentation technique "Quantitative Imaging" we measured the effective elastic modulus (E effective) of intervessel pit membranes of Clematis vitalba in dependence of size, age, and hydration state. The indentation-deformation behaviour was analysed with a non-linear membrane model, and paired with magnetic resonance imaging to visualise sap-filled and embolised vessels, while geometrical data of bordered pits were obtained using electron microscopy. E effective was transformed to the geometrically independent apparent elastic modulus E apparent and to aspiration pressure P b. The material stiffness (E apparent) of fresh pit membranes was with 57 MPa considerably lower than previously suggested. The estimated pressure for pit membrane aspiration was 2.20+28 MPa. Pit membranes from older growth rings were shrunken, had a higher material stiffness and a lower aspiration pressure than current year ones, suggesting an irreversible, mechanical ageing process. This study provides an experimental-stiffness analysis of hydrated intervessel pit membranes in their native state. The estimated aspiration pressure suggests that membranes are not deflected under normal field conditions. Although absolute values should be interpreted carefully, our data suggest that pit membrane shrinkage implies increasing material stiffness, and highlight the dynamic changes of pit membrane mechanics and their complex, functional behaviour for fluid transport.

Propagation Modeling of Rainfall-Induced Landslides: A Case Study of the Shaziba Landslide in Enshi, China

Geological disasters, especially landslides, frequently occur in Enshi County, Hubei Province, China. On 21 July 2020, a large-scale landslide occurred in Enshi due to continuous rainfall. The landslide mass blocked the Qingjiang River, formed a dammed lake and caused great damage to surrounding roads and village buildings. In this study, the geomechanical properties of the landslide mass were obtained through field surveys. A three-dimensional topography model of the slope was established using the particle flow code (PFC) and the numerical parameters of the model were calibrated. A 3D discrete element model (DEM) was used to simulate the propagation of Shaziba landslide, and the dynamic behavior of the landslide was divided into five stages. The simulation results show that the landslide movement lasted approximately 1000 s. The maximum average velocity of the landslide reached up to 7.5 m/s and the average runout distance was about 1000 m. The simulated morphology of the landslide deposits was in good agreement with the field data. In addition, the influence of effective modulus on the calculation results was analyzed. The results indicate that the propagation behavior of a landslide and the morphology of landslide deposits are closely related to the effective modulus in the contact model of the PFC3D.

In-plane elastic properties of the Euplectella aspergillum inspired lattice structures: Analytic modelling, finite element modelling and experimental validation

This study develops new analytical models for the two Euplectella aspergillum inspired 2D lattice structures. The analytical models for normal modulus and Poisson’s ratio are derived using Castigliano’s second theorem, where plate-like elements were considered Euler beams, subjected to stretching and bending deformations. The derived equations show the dependence of elastic properties on design and base material properties. The in-plane elastic properties are also simulated using finite element modelling (FEM). Furthermore, the theoretical parametric analysis is also carried out to investigate the effect of design variables on the elastic constants. Lastly, the modeled lattice structures are fabricated using the fused filament fabrication (FFF) process and used to validate the analytical and finite element results experimentally. The developed analytical models show good agreement with FEM and experimental results for effective modulus and Poisson’s ratio. The bio-inspired structures showed a wide range of elastic properties and suggested their applications in energy absorption and lightweight structure designs.

Brownian motion with radioactive decay to calculate the dynamic bulk modulus of gases saturating porous media according to Biot theory

We present a new stochastic simulation method for determining the long-wavelength effective dynamic bulk modulus of gases, such as ambient air, saturating porous media with relatively arbitrary microgeometries, i.e., simple enough to warrant Biot’s simplification that the fluid and solid motions are quasi-incompressible motions at the pore scale. The simulation method is based on the mathematical isomorphism between two different physical problems. One of them is the actual Fourier heat exchange problem between gas and solid in the context of Biot theory. The other is a diffusion-disintegration-controlled problem that considers Brownian motion of diffusing particles undergoing radioactive-type decay in the pore volume and instant decay at the pore walls. By appropriately choosing the decay time and the diffusion coefficient, the stochastic algorithm we develop to determine the average lifetime of the diffusing particles, directly gives the effective apparent modulus of the saturating fluid. We show how it leads to purely geometric stochastic constructions to determine a number of geometrical parameters. After validating the algorithm for cylindrical circular pores, its power is illustrated for the case of fibrous materials of the type used in noise control. The results agree well with a model of the effective modulus with three purely geometric parameters of the pore space: static thermal permeability divided by porosity, static thermal tortuosity, and thermal characteristic length.

Auxetics among Two-Layered Composites Made of Cubic Crystals. Analytical and Numerical Analysis

The results of calculations of the effective Young's modulus of longitudinally stretched twolayered plates made of identically oriented cubic crystals are presented on the basis of analytical analysis and the numerical finite element method. Analytical dependences of effective Young's modulus on Young's moduli and Poisson's ratios of crystals in layers are presented. Combinations of pairs of crystals with a significant deviation of the effective characteristics from ones found by the rule of mixtures are determined. The dependences of the effective Young's moduli on extreme values of the Young's moduli and Poisson's ratios of crystals in layers are established. They are presented graphically, and in some cases are reflected in the form of a table.

Statistical properties of effective elastic moduli of random cubic polycrystals

The homogenized elastic properties of polycrystals depend on the grain morphology and crystallographic orientations. For simplification purposes, the orientations of the grains are usually considered three independent Euler angles. However, experimental investigations reveal spatial correlations in these angles. The Karhunen–Loève expansion is used to generate random fields of Euler angles having exponential kernel functions with varying correlation lengths. The effective elastic moduli for numerically generated statistically equiaxed cubic polycrystals are estimated via the classical Eshelby–Kröner Self-Consistent homogenization model. The influence of the correlation lengths of the orientations’ random fields on the statistical properties of the effective elastic moduli has been investigated. Our results show that spatially correlated Euler angles could increase the variability of the homogenized elastic properties compared to the ones having uncorrelated Euler angles. Nevertheless, using independent random variables for Euler angles remains valid when correlation lengths are close to the average grain size.

AFM-based spherical indentation of a brush-coated soft material: modeling the bottom effect.

It is a common practice in the atomic force microscopy (AFM)-based studies of living cells to differentiate them by values of the elastic (Young's) modulus, which is supposed to be an effective characteristic of the mechanical properties of a cell as a heterogeneous matter. The elastic response of a cell to AFM indentation is known to be affected by a relative distance from an AFM probe to a solid support on to which the cell is cultured. Besides this so-called bottom effect, AFM measurements may carry significant information regarding the effect of molecular brushes covering living cells. Here, we develop a mathematical model for determining the intrinsic effective Young's modulus of a single brush-coated cell from the force-indentation curve with the bottom effect taken into account. The mathematical model is illustrated with the example of AFM data on testing of an eukaryotic cell taken from the literature.

ЖЕСТКОСТЬ ЖЕЛЕЗОБЕТОННЫХ КОНСТРУКЦИЙ ПРИ ИЗГИБЕ С УЧЁТОМ ПОПЕРЕЧНОЙ И ПРОДОЛЬНОЙ СИЛ (ЧАСТЬ 1)

The paper provides a physical and computational model for determining the parameters of limit states of reinforced concrete structures under complex stress state such as bending with effect of axial and shear forces. The forward and backward transitions for determining the stiffness matrix coefficients of reinforced concrete bar structures with inclined and normal cracks have been constructed on the basis of the adopted cross-section discretization scheme and the duality theorem between force and deformation parameters by A.R. Rzhanitsyn. Determination of the stiffness of structures in the zone of inclined cracks was performed on the basis of the model of composite strips into which the zone with inclined cracks is divided. It is assumed a hypothesis about the character of deformation distribution in a complexly stressed reinforced concrete element with inclined cracks. For this model the effective shear modulus has been obtained. It allows to determine the average relative linear and angular strains of concrete and reinforcement at the point adjacent to the shear joint between inclined cracks. Using this model and the experimentally obtained value of the relative shear in the inclined crack, the dowel forces in the reinforcing bar crossed by the inclined crack were determined. The use of the obtained analytical dependences in the practice of designing reinforced concrete structures allows to clarify significantly the definition of displacements and width of opening of inclined and normal cracks, as well as to bring the calculation and physical model based on experimental data as close as possible.

EFFECT OF THE TYPE OF UNIT CELL CONNECTION IN A METAMATERIAL ON ITS PROGRAMMABLE BEHAVIOR

In this work, samples of a mechanical metamaterial with tetrachiral topology were studied by mathematical modeling. Two types of unit cell connections in the metamaterial were considered: adjoining and overlapping. The adjoining method led to the formation of double-thickness internal walls in the sample, which were considered to be topological defects in the metamaterial. The mechanical response and effective properties of the metamaterials were determined and analyzed by numerical simulations of the uniaxial loading. The results showed that the sample with higher effective density exhibited a more compliant (i.e., a more pronounced) load-induced twisting effect and a lower effective Young's modulus. The results obtained can be used in the design of metamaterials with programmable properties.

FINITE ELEMENT CALCULATION OF DISK TRANSDUCER WITH CYMBAL-SHAPED END-CAPS AND ACTIVE ELEMENT FROM POROUS PIEZOCERAMICS WITH EXTREME CONDUCTIVITY OF PORE SURFACES

The paper presents a finite element analysis of a disk-shaped piezoelectric transducer with end-cap patches, which is usually called as Cymbal transducer. The efficiency of such a transducer is determined both by its geometric dimensions and by the values of the longitudinal and transverse piezoelectric moduli (piezoelectric charge coefficients) of the piezoceramic disc material. As was recently found, for porous piezoceramics with completely metallized pore surfaces, the effective transverse piezoelectric modulus does not decrease in absolute value with increasing porosity, as in conventional porous piezoceramics, but, on the contrary, increases, as does the longitudinal piezoelectric modulus. These unusual properties of porous piezoceramics with pore surface metallization are determined by the extreme properties of the phases that make up the piezocomposite material, and, in particular, the extremely high conductivity of the pore surface material inside the dielectric composite medium. In this regard, the main task was to study the efficiency of the Cymbal transducer depending on the type of porous piezoelectric disc material. Comparisons were made for solid piezoceramics, for ordinary porous piezoceramics, for porous piezoceramics with a very thin metal coating of the pores, and for porous piezoceramics with a relatively thick metallization layer on the surface of the pores with different porosities. In the ANSYS finite element package, steady-state oscillations of the cymbal transducer were calculated under nonresonant operating modes and near the first electrically active frequencies, which corresponds to the use of the transducer as a device for energy harvester and as a piezoelectric emitter of acoustic waves. In both cases, the results of computational experiments showed the promise of using new types of porous piezoceramic materials for the considered configurations of a disk piezoelectric transducer with end-cap cymbal patches. In this case, the best results were obtained for a porous piezoceramic material with a very thin metal coating of the pores.

The effective shear modulus of a random isotropic suspension of monodisperse liquid n-spheres: from the dilute limit to the percolation threshold.

A numerical and analytical study is made of the macroscopic or homogenized mechanical response of a random isotropic suspension of liquid n-spherical inclusions (n = 2, 3), each having identical initial radius A, in an elastomer subjected to small quasistatic deformations. Attention is restricted to the basic case when the elastomer is an isotropic incompressible linear elastic solid, the liquid making up the inclusions is an incompressible linear elastic fluid, and the interfaces separating the solid elastomer from the liquid inclusions feature a constant initial surface tension γ. For such a class of suspensions, it has been recently established that the homogenized mechanical response is that of a standard linear elastic solid and hence, for the specific type of isotropic incompressible suspension of interest here, one that can be characterized solely by an effective shear modulus n in terms of the shear modulus μ of the elastomer, the initial elasto-capillary number eCa = γ/2μA, the volume fraction c of inclusions, and the space dimension n. This paper presents numerical solutions-generated by means of a recently introduced finite-element scheme-for n over a wide range of elasto-capillary numbers eCa and volume fractions of inclusions c. Complementary to these, a formula is also introduced for n that is in quantitative agreement with all the numerical solutions, as well as with the asymptotic results for n in the limit of dilute volume fraction of inclusions and at percolation . The proposed formula has the added theoretical merit of being an iterated-homogenization solution.

Cell Membrane State, Permeability, and Elasticity Assessment for Single Cells and Cell Ensembles.

The phase state and especially phase transitions of synthetic lipid membranes are known to drastically modulate mechanical membrane properties like permeability and bending modulus. Although the main transition of lipid membranes is typically detected employing differential scanning calorimetry (DSC), this technique is not suitable for many biological membranes. Moreover, often single cell data on the membrane state or order is of interest. We here first describe how to use a membrane polarity-sensitive dye, Laurdan, to optically determine the order of cell ensembles over a wide temperature range from T=-40°C to +95°C. This allows to quantify the position and width of biological membrane order-disorder transitions. Second, we show that the distribution of membrane order within a cell ensemble allows for correlation analysis of membrane order and permeability. Third, combining the technique with conventional atomic force spectroscopy allows for the quantitative correlation of an overall effective Young's modulus of living cells with the membrane order.

Measuring Cell Mechanical Properties Using Microindentation.

Quantifying cell mechanical properties is of interest to better understand both physiological and pathological cellular processes. Cell mechanical properties are quantified by a finite set of parameters such as the effective Young's modulus or the effective viscosity. These parameters can be extracted by applying controlled forces to a cell and by quantifying the resulting deformation of the cell.Microindentation consists in pressing a cell with a calibrated spring terminated by a rigid tip and by measuring the resulting indentation of the cell. We have developed a microindentation technique that uses a flexible micropipette as a spring. The micropipette has a microbead at its tip, and this spherical geometry allows using analytical models to extract cell mechanical properties from microindentation experiments. We use another micropipette to hold the cell to be indented, which makes this technique well suited to study nonadherent cells, but we also describe how to use this technique on adherent cells.

Numerical and experimental study of porous NiTi anisotropy under compression

Porous NiTi samples were obtained by self-propagating high-temperature synthesis (SHS) and cut to specific dimensions by electrical discharge machining. Quasi-static compression of the porous SHS-NiTi alloy demonstrated that the deformation was elastic-plastic. Three characteristic types of fracture surfaces of bridges can be distinguished. 1) Ductile fracture of the austenite phase in the form of a cup and cone relief. 2) Brittle fracture with the formation of cleavage steps. 3) Large areas of plastic shear, where cup and cone, and cleavage facets are nucleated. An algorithm for obtaining a porous framework model suitable for finite element method calculations has been developed. The effective moduli of elasticity and shear for the porous volume of the material were determined. It is shown that the studied porous volume has orthotropic elastic properties due to the geometry of the porous framework.

Direct hydrocarbon identification in shale oil reservoirs using fluid dispersion attribute based on an extended frequency-dependent seismic inversion scheme

The identification of hydrocarbons using seismic methods is critical in the prediction of shale oil reservoirs. However, delineating shales of high oil saturation is challenging owing to the similarity in the elastic properties of oil- and water-bearing shales. The complexity of the organic matter properties associated with kerogen and hydrocarbon further complicates the characterization of shale oil reservoirs using seismic methods. Nevertheless, the inelastic shale properties associated with oil saturation can enable the utilization of velocity dispersion for hydrocarbon identification in shales. In this study, a seismic inversion scheme based on the fluid dispersion attribute was proposed for the estimation of hydrocarbon enrichment. In the proposed approach, the conventional frequency-dependent inversion scheme was extended by incorporating the PP-wave reflection coefficient presented in terms of the effective fluid bulk modulus. A rock physics model for shale oil reservoirs was constructed to describe the relationship between hydrocarbon saturation and shale inelasticity. According to the modeling results, the hydrocarbon sensitivity of the frequency-dependent effective fluid bulk modulus is superior to the traditional compressional wave velocity dispersion of shales. Quantitative analysis of the inversion results based on synthetics also reveals that the proposed approach identifies the oil saturation and related hydrocarbon enrichment better than the above-mentioned conventional approach. Meanwhile, in real data applications, actual drilling results validate the superiority of the proposed fluid dispersion attribute as a useful hydrocarbon indicator in shale oil reservoirs.

Investigation on mechanical properties deterioration of concrete subjected to freeze–thaw cycles

Concrete structures in cold regions are usually suffer from froze and thaw action. A combined investigation of nanoindentation technique and X-ray diffraction were adopted to demonstrate the microstructure change and micromechanical properties deterioration of concrete subjected to freeze–thaw (F-T) cycles in this study. The results showed that the indentation modulus and hardness of the main compositions in mortar, such as calcium-silicate-hydrates and calcium hydroxide, both gradually decreases as the F–T cycles increase, with the greatest reduction approximate 38% after 1500 F–T cycles, while the corresponding greatest reduction of the main compositions in interfacial transition zone (ITZ) is close to 50%. In addition, the micropores in mortar and ITZ both gradually converge and connect to form larger diameter pores, and the thickness of ITZ increased rapidly from 25 to 50 μm after 1500 F–T cycles. On this basis, the effective modulus of elasticity under different F–T cycles are analyzed through Mori–Tanaka scheme with consistent variation tendency of dynamic modulus of elasticity test. Subsequently, the mechanical properties deterioration of concrete under F–T cycles is mainly attributed to the decrease of mechanical properties (such as modulus and hardness) of microscopic components, and the increase and propagation of the internal micropores especially for micropores in ITZ.

Predictive abilities of pseudodiscretization and pseudograin discretization schemes of the Mori–Tanaka homogenization, benchmarked against real and virtual RVEs

In this article, the predictive abilities of two prevalent homogenization formulations, two-step Mori–Tanaka (MT–MT) and MT–Voigt are benchmarked using virtual representative volume element (RVE) involving full FE models and real RVE using prior published experimental data. MT–MT and MT–Voigt are interpreted as involving “pseudodiscretization” and “pseudograin discretization,” respectively. A comprehensive test campaign involving all possible permutations and combinations of modulus of inclusions and matrix (inclusions stiffer than the matrix and vice versa) and different loading types are conducted. The comparisons are done at three length scales: effective modulus, stresses in individual inclusions, stress distribution in the interphase, and strain at the onset of interphase debonding. Overall, both schemes have similar predictive capabilities for the effective modulus and phase average stress. The predictions of the stresses in the individual inclusions for complex RVEs with inclusions length and orientation distribution are correct as average trends but do not represent the full details of the FE-revealed strain scatter. Depending on the modulus mismatch, or loading direction, better predictions can be achieved by either MT–MT or MT–Voigt, even if the microstructure considered remains the same. The relative difference in the strain at the onset of debonding, predicted by MT–MT and MT–Voigt formulations, is about 10%. HIGHLIGHTS Two-step MT–MT and MT–Voigt are benchmarked against virtual and real RVEs Comparisons are done for all permutations of modulus mismatch and loading types Predictions are compared at three length scales: RVE, inclusions, and interphase

Investigation of the effective hydro-mechanical properties of soil-rock mixtures using the multiscale numerical manifold model

This study focuses on determination of the effective hydro-mechanical properties of a widespread geological mélange, the Soil-Rock Mixture (SRM), using the multiscale Numerical Manifold Method (NMM). Influences of the Volumetric Block Proportion (VBP), block size, block shape, block orientation angle and micro-dynamics on the effective properties are investigated thoroughly. The SRM structural models are generated within the NMM framework in a statistical manner. The effective properties are extracted using the multiscale theory where micro-dynamics is fully considered based on the extended Hill-Mandel lemma. Through numerical simulations, the VBP and block orientation angle prove to be the first and second most influential factors. A growing VBP leads to increasing deformation moduli but decreasing effective permeability and Biot’s factor. Normal components of permeability and deformation tensors are positively proportional to the corresponding normal intersecting areas formed by sample cross-sections and blocks while shear components are positively proportional to sums of the normal and shear intersecting areas. Introducing micro-dynamics and diminishing the time step make the effective permeability and deformation moduli rise while Biot’s coefficient decrease. The accuracy and stability of the multiscale NMM are validated by comparing present results with those of empirical formulae and single-scale numerical methods.

Determination of shear behavior of magneto-rheological elastomers under harmonic loading

Magneto-rheological (MR) materials can respond reversibly and quickly under the effect of an external magnetic field. MR materials contain micron-sized iron particles. These iron particles are typically dispersed in an elastomer or a liquid. These materials due to their properties constitute a kind of smart material in terms of engineering material. Such materials are used as isolators in various engineering applications, structures, and sound control subsystems. This study aimed to determine the mechanical properties for shear behavior of MR materials for under harmonic loading. Parameters such as matrix materials with different hardness values, powder types, magnetic field, frequency, and deformation were studied. The parameters related to the MR material itself were analyzed with the obtained data. The present study reveals that considering the sensitivity to magnetic field parameter, composite materials having the most suitable properties were produced with Shore 2 hardness value and SQ magnetic powder. It had been observed on increase about 200% at the rate of Shore A10 and A2 as a result of comparing the hardness scale. Also according to the powder rate while there was an increase on worth effect of relative MR, it is seen that the biggest increase had been in SQ powder with 199% worth. When looked some studies in literature, about comparing different hardness values such as matrix materials powder types etc. there aren’t any studies. The state of magnetic field thinks that features such as MR effect, Storage, and Loss modulus haven’t been examined yet.