Pre-peak Region Research Articles

Experimental study of the hydro-mechanical response of Opalinus Clay – Part 1: Pore pressure response and effective geomechanical properties under consideration of confinement and anisotropy

Consolidated drained and undrained tests with pore pressure measurements were conducted on back-saturated specimens of a clay shale to characterize the influence of confinement and anisotropy on the pore pressure response and effective geomechanical properties (i.e. first-loading E-modulus, stress at onset of dilation and peak strength). Opalinus Clay, a clay shale chosen as host rock for high level nuclear waste in Switzerland was utilized. The result showed that there is a dependency on the confinement of Skempton's pore pressure parameter A and B, the stress at the onset of dilation, and the first-loading E-modulus. Additionally, a change in behavior of the material was observed at effective consolidation stresses between 5 and 8 MPa. The specimens at lower effective consolidation stresses (i.e. heavily overconsolidated specimens) showed a dilatant behavior in the pre-peak region and a significant post-failure stress drop. Specimens consolidated at higher effective consolidation stresses (i.e. slightly overconsolidated to normally consolidated specimens) showed compaction from initial loading until post-peak and a brittle-ductile post-failure behavior. These observations were manifested in pore pressure response curves, effective stress paths and stress-strain curves. Furthermore, they could be correlated to a non-linear appearance of the peak strength failure envelope. An explanation for the non-linear failure envelope related to the dilatant structure of the material is suggested.

On the experimental investigation of pozzolanic lime mortar stress-strain behavior and deformation characteristics when subjected to unloading-reloading cycles

Two series of uniaxial and triaxial compression tests using unloading-reloading cycles (cyclic loading) were performed under different confining pressures, in order to study the stress-strain and the deformation behavior of pozzolanic lime mortar subjected to cyclic loading. A cyclic loading scheme with five loops in the pre-peak region was performed for each test. The experimental results showed that the ratio of plastic strain to total strain is very large in the case of the triaxial compression tests. The marked Young’s modulus degradation behavior in the pre-peak region is related to damage that occurs in each specimen. Future work will aim to experimentally investigate the post-peak region behavior of the material.

Failure Behavior of Granite Affected by Confinement and Water Pressure and Its Influence on the Seepage Behavior by Laboratory Experiments.

Failure behavior of granite material is paramount for host rock stability of geological repositories for high-level waste (HLW) disposal. Failure behavior also affects the seepage behavior related to transportation of radionuclide. Few of the published studies gave a consistent analysis on how confinement and water pressure affect the failure behavior, which in turn influences the seepage behavior of the rock during the damage process. Based on a series of laboratory experiments on NRG01 granite samples cored from Alxa area, a candidate area for China’s HLW disposal, this paper presents some detailed observations and analyses for a better understanding on the failure mechanism and seepage behavior of the samples under different confinements and water pressure. The main findings of this study are as follows: (1) Strength reduction properties were found for the granite under water pressure. Besides, the complete axial stress–strain curves show more obvious yielding process in the pre-peak region and a more gradual stress drop in the post-peak region; (2) Shear fracturing pattern is more likely to form in the granite samples with the effect of water pressure, even under much lower confinements, than the predictions from the conventional triaxial compressive results; (3) Four stages of inflow rate curves are divided and the seepage behaviors are found to depend on the failure behavior affected by the confinement and water pressure.

CO electrooxidation on Sn-modified Pt single crystals in acid media

The irreversible adsorption of Sn on the three Pt basal planes (Sn/Pt(111), Sn/Pt(100) and Sn/Pt(110)) and the oxidation of adsorbed carbon monoxide have been studied by cyclic and stripping voltammetry. The presence of Sn adatoms blocks the adsorption of hydrogen on platinum, and leads to the observation of a new oxidation peak ascribed to the four-electron oxidation of the Sn adatom at potentials above 0.5V. The oxidation of adsorbed carbon monoxide is enhanced by the presence of Sn on all three Pt single crystals. On Sn/Pt(111) and Sn/Pt(110), oxidation of adsorbed CO occurs in two distinct potential regions: a pre-peak region at potentials below 0.50V and the main peak at higher potentials. In the pre-peak, the oxidation of adsorbed CO is suggested to take place at the direct interface between Pt and Sn through the formation of an activated water species on Sn that is not observable in the blank voltammetry. In the main peak, the COad oxidation reaction is suggested to occur through the classical bifunctional mechanism of OH adsorbed on Sn with CO adsorbed on Pt atoms no adjacent to Sn atoms. On Sn/Pt(100), the “pre-peak mechanism” is not observed.

Evaluation of the temporal profiles and the analytical features of a laser ablation — Pulsed glow discharge coupling for optical emission spectrometry

The coupling of a glow discharge (GD) in pulsed mode (PGD) as secondary source for excitation/ionization of the material provided by laser ablation (LA) has been investigated using optical emission spectrometry (OES). The variation of the laser pulse delay with respect to the GD pulse allows to producing the ablation process during prepeak, plateau or afterglow GD regions. Emission properties of the LA-PGD plasma in each temporal region of the GD pulse have been evaluated for analytical lines of different elements. Resonant atomic lines have shown higher emission intensity in the prepeak region compared to non-resonant lines. Non-resonant lines showed higher enhancement of the emission intensity in the afterglow region. Moreover, the coupled LA-PGD system offered better linear correlation coefficients using a set of glass standards for calibration as well as lower detection limits (by at least a factor of two) when compared to laser induced breakdown spectroscopy.

Communication: Nanoscale structure of tetradecyltrihexylphosphonium based ionic liquids.

In a recent communication [J. J. Hettige et al., J. Chem. Phys. 140, 111102 (2014)], we investigated the anomalous temperature dependence of the X-ray first sharp diffraction peak (or prepeak) in the tetradecyltrihexylphosphonium bis(trifluoromethylsulfonyl)-amide ionic liquid. Contrary to what was expected and often observed, the first sharp diffraction peak in this system was shown to increase in intensity with increasing temperature. This implies higher intermediate-range periodicity at a higher temperature. Is this counter-intuitive behavior specific to the combination of cation and anion? The current work analyzes the structural behavior of the same cation coupled with six different anions ranging from the small and spherically symmetric Cl(-) to the more structurally complex and charge-diffuse NTf2 (-). In all cases, the same temperature behavior trend for the prepeak is observed independent of anionic nature. We will show that the intensity increase in the prepeak region is associated with the structural behavior of charged liquid subcomponents. Instead, upon a temperature increase, the apolar subcomponents contribute to what would be an expected decrease of prepeak intensity.

Electronic structure origin of conductivity and oxygen reduction activity changes in low-level Cr-substituted (La,Sr)MnO3.

The electronic structure of the (La(0.8)Sr(0.2))(0.98)Mn(1-x)Cr(x)O3 model series (x = 0, 0.05, or 0.1) was measured using soft X-ray synchrotron radiation at room and elevated temperature. O K-edge near-edge X-ray absorption fine structure (NEXAFS) spectra showed that low-level chromium substitution of (La,Sr)MnO3 resulted in lowered hybridisation between O 2p orbitals and M 3d and M 4sp valance orbitals. Mn L3-edge resonant photoemission spectroscopy measurements indicated lowered Mn 3d-O 2p hybridisation with chromium substitution. Deconvolution of O K-edge NEXAFS spectra took into account the effects of exchange and crystal field splitting and included a novel approach whereby the pre-peak region was described using the nominally filled t(2g) ↑ state. 10% chromium substitution resulted in a 0.17 eV lowering in the energy of the t(2g) ↑ state, which appears to provide an explanation for the 0.15 eV rise in activation energy for the oxygen reduction reaction, while decreased overlap between hybrid O 2p-Mn 3d states was in qualitative agreement with lowered electronic conductivity. An orbital-level understanding of the thermodynamically predicted solid oxide fuel cell cathode poisoning mechanism involving low-level chromium substitution on the B-site of (La,Sr)MnO3 is presented.

Experimental investigation on the energy evolution of dry and water-saturated red sandstones

In order to investigate the effect of water content on the energy evolution of red sandstone, the axial loading–unloading experiments on dry and water-saturated sandstone samples were conducted, and the distribution and evolution of elastic energy and dissipated energy within the rock were measured. The results show that the saturation process from dry to fully-saturated states reduces the strength, rigidity and brittleness of the rock by 30.2%, 25.5% and 16.7%, respectively. The water-saturated sample has larger irreversible deformation in the pre-peak stage and smaller stress drop in the post-peak stage. The saturation process decreases the accumulation energy limit by 38.9%, but increases the dissipated energy and residual elastic energy density, thus greatly reducing the magnitude and rate of energy release. The water-saturated sample has lower conversion efficiency to elastic energy by 3% in the pre-peak region; moreover, the elastic energy ratio falls with a smaller range in the post-peak stage. Therefore, saturation process can greatly reduce the risk of dynamic disaster, and heterogeneous water content can lead to dynamic disaster possibly on the other hand.

Effect of Water on the Deformation and Failure of Rock in Uniaxial Tension

To design and construct underground structures, it is essential to understand the mechanical properties of rock in not only compression but also tension. It is well known that water is one of the important factors affecting the deformation and failure of rock. In this study, laboratory tests and numerical simulations were conducted to understand the effect of water on rock properties in uniaxial tension. In the experiments, a testing machine previously used for uniaxial tension tests in dry conditions was modified for tests in wet conditions. Using this machine, complete stress–strain curves from the pre- to postpeak regions of water-saturated specimens in uniaxial tension were obtained. The results for granite, tuff, and two types of andesite showed that the stress–strain curves in wet conditions have a lower initial slope and lower strength than those in dry conditions, and they are strongly nonlinear in the prepeak region. Comparing the changes in the results for uniaxial tension versus compression due to water, it was found that the reduction rate of uniaxial tensile strength was greater than that of uniaxial compressive strength, while the ratio between the reduction rates was almost constant for various rocks. In numerical simulations, the stress–strain curves in the prepeak region under dry and wet conditions could be reproduced by crack extension models under uniaxial tensile stress. Numerical analyses indicated that the nonlinearity of the stress–strain curves is probably due to the longer crack extension in wet compared with dry conditions.

Direct STM Studies of CO Adsorption and Oxidation on Pt(111) Electrodes: (1) Electrochemical Measurements and STM Observations

The mechanism of the adsorption and electrochemical oxidation of CO in electrolyte solutions on Pt catalysts has long been studied. Significantly enhanced CO oxidation has been observed in the presence of a CO adlayer preadsorbed at low electrode potentials, giving rise to a well-known prepeak in the CO stripping voltammogram prior to the main CO oxidation peak. Evidence was presented to show an effect of the defect sites on the Pt(111) surface on the characteristics of the prepeak.1) Wieckowski and coworkers extensively investigated the role of defects for the CO electrooxidation in alkaline media,2) and Strmcnik et al. reported that platinum surfaces modified with platinum nanoislands have a high activity for CO oxidation at prepeaks.3) In the present study, the CO electrooxidation at Pt(111)-oriented surfaces with steps is investigated by combining electrochemical measurements and electrochemical (EC) STM.3) Single-crystal beads of Pt were made by crystallization of molten balls formed at the end of Pt wires in a hydrogen–oxygen flame. The (111)-oriented planes were exposed by mechanical polishing. The surfaces were then heat-treated in an infrared imaging furnace and cooled under hydrogen. The electrochemical measurements were carried out in 0.1 M HClO4. EC-STM measurements were carried out using a CO- or N2-saturated solution under a CO atmosphere. For the reference electrode, an RHE was used. Fig. 1(a) shows voltammograms obtained in CO-saturated HClO4 on Pt(111) with (111) steps The CO oxidation started at ca. 0.4 V in the prepeak region. After the electrochemical potential was cycled between 0.05 and 0.95 V 30 times, the prepeak observed at lower potentials completely disappeared.4) By examining CO stripping voltammograms with and without CO in solution (Fig. 1(b)), it was suggested that the origin of this prepeak is the oxidation of bulk CO in solution. Fig. 2 shows the STM images at a (111) step on Pt(111) recorded before and after the potential cycling. The (2x2) structure of the CO adlayer is clearly seen. Before the potential cycling, the step has defects, forming a zigzag line (Fig. 2(a)). After the potential cycling, the step became very straight running in the [110] direction, with no defects observed (Fig. 2(b)). The structure change at steps should be related to the reactivity. On Pt(20 19 19) with (100) steps, the prepeak was very small, and after the potential cycles disappeared completely. Fig. 3(a) shows an STM image on Pt(20 19 19) before cycling. The step is straight, which might explain the small prepeak on pristine Pt(20 19 19). Fig. 3(b) shows an image after the potential cycles. The (111) microsteps were introduced to the (100) step, and the step became zigzagged. From the results on Pt(111)-related surfaces with different steps, it can be understood that not every defect is active for the electrooxidation of CO in solution.This research was supported by MEXT and NEDO, Japan.ReferencesA. Lopez-Cudero, A. Cuesta, and C. Gutierrez, J. Electroanal. Chem. 579, 1 (2005).J. S. Spendelow, Q. Xu, J. D. Goodpaster, P. J. A. Kenis, and A. Wieckowski, J. Electrochem. Soc., 154, F238, (2007)D. S. Strmcnik, D. V. Tripkovic, D. van der Vliet, K.-C. Chang, V. Komanicky, H. You, G. Karapetrov, J. P. Greeley, V. R. Stamenkovic, and N. M. Markovic, J. Am. Chem. Soc., 130, 15332 (2008).J. Inukai, D. A. Tryk, T. Abe, M. Wakisaka, H. Uchida, and M. Watanabe, J. Am. Chem. Soc ., 135, 1476 (2013).

A Constitutive Model of Rocks under Uniaxial Tension

A constitutive model is proposed to simulate the completely deformation process of rocks under uniaxial tension. Based on the revised elastic modulus method derived from the hypothesis of strain equivalence, we analyzed the relationship between the damage variable and the strain. It is found that the relation can be modeled using a sigmoid curve. This model can describe the complete deformation process of rocks under uniaxial tension satisfactorily. In particular, the nonlinearity near the peak in the pre-peak region is accurately captured by the proposed constitutive model. The rapid decrease of rock strength after peak load can also be captured satisfactorily. The used mathematical function is simple and the damage evolution process is clear. The validity of the model is verified using laboratory test data.

Pre- and post-peak toughening behaviours of fibre-reinforced hot-mix asphalt mixtures

Recycled plastic fibre-reinforced hot-mix asphalt (HMA) mixtures have better fatigue resistance than plain HMA. The toughening effects of recycled plastic fibre-reinforced HMA were characterised using direct tensile loading tests. Adding a small quantity of recycled plastic fibres to HMA was found to significantly increase the mixture's fracture energy and toughness, which were calculated using the pre- and post-peak stages of tensile force–displacement curves. A theoretical model representing the pre-peak behaviour of fibre-reinforced HMA with direct tension-softening curves for various fibre contents is presented here. The enhanced toughness through post-peak analysis was also observed using toughness indices associated with fibre-bridging effect after the pre-peak composite stress. The pre-peak fracture energy model and post-peak toughness indices appeared to be governed by the direct tensile toughening of fibre-reinforced HMA's enhanced fibre-bridging effects. The pre-peak fracture energy model demonstrates the effect of fibre content on the strain energy density during the pull-out process within the pre-peak composite stress region. The maximum pre-peak fracture energy of a coarse-graded HMA mixed with recycled plastic fibres is achieved at a fibre content of 0.4% of the total weight of the HMA. The increases in the toughness indices within the post-peak composite stress region indicate that the fatigue resistance of fibre-reinforced HMA is at least 30% greater than that of control HMA.

Changes in COchem oxidative stripping activity induced by reconstruction of Pt (1 1 1) and (1 0 0) surface nanodomains

The Hupd and COchem oxidative stripping on preferentially oriented Pt nanoparticles exhibiting clean surfaces and different ratios of (100) and (111) surface domains are investigated in 0.5M H2SO4 aqueous electrolyte. Shorter range order (100) and (111) surface domains can be created in the early stage of the progressive surface reconstruction of the nanoparticles by cycling the electrode to an upper potential Eup=1.2V vs. RHE. By increasing the number of cycles, the reconstruction of the Pt nanoparticle surface leads to the disappearance of (100) and (111) ordered surface domains. Changes in the related oxidative stripping voltammograms (OSV) recorded on the reconstructed nanoparticle surfaces as a function of the number of potential cycles at 1.2V confirm that the COchem oxidative feature from 0.3 to 0.8V is composed of different contributions which are related to different surface microstructures and different COchem oxidation mechanisms. Detailed analysis of the charge difference between the signal recorded on reconstructed nanoparticles and that recorded on fresh catalysts allows moreover evidencing a surface domain size effect. The COchem oxidation contribution is shifted towards higher potentials on shorter (100) and (111) surface domains, likely due to an increase of COchem adsorption strength on small isolated domains. At last, it is shown that the occurrence of the COchem oxidation prepeak involves not only the presence of surface defects, but also their coexistence with long range order (111) and (100) surface domains. Rationalization of results obtained in the present paper with data from the literature supports an Eley–Rideal mechanism in the COchem oxidation prepeak region.

Pulsed rf-GD-TOFMS for depth profile analysis of ultrathin layers using the analyte prepeak region

Direct solid analysis of ultrathin layers is investigated using pulsed radiofrequency (rf) glow discharge (GD) time-of-flight mass spectrometry (TOFMS). In particular, previous studies have always integrated the detected ion signals in the afterglow region of the rf-GD pulse, which is known to be the most sensitive one. Nevertheless, the analytical capabilities of other pulse time regions have not been evaluated in detail. Therefore, in this work, we investigate the analyte prepeak region, which is the pulse region where the analyte ions peak after the initial sputtering process of each GD pulse, aiming at obtaining improved depth profile analysis with high depth resolution and with minimum polyatomic spectral interferences. To perform these studies, challenging ultrathin Si-Co bilayers deposited on a Si substrate were investigated. The thickness of the external Si layer was 30 nm for all the samples, whilst the internal Co layer thicknesses were 30, 10, 5, 2 and 1 nm, respectively. It should be remarked that the top layer and the substrate have the same matrix composition (Si > 99.99%). Therefore, the selected samples are suitable to evaluate the response of the Si ion signal in the presence of an ultrathin Co layer as well as the possible oxygen contaminations or its reactions. Additionally, these samples have been evaluated using time-of-flight secondary ion mass spectrometry, and the results compare well to those obtained by our pulsed rf-GD time-of-flight mass spectrometry results.

The influence of the intermediate principal stress on rock failure behaviour: A numerical study

The influence of the intermediate principal stress on rock strength has been studied comprehensively by previous researchers. However, the reason why rock strength firstly increases and subsequently decreases with the increase of intermediate principal stress is still unclear. In this paper, the mechanism of the intermediate principal stress effect on rock failure behaviour is revealed through a numerical method using the EPCA3D system (Elasto-Plastic Cellular Automaton). In this study, both homogeneous and heterogeneous rocks are considered. The heterogeneity of a rock specimen is modelled by introducing Weibull's statistical distribution. Two criteria, i.e. the Drucker–Prager and Mohr–Coulomb models, are used to determine whether a meso-scopic element in the rock specimen is in a failure state or not during the polyaxial stress loading process. The EPCA3D simulation reproduces the typical phenomenon of the intermediate principal stress effect that occurs in some rock experiments. By studying the EPCA3D simulated acoustic emission and complete stress–strain curves illustrating failure initiation, propagation and coalescence in the failure process of rocks, the essence of the intermediate principal stress effect is tracked. It is concluded that the heterogeneous stress distribution induced by the natural heterogeneity of rocks and the effect of the loading platen are two of the reasons producing the intermediate stress effect. Studies indicate that a moderate intermediate principal stress delays the onset of local failure, which in turn leads to an increase in the rock strength. However, once the intermediate principal stress reaches a certain value, local failure will be formed through the application of the intermediate principal stress. It is the number of failed elements in the pre-peak region that determines whether the rock strength decreases or not. The extent of rock strength reduction when the intermediate principal stress reaches a certain value is lessened with the increase in the minimum principal stress.

The Oxidation of Adsorbed CO on Pt(100) Electrodes in the Pre-peak Region

The oxidation of CO adsorbed on Pt(100) electrodes in the pre-peak region (between 0.30 and 0.60 V) was studied using cyclic voltammetry, current–time transients and Fourier transform infrared spectroscopy. According to our results, the pre-peak corresponds to the oxidation of a small fraction (<15%) of the CO adlayer, adsorbed on the terraces and adjacent to the step sites, the rate of CO oxidation being limited, within this potential region and at these high CO coverages, by the diffusion of CO to the reactive sites. The picture emerging from the results reported is as follows: the reaction is initiated by a one-dimensional nucleation-and-growth oxidation of COads along the steps, immediately followed by surface diffusion-controlled oxidation of COads diffusing from the terraces to the steps and by a two-dimensional nucleation-and-growth process. The analysis of the Tafel slopes, as obtained from cyclic voltammograms at different scan rates and from plots of the logarithm of the current at the maximum, the time at the current maximum and the current at the minimum vs. the potential, suggests that the two-dimensional nucleation-and-growth process occurs more slowly than the other two processes. Only the process responsible for the two-dimensional nucleation and growth has not been clearly identified, although two possibilities are given.

Study on the Strength of Jointed Rock Mass

Based on the structure of the rock mass surrounding a highway tunnel under construction, a new methodology for defining the strength of jointed rock mass is proposed. The laboratory experiments and numerical simulations of rock samples, including both intact rock and rock with a single typical joint, are carried out to ensure that the mechanical parameters of the rock and the joint can be obtained. In addition, the strength of the rock mass surrounding the tunnel, without resorting to the difficult task of sampling and testing of large-scale rock mass, is evaluated by using the proposed method. It is shown that the strength reduction of rock mass is governed by the geometric configurations as well as the mechanical properties of the joints, and that the presence of joints results in the non-linearity of the pre-peak region.

A three dimensional computational model of the mechanical response of a dual-phase ceramic

This paper presents a constitutive model of a fired ceramic consisting of two phases each with a different thermal expansion coefficient. Each phase is linear elastic but the stiffness of one of the phases is progressively reduced anisotropically to simulate the growth of microcracks under tension. This damage, in any orientation, is proportional to the normal tensile traction in that direction and no damage is produced by compressive stresses. The damage is recorded as a damage orientation function held numerically at 20 orientations.The model is specifically designed to be used in the pre-peak region of the stress–strain curve and to be robust in use in finite element programs. To this end, while the stresses in the phases are determined assuming that the strains in each phase are equal, the overall compliance of the composite is calculated from the complementary energy.The model reproduces non-linear stress–strain behaviour when loaded in tension and, because of the thermal mismatch, also shows permanent deformation on the removal of the load. A user defined subroutine has been written for the commercial finite element program ABAQUS and used to simulate an experimental test on a commercial refractory and the results compared with experimental data. The UMAT is also used to simulate a hollow axisymmetric cylinder in generalised plane strain subject to moderately rapid heating on the inner surface; and the results for linear elasticity and the damaging model are compared.

Viscoelastic–Viscoplastic Model with Damage for Asphalt Concrete

A viscoelastic (VE)–viscoplastic (VP) model for characterizing asphalt concrete behavior is described. The parameters of the model are determined in the prepeak region of the loading, under small load. It includes two separate damage functions, one for each component of the deformation, to describe the material behavior under heavy load and in the postpeak region of the fracture. In order to extend the material characterization to the postpeak region, the size of the fracture process zone (FPZ) is evaluated from mapping the strain in a fracture test. The deformation in the FPZ, in the continuum framework is computed from total and local measurements. Uniaxial tests, including frequency sweep for the undamaged, linear VE component, repeated triaxial load for the undamaged VP component are conducted and used to derive the material properties in the prepeak region. A tension up to failure test is used to determine the damage functions.

Development of Displacement-Softening Model for Interface Shear Behavior Between Geosynthetics

This paper presents two kinds of constitutive model applicable for geosynthetic interfaces, namely a combined model (MODEL 1) and DSC model (MODEL 2). In order to verify the performance of the two models, back­ predictions were carried out on smooth geomembrane (S-GM) and textured geomembrane (T-GM) interfaces with geotextile (GT), namely S-GM/GT and T-GM/GT interface using the parameters obtained from test results For the combined model (MODEL 1), the total stress field is divided into two regions, i.e. pre-peak and post-peak region, to take into account the displacement-softening effect on the interface shear behavior. The DSC model (MODEL 2) was also considered to model the interface shear behavior between geosynthetics. This model is comprised of two reference states, namely the relative intact (RI) and the fully adjusted (FA) state, and one function, namely the disturbance function. Though the comparisons between measured data and back-prediction results for MODEL 1 and MODEL 2 (DSC model) showed good agreements with each other, MODEL 1 has a critical limitation related to the boundary value problem as it is inconvenient to implement this model into FEM. Finally, DSC model (MODEL 2) was suggested as an appropriate model for simulating large-displacement shear behaviors with the characteristics of plasticity because the DSC model has been widely implemented in FEM process by many researchers.