Composite Armor Research Articles

Структурные особенности и технология получения легких броневых композиционных материалов с механизмом локализации хрупких трещин

Introduction. Monometallic armor traditionally used in military and special equipment armaments has a number of key disadvantages that have a significant impact on the tactical and technical characteristics of the products, namely, significant weight and thickness. At the same time, composite non-metallic armors, which have been widely used recently as an alternative, in turn, are not able to withstand multiple hits in local areas of the structure due to its complete destruction or delamination. The purpose of the work: to develop the technology of obtaining a new class of multilayer metal armor materials based on light metals and alloys by explosive welding, combining high indicators of bullet resistance and structural strength along with low specific gravity. The work presents a new scheme for reinforcing the composite using explosive welding technology, which allows localizing the development of brittle cracks along interlayer boundaries with external ballistic impact on the object. Results and discussion. Reinforced composite material based on titanium and aluminum alloys is obtained by explosive welding. Rational modes of shock-wave loading, which ensure production of composite material of required quality are determined; evaluation of strength of composite is carried out. In order to improve the tactical and technical characteristics of the composite, it was proposed to form high-solid intermetallic layers in its structure due to heat treatment. Rational modes of high-temperature annealing are defined, which ensure formation of intermetallic layers of preset thickness in composite structure. The phase composition of intermetallic pro-layers is studied. Structural features of the composite material are investigated. Mechanism of brittle cracks localization in composite structure at ballistic impact on it is described.

Prediction of shear deformation and thickness gradients in deep-draw forming of ultra-high molecular weight polyethylene

Ultra-high molecular weight polyethylene (UHMWPE) composite armor offers a high level of lightweight protection. In the manufacturing of complex curvature UHMWPE based protective materials, UHMWPE composites are transformed from flat sheet stock to a near net shape complex curvature preform through deep-draw forming. The development of a deep-draw forming process model is critical for predicting UHMWPE sheet deformation during processing and knowing the fiber orientations at each location in the entire final part. This work introduces a robust methodology to model the deep-draw forming process. The model is validated by comparing critical output with experimental results for multiple UHMWPE materials and over a range of part thicknesses. A hemispherical geometry is used to demonstrate the methodology. A homogenization strategy for grouping sheets is presented and validated, which is critical for keeping computational times manageable. The influence of the material in-plane shear response, a critical model input, is investigated. The model developed in this work represents a valuable tool for selecting deep-draw forming parameters and accelerates the evaluation of new and emerging UHMWPE materials for application in manufacturing complex curvature protective armor.

Multiple ballistic damage of segmented SiC/BN laminated ceramic composite armor

This article investigated the structure of the laminated ceramics to improve the multiple ballistic performance of segmented ceramic composite armors. The multiple ballistic experiments were conducted with 5.8 mm caliber steel core bullets at the impact velocity of about 920 m/s. The experiments verified that two laminated SiC/BN structures (GLC and ULC) exhibit higher residual ballistic performances than the monolithic SiC structure (MC). Moreover, through damage evolution analysis, two laminated SiC/BN structures (GLC and ULC) exhibit less sensitivity to the multiple ballistic impacts damages, and possess more energy absorption mechanisms than the monolithic ceramics. The structure design of the laminated of ceramics is beneficial for improving the multiple ballistic performances of composite armors and reducing the crater deformation.

Dynamic failure of composite strips under reverse ballistic impact

Mesoscale impact experiments on composite strips were conducted in this study to reveal the fundamental failure mechanisms of fiber-reinforced composites (FRCs) under transverse impact by different projectiles. The componential material of composite armor, S-2 glass/SC-15, was manufactured into a single ply and sectioned into strips. The strip specimens were first characterized by X-ray computed tomography and scanning electron microscopy (SEM). The impact experiments were performed using a light-gas gun, shooting the strip specimens to the static wedge-nose projectiles with different nose diameters of 4, 40, and 400 µm. A high-speed camera recorded the strip's failure process from the side. Such a reverse ballistic impact scheme enabled to focus the camera on the projectile nose where the strip was deformed and fractured so that the entire failure process was recorded in real time. These experiments identified three failure modes of the composite strip for each projectile type, defined by no, partial, and complete local failure by the impact loading. The critical velocity region was quantified, showing rising upper and lower boundaries corresponding to the projectile nose diameter. The experimental data were compared with theoretical predictions by Smith's theory. The transverse wave speed deviated from Smith's prediction as the projectile nose diameter decreased, demonstrating a possibly significant error when the pure-tension assumption is employed to model the composite's impact behavior by sharper projectiles. Besides, a sharper projectile was more likely to induce a smaller tent angle, indicating a larger local deformation, considered owing to the stress concentration at the projectile nose.

Dynamic Response of UHMW-PE Composite Armors under Ballistic Impact of Blunt Projectiles.

To study the dynamic response of UHMW-PE composite armor under ballistic impact, two kinds of UHMW-PE composite armors are designed. Both of them are composed of UHMW-PE laminates and steel face sheets of Q235. The blunt projectile is made of 35CrMnSiA, with a cylinder shape. By numerical simulation, the dynamic response and deformation of composite armors are obtained under the penetration of the projectile. With the increase of impact velocity, the penetration depth increases nearly linearly, with a more severe tendency of swaging in the projectile. Then, experiments are carried out to validate the numerical simulation results. Based on a ballistic gun with a caliber of 14.5 mm, the projectiles are fired with a velocity from 680 m/s to 1300 m/s. The penetration into the composite armor can be divided into an initial shear plugging stage and the following bulging and delamination stage. Based on the theoretical analysis, the shear strength in the shear plugging stage can be estimated. Associated with typical experimental results, numerical simulation is suitable to predict the bulging characteristics of the composite armor. The failure mode of the composite armors under the impact of blunt projectiles is determined, and the failure mechanism is analyzed. The penetration results in the experiment agree well with the numerical simulation results, which validate the correctness of the numerical simulation models. The research results can be significant in the design of composite armor with UHMW-PE laminates.

Deflection effect and mechanism of semi-cylindrical ceramic composite armor for flat-ended rod projectile

Based on the idea of using deflection and yaw induced by specially shaped ceramics for the purpose of defense, composite armors composed of semi-cylindrical ballistic ceramics and metal back plates are designed to resist the penetration of high-velocity flat-ended rod projectiles. Ballistic impact tests and numerical calculation method are adopted to study the deflection effects and mechanism of the flat-ended rod projectile when penetrating the Semi-Cylindrical Ceramic composite armor. The penetration and deflection process of the projectile, deformation and failure mode of the projectile and target plate, as well as the residual characteristics of the projectile are analyzed. The results show that the process of the flat-ended cylindrical projectile penetrating the Semi-Cylindrical Ceramic composite armor can be roughly divided into four stages: asymmetric erosion, Ceramic cone squeezing movement, non-ideal penetration and exit. In the early stage of penetration, the specially shaped ceramic erodes the projectile into a non-axisymmetric shape and deflects the asymmetric force on the projectile; in the later stage of penetration, the projectile penetrates the back plate with its non-axisymmetric nose and non-ideal attitude, resulting in the deflection of the non-axial force on the projectile; and the back plate displays dishing deformation and petaling failure.

Broadband stealth composite metastructure with high penetration protection

Microwave absorption plays an important role in modern electromagnetic protection and compatibility. However, lack of mechanical and impact design restricts their practical applications. Herein, a composite armor (CA) incorporating metastructure design with mixed characteristic periods was optimized by embedded genetic algorithms and inversion framework of equivalent impedance derivation. The −10 dB absorption bandwidth was covered from 2 GHz to 18 GHz. The impact-penetration ballistic experiments and simulation verified the penetration protection of CA against large caliber armor-piercing incendiary (API) with target impact speed of more than 745.1 m/s. The CA fabricated by ultra-high molecular weight polyethylene fiber reinforced polymer (UFRP), carbon fiber reinforced polymer (CFRP) and alumina ceramics showed better penetration protection performance than the counterparts with titanium and aluminum alloys with the same weight. Compared with traditional armor steel with similar protection performance, more than 30% weight is reduced for the proposed composite armor.

Impact mechanics of multilayer composite armors: Analytical modeling, FEM numerical simulation, and ballistic experiments

An analytical model is developed to study the ballistic behavior of multilayer composite armors subjected to the high-velocity impact of projectiles with arbitrary angle of incidence, shape, size, and frictional characteristics. The thickness compaction resulting from the production process is also accounted for, quantifying the role of the curing pressure on the enhancement of the impact toughness of composite laminates. Finite element method simulations are used in a complementary manner to study damage and failure mechanisms within the targets. Both approaches are validated by extensive experimental ballistic tests on multilayer composite targets. The role of the layer stacking sequence is also investigated. It emerges that graded multilayer configurations yield higher toughness when the projectile penetrates plies with decreasing fracture strength. These results can explain common structural arrangements in biological armors as well as be exploited in the design and optimization of shielding structures against high-velocity projectiles.

Damage delocalisation in skeletal muscle-inspired hierarchical armoured structures for impact protection

We propose a skeletal muscle-inspired hierarchical structure for the alumina ceramic layer in ceramic composite armour structures to achieve greater energy dissipation under impact. We mimic the nano-architecture of skeletal muscle tissues by introducing hierarchy both with self-similarity using a fractal design, and without self-similarity in the hierarchical levels to explore the function of hierarchy in improving the protective capability of the armour structure. The numerical simulations showed that increasing the structural hierarchy can boost stress reduction by up to 30% for the third order hierarchical structure without self-similarity compared to the first order hierarchical structure with the same weight. The underlying mechanism that increases the impact resistance in the higher order hierarchical structures is the delocalisation of the damage over multiple crack paths in the different hierarchical levels. This bio-inspired concept can be used to generalise the design of future impact-resilient structures which optimise the suppression of stresses and reduce the associated weight penalty for use in protective gear and armoured structures.

Investigation on anti-penetration capability of water filled aluminum alloy cell structure to the shaped charge jet

Passive protective armor is reliable and cheap, and is favored by many armored weapons and equipment. However, reports on metal-liquid composite armor are not sufficient and systematic. Based on the shaped charge jet (SCJ), the anti-penetration capabilities of water filled aluminum alloy cell structure were studied. The hourglass cell structure (HCS) was designed according to the shock wave propagation characteristics in liquid, and the expansion-convergence cell structure (E-CCS) was derived. Based on the virtual origin theory, the residual tip velocity of jet after SCJ penetrated the cell structure was calculated. According to the theory of supersonic disturbance propagation, the Mach cone half angle of SCJ shock wave propagation in liquid was defined and corrected. The propagation and reflection behavior of shock wave were discussed to analysis the radial convergence of liquid. Via the Van Leer Arbitrary Lagrangian Euler finite element simulation model verified by experiments, the simulation studies of SCJ penetrated the circular cell structure (CCS), HCS, E-CCS and convergence/expansion multi-cell structure were performed. The results show that HCS has better effect of interfering with SCJ than that of CCS and E-CCS. An important discovery is that when the liquid composite multi-cell structure is penetrated by SCJ, the attacked cell will not affect other cells due to the shock wave has been trapped in a single cell.

Analysis of the influence of different constraints on the ballistic performance of B4C/C/UHMWPE composite armor

A lightweight composite armor system composed of boron carbide (B4C) ceramic panels, carbon-fiber interlayer, and ultra-high molecular weight polyethylene (UHMWPE) backplate has been widely used. This study aims to explore the effect of different constraint conditions on the ballistic resistance of lightweight composite armor. Thus, ballistic experiments of 12.7 mm armor-piercing incendiary (API) projectiles impacting armor targets under different constraint conditions are designed, and numerical simulations are performed to simulate the structural impact response of composite armor. A satisfied consistency is revealed by comparing the numerical results and the ballistic experimental results. Besides, the numerical simulation method is used to research the influence of the distance between the impact point and the constraint conditions on the ballistic performance of the composite armor. The results demonstrate that the ballistic performance of the composite armor is better if the impact point is farther from the constraint conditions as this can enhance the flexibility of composite armor. In conclusion, the flexibility of the constraint conditions is positively correlated with the ballistic performance of B4C/C/UHMWPE composite armor. This conclusion provides a guideline for the design and application of composite armor.

Failure and fragmentation of ceramic target with varying geometric configuration under ballistic impact

The failure and fragmentation of monolithic bare alumina 99.5% ceramic target and energy dissipation of steel 4340 projectile have been studied in a series of ballistic experiments carried out, with the incidence velocities in a range, 122–290 m/s. The velocity drop and energy dissipation increased with incidence velocity for 10 mm thick target with damage zone extended upon the whole area of rear face at higher velocities. The ballistic results obtained with the 10 mm thick target have been compared with the ballistic performance of the 5 mm thick target used in a previous study to explore the effects of target thickness on the failure mechanism. A model for the residual velocity of projectile after perforation of the single layered ceramic target has been developed based on the Lambert Jonas model by using the experimental data available for 5 mm and 10 mm thick alumina 99.5% target against 10.9 mm projectile. The residual velocities and damage patterns were reproduced with a reasonable amount of accuracy by a three-dimensional finite element model developed on commercial ABAQUS/CAE. The effect of obliquity and projectile diameter to target thickness ratio (D/T) on ballistic performance has been determined by the numerical simulation model with impact velocity in a range of 300–500 m/s. A spatial variation of ejected fragments velocity at different time steps was plotted to develop a velocity profile for the ceramic fragments coming out of the target. A semi-empirical model has been proposed for residual velocity after perforation of a monolithic ceramic target, relating to the incidence velocity and projectile diameter to target thickness ratio. The monolithic ceramic targets have been investigated for a comparative assessment of energy dissipation by the ceramic layer to eventually design an efficient front layer of a ceramic based composite armour in future studies.

Lightweight Design and Experimental Study of Ceramic Composite Armor

Ceramic/fiber composite armor is a hot research topic of bulletproof equipment. The lightweight design of ceramic materials and structures has attracted much attention. In this work, in the light of the remarkable performance of ceramic against elastic and oblique penetration, a novel honeycomb ceramic panel with a hexagonal prism and spherical body was designed. The splicing ceramic/fiber composite plate was bonded with a PE plate. The splicing ceramic/fiber composite was prepared, and the target test of the composite was conducted. The results show that the bulletproof performance of the hexagonal prism spherical crown ceramic/fiber composite plate is better than that of the conventional ceramic/fiber composite plate of the same thickness. The honeycomb spherical crown structure of the ceramic surface can convert the nominal forward penetration into the actual oblique penetration. This surface structure provides an effective lightweight design of ceramic/fiber composite armor.

A numerical model for analysis of layer thicknesses on ballistic resistance of a multilayer armor

The interest in composite materials, which are lighter and have better mechanical properties (strength, fatigue resistance, corrosion resistance, etc.) than traditional engineering materials, is increasing day by day. In particular, their responses to low or high-velocity impact loads have been among the important research topics of recent years. In this study, unlike the traditional ceramic-based composite armor structures used in the defense industry, the effect of total carbon fibers specifically parallel oriented into impact direction on penetration resistance has been investigated, and penetration resistance of a multilayer hybrid composite armor which is composed of carbon fiber composite blocks sandwiched by two armor steel plates exposed to high-velocity impact has been analyzed numerically. Carbon fibers are normally very brittle to the transverse loading direction, contrarily, to their axial tension or compression direction. This is the reason why it is claimed that this high compression strength property of carbon fibers could be used as a layer in order to replace ceramics in add-on multilayer composite armor. The numerical model created in the ANSYS LS-DYNA program was verified by using the experimental data obtained in an earlier study. The verified numerical model was used to analyze high-velocity impact simulations of multilayer hybrid composite armor for different thicknesses of armor steel to reduce the areal density. By these simulations, minimum areal density compared to Rolled Homogeneous Armor steel for equivalent protection was finally achieved, and thus the hypothesis saying that carbon fibers parallel oriented to impact direction can give high penetration resistance was proved by showing that developed multilayer carbon fiber reinforced epoxy composite–armor steel hybrid panels have indicated a better protection level than STANAG 4569 Level-4 with a lower areal density.

Средства индивидуальной бронезащиты (СИБ) – бронежилеты как объекты баллистических и медико-криминалистических исследований

Introduction. The cases of gunshot injuries (wounds) of persons using personal protective equipment (body armor based on textile and composite organoplastic armor), that occur in investigative and expert practice, require a comprehensive approach to diagnostic studies of traces and injuries, both on the human body and on non-biological objects (materials of body armor and clothing items). Methodology and results of the study. The organization of studies of gunshot injuries on the human body and on the means of individual armor protection is possible in the form of a comprehensive medical and forensic examination or a complex of forensic medical and criminalistic examinations. In the course of diagnostic complex studies of gunshot injuries on the human body, materials of his or her body and clothing items, the circumstances of causing a gunshot wound to a person are confirmed with an explanation of the mechanism of damage formation on the human body, body armor and clothing items. Discussion of results. The methodology (algorithm) of studies of gunshot injuries of SIB – bulletproof vests does not differ from traditional comprehensive medical and forensic studies of gunshot injuries on a person’s body and items of his or her clothing, but it requires taking into account the structural features of personal protective equipment that affect the volume and morphological signs of personal protective equipment injuries (including taking into account the protection class of a particular instance of the body armor under study). As a result of the study of the SIB – bulletproof vest, important circumstances of causing a person a gunshot injury can be established and explained – the mechanism of damage formation on the body and objects of the personal protective equipment and clothing of the victim, the posture of the victim at the time of injury, the presence of combined bodily injuries on the victim’s body, if there is a projectile that caused the injury or its fragments extracted from the parts of the personal protective equipment, the causes and mechanism of deformation of the projectile or the causes of its fragmentation (dismantling).

Numerical investigation of ballistic performance of SiC/TC4/UHMWPE composite armor against 7.62 mm AP projectile

With the development of weapons, monolithic armor is hard to resist these threats. Therefore, a SiC/TC4/UHMWPE laminates multi-layered composite armor against 7.62 mm armor piercing projectile is proposed in this paper. To investigate the ballistic performance of the SiC/TC4/UHMWPE laminates composite structure, a finite element model (FEM) is created in LS-DYNA. Verification FEMs are carried out on the materials of the silicon carbide (SiC) material, Ti–6Al–4V (TC4) material and ultra-high molecular weight polyethylene (UHMWPE) fiber to verify the accuracy of these materials. Furthermore, it is shown that establishing FEM of SiC/TC4/UHMWPE laminates structures can be reasonably implemented. Based on simulation results, SiC/TC4/UHMWPE laminates composite structure has a better ballistic performance than other systems using only two of the above materials. In addition, results also reveal that the SiC plate is suitable for face-sheet to wear the weight and kinetic energy of the projectile, while TC4 plate can enhance the penetration resistance of SiC plate and UHMWPE laminates backplane can maintain the integrity of the composite structure to resist higher initial velocity impact, thus providing an innovative way to improve the ballistic performance under the high-velocity impacts.

Performance evaluation of multilayered ceramic composite armors: New design and advanced predictive method

Novel body armors are designed to protect against ballistic threats in the most vulnerable organs within the thorax and abdomen. Decreasing the armor weight without affecting its total integrity after the impact is one of the most challenging tasks. In this study, we combine advanced numerical simulations and experimental tests to investigate the ballistic performance of multilayered armor systems (MAS) consisting of laminated alumina (Al2O3) ceramic plates with multi-curve form and a hybrid composite backing. The ballistic trauma absorption and ceramic fracturing morphology are considered evaluation criteria. The investigation provides enough data on the measured trauma and the results are compared to advanced monolithic ceramics. The ballistic tests showed that bonding three or two ceramic plates with polymeric interlayer decreases considerably the eroded ceramic mass in comparison to monolithic ceramic tiles. Furthermore, the layup of two thin Al2O3tiles with frontal confinement gives the same trauma-weight index as monolithic silicon carbide and reaction-bonded boron carbide plates. The combination of K129 and KM2 aramid weave fabrics decreases the composite backing weight by 33% and increases its ballistic performance in comparison to homogeneous aramid fabrics. Numerical simulations that involve the use of solid Lagrange and adaptive solid/smooth particles hydrodynamics (SPH) numerical approaches with detailed 3D models of the bullet and the MAS are presented in this work. Based on the statistical analysis, a better prediction of the back face deformation and bullet residual length is obtained by the adaptive solid/SPH method, which is found more suitable for the simulation of multilayered armor impact scenarios.

Progress in Transparent Nano-Ceramics and Their Potential Applications.

Transparent nano-ceramics have an important high-transmittance, material-integrating structure and function and a variety of potential applications, such as use in infrared windows, optical isolators, composite armors, intelligent terminal screens, and key materials of solid-state lasers. Transparent ceramics were originally developed to replace single crystals because of their low fabricating cost, controllable shape, and variable composition. Therefore, this study reviews and summarizes the development trends in transparent nano-ceramics and their potential applications. First, we review the research progress and application of laser nano-ceramic materials, focusing on the influence of controllable doping of rare earth ions on thermal conductivity and the realization of large-scale fabrication technology. Second, the latest research progress on magneto-optical transparent nano-ceramics, mainly including terbium gallium garnet (Tb3Ga5O12, TGG) ceramics and terbium aluminum garnet (Tb3Al5O12, TAG) ceramics, are summarized, and their performance is compared. Third, the research progress of transparent armor nano-ceramic materials, represented by MgAl2O3 and Aluminum oxynitride (AlON), are reviewed. Lastly, the progress in electro-optical transparent nano-ceramics and scintillation transparent nano-ceramics is reported, and the influence of the material-fabrication process on electro-optic effect or luminous intensity is compared. Moreover, the effect of particle diameter on fabrication, the relationship between nano powder and performance, and different sintering methods are discussed. In summary, this study provides a meaningful reference for low-cost and sustainable production in the future.

Study on the Penetration Power of ZrO2 Toughened Al2O3 Ceramic Composite Projectile into Ceramic Composite Armor.

This work aims to improve the penetration ability of a 14.5 mm standard armor-piercing projectile into ceramic/armor steel (Al2O3/RHA) composite armor. To this end, ZrO2 toughened Al2O3(ZTA) is prepared as the material for bullet tips, utilizing in situ solidification injection molding that is realized via ceramic dispersant hydrolytic degradation. The penetration power of ZTA ceramic composite projectile, compared with standard armor, against 15 mm armor steel (RHA) and 30 mm Al2O3/RHA composite armor, is studied by ballistics testing combined with numerical simulation. The Tate theory is optimized and then employed to calculate the penetration depth and bullet core’s residual mass when ZTA ceramic composite projectile penetrates into Al2O3/RHA composite armor. The results show that when penetrating RHA of 15 mm, the penetration area of ZTA ceramic composite projectile into RHA increases by 27.59% and the exit area by 42.93%. While the standard projectile fails to penetrate the 30 mm Al2O3/RHA composite armor, the ZTA ceramic composite armor-piercing projectile succeeds, with the mass loss reduced by 66.67% over the standard one. The ZTA ceramic composite bullet has a better performance than the standard bullet in penetrating RHA and Al2O3/RHA composite armors. The test results, simulation, and theoretical analysis are consistent. This study has practical values for engineering applications to design new ceramic composite bullets.

Nonlinear Multi-Fidelity Bayesian Optimization: An Application in the Design of Blast Mitigating Structures

<div class="section abstract"><div class="htmlview paragraph">A common scenario in engineering design is the availability of several black-box functions that describe an event with different levels of accuracy and evaluation cost. Solely employing the highest fidelity, often the most expensive, black-box function leads to lengthy and costly design cycles. Multi-fidelity modeling improves the efficiency of the design cycle by combining information from a small set of observations of the high-fidelity function and large sets of observations of the low-fidelity, fast-to-evaluate functions. In the context of Bayesian optimization, the most popular multi-fidelity model is the auto-regressive (AR) model, also known as the co-kriging surrogate. The main building block of the AR model is a weighted sum of two Gaussian processes (GPs). Therefore, the AR model is well suited to exploit information generated by sources that present strong linear correlations. Recently, the non-linear auto-regressive Gaussian process (NARGP) model has appeared as an alternative to integrate information generated by non-linearly correlated black-box functions. The performance of the NARGP model in structural optimization has remained largely unexplored. This investigation presents a Bayesian optimization approach that implements the NARGP model as the multi-fidelity surrogate model. The optimization strategy is utilized in the design sandwich composite armors for blast mitigation. The armors are made of four layers: steel, carbon fiber reinforced polymer (CFRP), aluminum honeycomb (HC), and CFRP. The optimization problem has three design variables, which are the thickness of the CFRP and aluminum HC layers. Two objectives are minimized: the armor’s penetrations and the reaction force at the armor’s supports. The black-box functions are two finite element models with different levels of fidelity. The low-fidelity model assumes elastic behavior of the sandwich composite. The high-fidelity model considers the nonlinear behavior of each layer of the armor. The results show that the proposed non-linear multi-fidelity Bayesian optimization approach produces a more stable expansion of the Pareto front than an optimization strategy that employs the AR model. This outcome suggests that the NARGP model is an appealing alternative in design problems with a limited number of function evaluations of the high-fidelity source.</div></div>