Material Parameters Research Articles

Study of the effect of technological clearances on electrophysical parameters of heated polymer materials

Among the reasons for the rejection of products made of polymer materials manufactured using HF electrothermy, an important place is occupied by the lack of available reference data on the modes of their processing. The inaccuracy of some electrical parameters, e.g., the dielectric loss tangent (tan δ) and the dielectric constant (ε) are attributed to neglecting the effect of gaps in granular multicomponent polymer materials or technological system, as well as subjective factors of the control process. We present the results of studying the impact of gaps of a technological system on the electrophysical parameters of polymer and composite materials. We studied samples of granular materials «Bimodal polypropylene» and «Basco» stabilizing additive which are used in production of UV-resistant films for packaging. It is shown that a resonance method with the possibility of using two- and three-electrode system is most appropriate when determining the electrophysical parameters of polymer materials, their multicomponent mixtures and the optimal frequency of exposure. Refined (determined with allowance for gaps) electrophysical data for the materials under study obtained at a frequency of 27.12 MHz and heating to 120°C are presented. Comparison of the results obtained with and without taking into account the impact of gaps revealed that the difference reaches up to 12 (for tan δ) and 9% (for ε) of their absolute value. Note that the parameter tan δ has the greatest effect on the heating efficiency. The optimal temperature of polymer heating at which tan δ reaches the maximum value is 50°C. The results obtained can be used to improve the quality of products produced from a wide range of multicomponent polymer and composite materials by optimizing the modes of their electrothermal processing.

Effect of drill gash rake angle on drillability in plain carbon and low alloy steels

In this study, the effects of the gash rake angle (γa), which is an important component of the drill geometry, on the thrust force and drilling torque occurring in the drilling of ordinary carbon steels (AISI 4140 and Ck 45) were examined through experimental and FEM-supported numerical simulation studies on surface roughness, tool surface roughness, wear and diameter deviation values were investigated experimentally. In the experiments, 6.8 mm diameter solid cementite carbide, coated and internal cooling channel drills with +10°, 0°, −10° gash rake angle were used. Three different feed rates and cutting speed levels were selected as cutting parameters. Determination of material-specific gash rake angle and cutting parameters for different materials was carried out by Taguchi-assisted variance analysis of experimental data. In experimental studies, the gash rake angle was 65.9% effective on the thrust force for AISI 4140 tempered steel, while it was the second effective parameter with 29.22% for Ck 45 manufacturing steel. While the feed rate is the more effective parameter in the drilling moments that occur when drilling different materials, it has been observed that γa also has a significant effect. It has been determined that chisel edge wear, main cutting edge wear and crater wear occur in the drill when drilling AISI 4140 tempered steel and Ck 45 manufacturing steel. The data obtained from the finite element-assisted chip removal analyses support the experimental results and provide guiding results in the selection of material-specific gash rake angle.

Numerical Investigation of Fracture Behaviour of Polyurethane Adhesives under the Influence of Moisture.

The mechanical behaviour of polymer adhesives is influenced by the environmental conditions leading to ageing and affecting the integrity of the material. The polymer adhesives have hygroscopic behaviour and tend to absorb moisture from the environment, causing the material to swell without applying external load. The focus of the work is to investigate the viscoelastic material behaviour under ageing conditions. The constitutive equations and the governing equations to numerically investigate the fracture in swollen viscoelastic material are discussed to describe the numerical implementation. Phase-field damage modelling has been used in numerical studies of ductile and brittle materials for a long time. The finite-strain phase-field damage model is used to investigate the fracture behaviour in aged viscoelastic polymer adhesives. The finite-strain viscoelastic model is formulated based on the continuum rheological model by combining spring and Maxwell elements in parallel. Commercially available post-cured crosslinked polyurethane adhesives are used in the current investigation. Post-cured samples of crosslinked polyurethane adhesives are prepared for different humidity conditions under isothermal conditions. These aged samples are used to perform tensile and tear tests and the test data are used to identify the material parameters from the curve fitting process. The experiment and simulation are compared to relate the findings and are the first step forward to improve the method to model crosslinked polymers.

Cu-Zn layered double hydroxides as high-performance electrode for supercapacitor applications

Supercapacitors have evoked considerable attention nowadays under the realm of energy storage devices due to some of their intriguing properties such as long cycling stability, high power density, and low cost. Layered double hydroxides, known for their unusual structural and electrochemical properties, have gained prominence among electrode materials due to their high specific capacitance and exceptional cycle stability. This study investigates the viability of Cu-Zn layered double hydroxides (LDH) as electrode material for supercapacitor applications. Copper (Cu) and Zinc (Zn) present in the LDH framework create synergistic effects that increase the material's electrochemical properties. The current study investigates the morphology and electrochemical behaviour of Cu-Zn LDH, emphasizing their suitability as supercapacitor electrodes. Furthermore, various characterization techniques such as XRD, FTIR, SEM, TEM, and XPS were employed to uncover the material's inherent properties. A specific capacitance of 265 F/g was obtained at a current density of 1 mA/cm2 in the three-electrode configuration. Further, an asymmetric device furnished a specific capacitance of 51 F/g with an energy density of 7.14 Wh/kg and a power density of 121.94 W/kg. Additionally, the material maintains 75 % of its original capacitance after 1000 cycles, demonstrating its exceptional stability. The obtained electrochemical parameters for the as-synthesized material demonstrate its feasibility as an energy storage device.

Experimental Determination and Simulation Validation: Johnson–Cook Model Parameters and Grinding Simulation of 06Cr18Ni11Ti Stainless Steel Welds

Hydrogen permeation resistance in the welded region of 06Cr18Ni11Ti steel is relatively weak due to surface defects, which need high integrity surface machining. The parameters of the welding material for 06Cr18Ni11Ti steel are currently unavailable, which causes some inconvenience for simulation studies. To fill the lack of 06Cr18Ni11Ti steel weld material parameters in the relevant literature at the present stage, the quasi-static tensile test at different strain rates and notch specimen tensile tests were conducted in this paper and determined the Johnson–Cook (J-C) constitutive model parameters and Johnson–Cook failure model parameters. Subsequently, a multi-grain grinding simulation model was built based on W-M fractal dimension theory by using the determined material parameters. The influence of processing parameters on grinding heat was analyzed. Grinding experiments were conducted to analyze the influence of processing parameters on grinding heat and grinding force. By comparing the simulation and experimental results, it is revealed that the average error is 9.37%, indicating relatively small discrepancy. It is demonstrated that the grinding simulation model built in this paper could efficiently simulate the grinding process, and the determined weld material parameters of 06Cr18Ni11Ti steel have been verified to possess high accuracy and reliability.

A π−π stacked porous framework for highly efficient second near-infrared photothermal effects and photo-thermo-electric conversion

Near-infrared (NIR) photothermal compounds, which convert low-energy NIR photons into heat, have recently attracted significant attention due to their potential applications in many areas such as photothermal imaging, diagnosis and therapy, photosensors, and catalysis. Photothermal conversion efficiency (PCE), a critical parameter of NIR photothermal materials, significantly influences their practical performance. However, exploring highly efficient NIR photothermal compounds, particularly in the NIR-II domain, remains a significant challenge. Herein, we report on a highly efficient NIR-II photothermal compound based on a novel π−π stacked porous framework {[Ni4Cl2(ONDI)2(bpy)4]⋅2Cl⋅2H2O⋅xDMF⋅yH2O}n (1). This compound features a porous supramolecular framework constructed through intermolecular π−π interactions. Additionally, compound 1 exhibits broad optical absorption spanning from the ultraviolet to the NIR region, with an edge extending to 1600 nm. Under irradiation with a 1064 nm laser, compound 1 demonstrates significant NIR-II photothermal effects, achieving a remarkable PCE of 84.4 %, attributed to the formation of charge states and the abundant π−π interactions in its crystal structure. When integrated with commercial thermoelectric generators, compound 1 shows promising potential for photo-thermo-electric conversion, with a maximum open-circuit voltage of 250 mV and 350 mV under irradiation of 1 sun and 2 suns, respectively. Furthermore, the output power density of 1@TEC1-12701 reaches 0.53 W/m2 under 1 sun and 1.23 W/m2 under 2 suns.

Assessing swelling-induced damage in shale samples during triaxial testing

In shale testing, understanding the impact of effective stress and saturation conditions is crucial for accurate material behaviour assessment and parameter determination. In some cases, saturation in triaxial testing starts at low effective stress before ramping up for shearing. However, when in contact with water (or saline water), shales are prone to swelling, particularly at low effective stress levels, which can induce fissures and alter material properties. This study investigates the influence of fluid saturation strategies and stress/pressure variations on the mechanical behaviour of shales, particularly under low effective confinement. Building upon the comprehensive testing campaign (>140 tests) in Crisci et al. (2024), additional tests were conducted on Opalinus Clay shale, focusing on sample saturation methods and loading histories before shearing. The conditions under which tested specimens experience damage were detected through diagnostic indicators such as differences in stress path and lower strength and stiffness compared to intact specimens with identical basic properties. Micro CT scanning confirms that damage is related to the development of fissures. The volumetric changes in specimens were quantified throughout the testing phases and thresholds for tolerable strains and effective stresses, specific to this material, were established. Comparative analysis with Opalinus Clay from shallower depths and other shales globally revealed consistent findings. Notably, it is shown that, for all shale types analyzed, a linear failure envelope emerges in the low to intermediate effective stress regime when filtering out "damaged" specimens. This suggests that non-linear failure envelopes observed in some cases may stem from exposing specimens to low effective stress before shearing.

The study on fracture response of cracked pipeline considering the Lüders effect

Since pipeline steel typically exhibits yield discontinuities, some pipelines may experience high local strains during service that exceed the strain limits required by existing fracture assessment methods, thereby posing a significant threat to pipeline integrity. By establishing a finite element fracture model of a cracked pipeline with the Lüders effect and incorporating a developed constitutive model with a trilinear stress-strain relationship, the mechanical and fracture responses of the cracked pipeline with the Lüders effect under uniaxial tensile loading are analyzed in this study. The effects of crack configurations and material parameters on the crack driving force are discussed in detail. The results indicate that an increase in crack length and strain hardening exponent lowers the crack driving force plateau and shortens its length. Conversely, increases in crack depth, softening modulus, and Lüders strain raise the crack driving force plateau. Specifically, as crack depth increases, the plateau length of the crack driving force shortens, while an increase in the softening modulus and Lüders strain extends the plateau length. These conclusions provide guidance for the fracture analysis and assessment of pipelines with cracks affected by the Lüders effect.

Mechanical properties and acoustic emission characteristics of basalt fiber reinforced cemented silty sand subjected to freeze–thaw cycles

Freeze–thaw (F–T) cycling poses a significant challenge in seasonally frozen zones, notably affecting the mechanical properties of soil, which is a critical consideration in subgrade engineering. Consequently, a series of unconfined compressive strength tests were conducted to evaluate the influence of various factors, including fiber content, fiber length, curing time, and F–T cycles on the unconfined compression strength (UCS) of fiber-reinforced cemented silty sand. In parallel, acoustic emission (AE) testing was conducted to assess the AE characteristic parameters (e.g., cumulative ring count, cumulative energy, energy, amplitude, RA, and AF) of the same material under F–T cycles, elucidating the progression of F–T-induced damage. The findings indicated that UCS initially increased and then declined as fiber content increased, with the optimal fiber content identified at 0.2%. UCS increased with prolonged curing time, while increases in fiber length and F–T cycles led to a reduction in UCS, which then stabilized after 6 to 10 cycles. Stable F–T cycles resulted in a strength loss of approximately 30% in fiber-reinforced cemented silty sand. Furthermore, AE characteristic parameters strongly correlated with the stages of damage. F–T damage was segmented into three stages using cumulative ring count and cumulative energy. An increase in cumulative ring count to 0.02 × 104 times and cumulative energy to 0.03 × 104 mv·μs marked the emergence of critical failure points. A sudden shift in AE amplitude indicated a transition in the damage stage, with an amplitude of 67 dB after 6 F–T cycles serving as an early warning of impending failure.

AI optimization and mathematical simulation validated by nondestructive testing for resonance frequency in advanced composite structures for bridge applications

This paper presents a novel approach integrating artificial intelligence (AI) optimization and mathematical simulation to predict the resonance frequency of nanoclay-reinforced concrete cylindrical shell structures intended for bridge applications. These composite structures, known for their enhanced mechanical properties, require precise evaluation of their vibrational behavior to ensure structural stability and longevity. Traditional methods for predicting resonance frequencies are often time-consuming and prone to inaccuracies, especially in complex materials like nanoclay composites. To address this, an AI-based optimization algorithm was developed, incorporating Particle Swarm Optimization (PSO) and a mathematical modeling to simulate resonance characteristics under varying material and geometric parameters. The mathematical modeling is validated using nondestructive testing (NDT) techniques, such as modal analysis, which provided real-world resonance data without damaging the structure. The nondestructive testing results is compared against the mathematical model to ensure accuracy and reliability. The integration of nanoclay into the concrete matrix significantly altered the vibrational properties, enhancing the stiffness and reducing damping losses, which is crucial for bridge applications where dynamic loads are prevalent. The optimized model not only predicted resonance frequencies with high accuracy but also demonstrated its potential for large-scale bridge infrastructure. This methodology offers a streamlined and robust tool for engineers, reducing the need for physical prototyping and providing enhanced design capabilities. Future research will focus on expanding the model to incorporate additional material behaviors and load conditions, furthering its application in civil engineering.

Stability and evolution of skyrmionium and skyrmions in a spherical shell

The study of magnetic structures, particularly those with curved geometries such as spherical shells, has obtained significant interest due to their potential applications in data storage, spintronics, and other advanced technologies. However, the effects of material parameters, geometric dimensions, and magnetic fields on the equilibrium and induced behaviors of skyrmions remain largely unresolved. Here, based on micromagnetic simulations, we firstly investigate the influence of spherical shell dimensions, magnetic anisotropy, exchange interaction, and Dzyaloshinskii–Moriya interaction on the magnetic states of spherical shells. We find that curvature effects become more pronounced with increasing thickness and decreasing radius, providing evidence for the role of curvature-induced DMI-like interactions in skyrmion formation. Additionally, we observe that applying a magnetic field to the spherical shell induces behaviors similar to those in disks, including the topological transition between skyrmionium and skyrmion states, the annihilation of skyrmions, and polarity reversal. Our study aims to advance the understanding of magnetic phenomena in curved geometries and contribute to the development of novel magnetic devices.

Continuum versus micromechanical modeling of corneal biomechanics

Two alternative numerical models of the human cornea are used to simulate the mechanical response under the action of a physiological intraocular pressure (IOP). The first model is continuum or macromechanical, considering the stromal tissue as a bulk material with stochastic distribution of the spatial variability of reinforcing collagen fibers. The second model is discrete or micromechanical, considering the sole collagen-crosslink stiffening micro-structure. The geometry of the two models is reconstructed from corneal topographer images. Simulations consider the behavior of a healthy cornea and of a keratoconus cornea. For the keratoconus the material properties of a portion of the cornea are reduced to 1/8 of the values used for the healthy tissue. It is found that, for suitable choice of the material parameters for the discrete model, in the healthy case the mechanical responses of the two models are fully comparable. In the keratoconus case, both models capture with comparable accuracy the anterior shape of the conus; in addition, the discrete model is able to describe the tissue thinning typical of the pathology. Despite the inclusion of stochastic material properties, starting from a healthy condition, continuum models of the cornea are not able to predict the thinning of a keratoconus cornea, while the inclusion of the underlying collagen microstructure allows for a proper description of pathologic mechanical behaviors.

Heterogeneous Transfer Learning of Electrohydrodynamic Printing Under Zero-Gravity Toward In-Space Manufacturing

Abstract As we continue to commercialize space and mature in-space manufacturing (ISM) processes, there is a strong need to transfer the knowledge we learn from experiments on the ground to zero-gravity environments. Physics-motivated manufacturing processes, like additive manufacturing, experience a shift in fabrication parameters due to the absence of gravity and the change of environments. Thus, we found traditional machine learning methods are not capable of addressing this domain shift and present a transfer learning scheme as a solution in this paper. We tested a kernel ridge regression model built for heterogeneous transfer learning (KRR-HeITL) on data from the electrohydrodynamic inkjet printing (EHD printing) process. EHD printing is a process that uses electrical force to control material flows, thus achieving the fabrication of electronics without requiring gravity. Our team has successfully conducted three rounds of parabolic flights to validate this technology for ISM. We trained on multiple datasets built from on-ground experiments and tested using zero-gravity printing data obtained from parabolic flight tests. Measurements of the Taylor cone both on-ground and in zero-gravity were taken and exploited as a part of the training data. We found that our method obtains good interpolation accuracy (MAPE 3.85%) compared to traditional machine learning methods (MAPE 16.84%) for predicting the printed line width. We concluded that the KRR-HeITL method is well suited for zero-gravity domain shifts of EHD printing parameters. This study paves the way for future predictions of ISM parameters when there are only on-ground experiments or very limited zero-gravity datasets for a given process.

Experimental analysis of a beam with a 2D triangular substructure

AbstractThe aim of this study is to determine experimentally the higher material parameter of a metamaterial with a triangular substructure and to verify a higher‐gradient elasticity model for beams with internal substructures or microstructures. The investigations of the higher‐gradient elasticity models of Bernoulli‐Euler and Timoshenko beams with a periodic triangular substructure in Khakalo et al. show that the bending stiffness strongly depends on the geometrical parameters of the lattice structure. To achieve this goal, beams with triangular substructures were additively manufactured using fused deposition modeling and stereolithography. They were experimentally investigated in tensile and bending tests. Three different types of beams with triangular substructures were produced, consisting of one, two and four layers of triangular beams, using two different materials: Polylactide and epoxy resin. The higher material parameter g was quantitatively determined based on the experimental results using inverse analysis. The results are valid for these specific variations of the substructure and can adequately represent the elastic size effects. In addition, this study investigates the relationship between the bending stiffness and the geometric parameters of the lattice structure as well as the influence of the curing time on the elastic properties of epoxy resin. The experiments involved testing the triangular beams under tensile and bending loads. The numerical and experimental results were compared using digital image correlation. Based on the experimental data, a higher gradient material parameter representing the geometric structure of the lattice was determined.

Application of selenium for enrichment of wheat flour to obtain a quality final product in accordance with consumer characteristics

Enrichment of flour with microelements and vitamins increases its nutritional value and can solve the urgent problem of improving the health of the population of Kazakhstan through the daily consumption of food products obtained from such flour, for example, bread, bakery, pasta and confectionery products, which are almost always on the tables of Kazakh consumers . Natural sources of many vital micronutrients, unfortunately, are not always available to some categories of our people, so consuming processed products from fortified flour will help compensate for the deficiency of some microelements, for example, iron, iodine and zinc. However, the need to enrich flour with other microelements, no less important for the human body and which are present in products not often consumed by Kazakhstanis, has become the goal of our research, namely an element such as selenium, the main function of which in the body is to maintain the immune system and the formation of thyroid hormones. The article presents the results of research on the development of technology for enriching wheat flour with selenium with the study of the baking properties of fortified flour. The research methodology was based on experimental methods, including the preparation of samples for research, instrumental methods for determining the physicochemical parameters of raw materials, intermediate products and finished products, as well as expert methods for determining the organoleptic properties of the final product. It has been established that the highest and first grades of flour are almost completely absent of any mineral substances, which confirms the conclusion that existing grain processing technologies transfer the mineral elements originally present in the grain into plant waste, which means it needs to be enriched. It has been established that selenium must be used in a form that ensures its safety for the human body - L-Selenomethionine. It has been established that to ensure the body’s daily requirement of selenium, the selenium-flour ratio is 0.15 mcg per 100 g. To control the selenium content in products, it has been established that the most suitable method is Raman spectroscopy using a Romanov microscope - a spectrometer, which allows determine selenium in spectra from 465 to 2900, which confirms the sensitivity of the method to microconcentrations of the element under study. It has been established that the consumer characteristics of finished products obtained using traditional technology from flour enriched with selenium are consistent both in organoleptic and physico-chemical indicators.

Sustainable EDM production of micro-textured die-surfaces: Modeling and optimizing the process using machine learning techniques

The present research explores the role of die-sinking EDM parameters, such as peak current, pulse duration, and gap voltage, and their proper selection for the cost-effective fabrication of negative micro-pillar-textured surfaces using a die-material of H13 steel alloy. The developed artificial neural networks (ANN) models of surface roughness and overcut outperform the response surface methodology models in predicting responses as higher ‘R2 values’ and lower ‘mean squared error’ with ANN models. A lower peak current of 2 A, lower pulse duration of 55.46 µs, and intermediate gap voltage of 37.83 V is selected from metaheuristic optimization approaches such as teaching–learning-based optimization and particle swarm optimization that are efficient and comparable with the desirability function-based approach while finding optimum parameter values. Further, sustainable fabrication of micro-textured H13 die surfaces is carried out on large areas using selected optimized parameters with a form tool electrode. The negative micro-pillar pattern surface demonstrates an average overcut of ∼ 40 ± 15 µm in comparison to the dimensions of the form tool. This research emphasized the sustainability of the EDM process by utilizing reusable dielectric fluid, prioritizing optimal parameters for high-quality fabrication using low electrical-energy utilization, and enabling large-scale production using a form tool.

A simulation model of thermal uniformity ratio applied in conductive thermal woven fabrics

Wearable technology based on conductive textiles generally focuses on the development of textile sensors and electric thermal textiles. The primary preparation methods currently used are coating and interweaving. Compared with the coating method, interweaving provides better deformability, durability, and a larger target functional range. Among them, woven conductive fabrics offer good stability, and by designing various jacquard patterns, multi-layer material structures can also be formed. Using woven conductive thermal textiles as a base, this paper established a thermal uniformity ratio simulation model through the design of fabric structure parameters and the analysis of thermal performance. This methodology provides possible design direction for such textiles, thereby enabling a reduction in production expenditure. Furthermore, it offers avenues for the realization of personalized adaptation and the transition towards the industrial-scale manufacturing of woven thermal textiles.

Study on the bond-slip numerical simulation in the analysis of reinforced concrete wall-beam-slab joint under cyclic loading

This paper presents the finite element analysis (FEA) of a full-scale RC wall-beam-slab joint under reversed cyclic loading. Five different approaches in ABAQUS are introduced to simulate the bond-slip effect between reinforcement and concrete. The concrete damaged plasticity (CDP) model and the combined hardening constitutive model are illustrated and adopted for concrete and reinforcement, respectively. By comparing the overall mechanical behavior of the wall-beam-slab joint predicted by FEA models to that of the test results, the predictive capability of FEA models with different bond-slip simulation methods are studied. In general, the analysis results indicate that the numerical results without the bond-slip effect present a gross overestimation of the overall mechanical behavior, while the numerical results with the bond-slip effect are in good agreement with the test results. Wherein, the FEA models with the bond-slip effect simulated by spring elements or implemented by user-defined subroutine predict more consistent results with the test results. Moreover, the disadvantages of each method utilized to simulate the bond-slip effect have also been described. A comprehensive study on material parameters of concrete is accomplished to obtain the influence of parameters such as the dilation angle(ψ), the ratio of the second stress invariant on the tensile meridian to that on the compressive meridian(Kc), and the viscosity parameters(υ).

Vibrational Analysis of Composite Conical-Cylindrical Shells with Functionally Graded Coatings in Thermal Environments.

This article studies the vibrational behavior of composite conical-cylindrical shells (CCSs) with functionally graded coatings (FGCs) in thermal environments using the first-order shear deformation theory. Firstly, the equivalent material parameters, fundamental frequency, and resonant displacement responses of the CCSs with FGCs are derived using the mixture principle, complex modulus method, and transfer function approach. Then, detailed thermal vibration tests are performed on CCS structures with and without coatings to assess the reliability of the proposed model, revealing that the current model accurately forecasts the thermal vibration behavior of the CCSs with FGCs. Finally, the effect of key parameters on the vibrational properties of the CCSs with FGCs is investigated. The results demonstrate that increasing the functionally graded index, coating thickness, and Young's modulus ratio can greatly enhance the vibration suppression capability of the structure.

Anisogrid lattice structure in thermoplastic composite by filament gun deposition

A new method to manufacture thermoplastic composite parts has been used to produce anisogrid lattice structures. Filament gun deposition consists of a hot-melt gun loaded with narrow thermoplastic prepreg tapes. Anisogrid lattice structures have been prototyped with 3 different geometries and 5 different numbers of layers (from 4 to 8) by using a metallic pattern and E-glass/polypropylene prepregs. Scanning calorimetry and bending tests of multi-layer samples have been used to characterize thermoplastic prepregs. Anisogrid lattice structures have been tested under tensile loads. A finite element model has been used to predict mechanical stiffness of these structures by using material properties coming from the sample characterization. Numerical models have been developed with a batch-type parametric approach to rapidly evaluate the combined effect of geometric and material parameters. A good agreement has been found between experimental and numerical data with an average difference about 4%.