The effect of geometrical parameters on blast resistance of sandwich panels—a review

Many engineering structures, especially defense applications, need to be reinforced against blast loads due to a nearby explosion. Today, much more attention needs to be given to this issue because of increased exposure to explosions, and natural disasters. Different solutions have been used in the literature to mitigate blast-loading effects. One of these applications, sandwich panels, are a good candidate for blast-loading applications. In a sandwich panel structure, several parameters have considerable effects on deflections, deformations, and energy absorption capability. The most important of these parameters are: (i) the material and thickness of the front and back face sheets and core; (ii) core density and grading; (iii) core and face sheet types; (iv) filling and stiffening strategies of the core; (v) radius of curvature of the panel; (vi) mass of explosive charge; and (vii) standoff distance. The aim of this paper is to review these critical aspects of blast loading of sandwich panels to provide an overall insight into the state of the art of the application.


Introduction
Aircraft, automotive or marine structures may undergo severe loads and strain rates higher than their expected levels during their operation, which threats their structural integrity. One of the reasons for this type of extreme load and strain is the detonation of an explosive nearby, commonly referred to as blast loading. After a nearby explosion, a shock wave with a high velocity and pressure is released from the explosive and moves toward the target. This shock wave or blast loading can generate severe damages on the target and cause penetration [1]. When there is a risk or possibility of strong explosion in the normal operation of a vehicle, such as explosions or natural disasters, engineering structures or defense applications must be protected against blast loads and supported with blast resistant solutions. These solutions are required to absorb maximum amount of blast energy and transmit minimum amount of this energy to the mating structure without a weight penalty [2].
Different applications have been tried in literature to mitigate the blast load effect on structures. One that is frequently used is sandwich panels. Sandwich panels are made of front (facing blast load) and back (facing mating structure) face sheets and a core material [3] (figure 1). Sandwich panels with crushable cores are good candidates for blast-loading applications due to their high energy absorption characteristics, low weight and high strength-to-weight ratios [4]. Moreover, the core between the front and back face sheets can dissipate a very large amount of energy in a blast scenario and weakens the transmitted shockwave to back face sheets and therefore protects the applications from failure [5]. In addition, the core increases the second moment of area, therefore, stiffens the panel against bending moments without increasing the total panel weight [6]. For these reasons, they are extensively used in aviation, automotive, marine and civil engineering applications. For instance, Wahab et al exploited composite sandwich structures including aluminum foam cores in order to protect the bottom of the armored vehicle and passengers against explosion and blast wave propagation beneath the vehicle [7]. Thus, it is expected that the sandwich structures absorb the explosion energy and prevent the passengers and critical components to be damaged. In this situation, the penetration  . Different deformation modes on face sheets due to blast loading [8]. Reprinted from [8], Copyright 2014, with permission from Elsevier. or deformation of back face sheet is the critical parameter that needs to be considered as a main driver in the design.
The blast response of sandwich panels is affected by the front and back face sheet, core thicknesses and materials, core density, core configuration, and the mass of the explosive charge and standoff distance which is the distance between explosive charge and the target. All of these parameters affect the failure modes of sandwich panels and depending on the parameter selection, front and/or back face sheets tearing, debonding of sheets from the core and core collapse deformation modes occur [3].
According to Li et al, three failure/deformation modes can be observed on face sheets [8]: • Pitting and fragment accompanied with plastic deformation and tearing (figure 2(a)).
This literature review focuses on the blast resistance of sandwich structures including the effect of aforementioned parameters on failure/deformation modes of sandwich structures subjected to blast loading. In section 2, all of these parameters were investigated detailly based on the findings in literature. In conclusion, main findings and research gaps were presented.

The effect of parameters on blast resistance of sandwich panels 2.1. The effect of material
The material of front and back face sheets and core section directly affects the energy absorption and transmission from a blast load. In literature, different materials have been applied and used to mitigate blast loading effects. Langdon et al compared sandwich panels with aluminum and glass fiber reinforced polymer face sheets and aluminum honeycomb core. They stated that composite face sheets absorb more energy and showed better blast resistance than aluminum face sheets [9]. Arora et al performed a study on anti-blast behavior of full-scale glass-fiber reinforced polymer sandwich structures and digital image correlation was utilized to observe failure mechanism [10]. Qi et al investigated the blast response of aluminum foam-cored sandwich panels with front and back face-sheets of different materials (aluminum alloy (2024-T3), mild steel (AS3678-250) or rolled homogeneous armor (RHA) steel). They stated that low stiffness materials used in front face-sheets resulted in large energy absorption and foam core compression. On the other hand, high stiffness materials used in back face-sheets resulted in less deflection [11]. Santosa et al investigated the blast response of sandwich panels with 4 mm thick martensitic steel 1200 T front face sheet and 10, 12 and 14 mm thick aluminum back face sheet of different materials (Al115H2U, Al110H5E, A356-T6) or 10, 12 and 14 mm thick AlSi6Cu4 foam back face sheet of different densities (0.39, 0.44, 0.53 kg m −3 ). Their results revealed that A356-T6 back plate showed the lowest and Al110H5E showed the highest central node displacement [12]. Traditional sandwich panels consist of metal front and back face sheets but in some researches fiber metal laminates (FMLs) were used as face sheets. Since these materials have high impact resistance, the blast response of sandwich panels with FML face sheets showed higher blast resistance than traditional sandwich panels [13]. It was also stated in the literature that heat treatment to a part relieved the stress due to related manufacturing process and consequently reduced the blast load transmitted to back face sheet [14]. Apart from changing the material of front and back face sheets, some researchers investigated the effect of addition of a plate of different material between face sheets and core section of sandwich panels on blast response. Bahei-El-Din et al stated that polyethylene elastomeric foam addition between AS4/3501-6 carbon/epoxy face sheet and H100 Divinycell foam core increased blast resistance of sandwich panels [15]. In another study, the same authors stated that thin polyurea sheet addition between AS4/3501-6 carbon/epoxy face sheet and H100 Divinycell foam core also increased the blast resistance of sandwich panels [16,17].
Related with core material, Kelly et al investigated the blast response of sandwich panels with glass fiber reinforced polymer front and back face sheets and three different polymeric foam core materials: styrene acrylonitrile (SAN), polyvinylchloride (PVC) and polymethacrylimide (PMI). They stated that SAN showed the least and PMI showed the highest deflection and front face sheet cracking [18,19]. Karagiozova et al investigated blast response of sandwich panels with steel front and back face sheets and polystyrene or aluminum honeycomb cores. They stated that aluminum honeycomb cores showed higher blast resistance than polystyrene cores [20]. Abbas et al studied the blast behavior of reinforced concrete (RC) sandwich panels including expanded polystyrene foam core and covered by spray-on concrete skin [21]. Shirbhate and Goel [22] investigated the utilization of Saffil foam core in the sandwich panel including equal steel plates. For the evaluation, steel plates were modeled using piecewise linear plasticity and Saffil foam was modeled using crushable foam material in LS-DYNA ® . Results showed that the foam usage was found to be beneficial in the reduction of the response of the sandwich structure. Beyond the sandwich structures constituted of metal or composite sheets, precast concrete sandwich panels (PCSPs) are extensively used for blast mitigation. Ye et al investigated blast performance of PCSPs opposing to the conventional RC slab and showed that PCSP anti-blast performance is weaker than the conventional RC [23].
Blast is the loading in which high strain rate loading occurs; thus, the strain rate performance of materials that are used to compose sandwich structures is important. The strain rate that occurs during blast scenarios is divided into two groups, low blast ranging between 1 s −1 and 49 s −1 , and high blast in the range of 50 s −1 -10 3 s −1 [24]. Furthermore, different types of materials experience non-identical strain rate sensitivity according to loading rate, which can cause different elastic and plastic properties deviating from the static loading behaviors. Orton et al investigated the strain rate effects in carbon fiber reinforced polymer laminates under blast loads ranging 0.0015 s −1 -7.86 s −1 . The results showed that there is no considerable difference in tensile strength and stiffness; however, a significant scatter is observed in tensile strengths which are explained by the manufacturing problems [25]. However, glass fiber reinforced composite shows high strain-rate sensitivity with an increase in tensile strength, maximum strain and toughness by the increase of strain rate [26]. Staab and Gilat showed that both matrix and fiber materials of glass/epoxy composite are sensitive to strain rate and fibers effect the strain rate sensitivity of laminates more than the matrix. Thus, fiber orientation, composite weave types, constituent materials, and fiber and matrix volume ratio directly influence the strain rate sensitivity [27]. Chen et al showed that AA6xxx aluminum alloys experience inconsiderable strain rate sensitivity, however, AA7xxx aluminum alloys exhibit a considerable degree of sensitivity [28]. Positive strain rate sensitivity is displayed in AA5182 aluminum alloy at temperatures of 296 K, 338 K, 373 K, 423 K, and 473 K [29]. Different type of materials utilized in the front and back face sheet, and core structures to increase the blast resistance of sandwich panels, which compromises with the weight of the structures. Composite materials were selected in accordance with their higher strength/weight ratio, and aluminum alloy materials were selected due to their high plastic deformation ability and less sensitivity to strain rate effects [30].

The effect of thickness
The thickness of front and back face sheets and core section directly affects the blast resistance of sandwich panels as stated in different studies in literature. Some of them are presented below in chronological order. Radford et al investigated the blast response of sandwich panels with AISI 304 stainless steel front and back face sheets and aluminum alloy metal foam cores. They stated that sandwich panels showed higher blast resistance than monolithic plates of equal mass and an increase in core thickness increased the blast resistance [31]. Zhu et al investigated the blast response of sandwich panels with Al-2024 face sheets and Al-5052-H39 hexagonal honeycomb core. Their experimental results revealed that increasing face sheet and core thicknesses decreased back face sheet deflection. Localized deformation was observed on the front face sheet if face sheets thicknesses, core density and charge mass increased, and global deformation was observed if the situation was opposite [32]. Theobald et al investigated the blast resistance of sandwich panels with steel face sheets of two thicknesses and hexagonal honeycomb or unbonded aluminum foam (Alporas, Cymat) cores. Compared with monolithic plates, Alporas and hexagonal honeycomb cores showed higher blast performance which increased with an increase in face sheet and core thicknesses [33]. Shen et al compared curved sandwich structures with flat ones to show the benefit of curved structures. The study showed that curvature changes the deformation and collapse pattern of the structure and experienced better performance in comparison to equivalent solid counterpart and flat sandwich structures [34]. In a different study, Shen et al investigated the blast response of curved sandwich panels with Al-5005 H34 aluminum face sheets and Alporas aluminum foam core. Experimental results revealed that an increase in front and back face sheet and core thicknesses decreased back face deflections [35]. Chi et al investigated the blast response of sandwich panels with mild steel face sheets and hexagonal AA3003 aluminum honeycomb cores of three different heights: 13 mm, 29 mm and 150 mm. Their experimental study revealed that core support against blast load was more crucial when thinner front face sheets were used, and back face sheet deflection decreased with an increase in core height [36]. Wang et al investigated the blast response of sandwich panels with Al 2024 front and back face sheets and foam core and stated that an increase in face sheet thicknesses or core thickness decreased back face sheet deflection [37]. Fatt and Surabhi investigated the blast response of sandwich shells with E-Glass Vinyl Ester face sheets and Divinycell H30, H100, H200, Klegecell R300 and Divinycell HCP100 foam cores. They stated that an increase in core thickness resulted in higher blast resistance [38]. Sousa-Martins et al investigated the blast response of sandwich panels with 5754-H22 aluminum alloy face sheets and micro-agglomerated cork core. They used five core thicknesses (10, 15, 20, 25 and 30 mm) and stated that an increase in blast resistance with an increase in core thickness was observed [39]. Li et al investigated the blast response of sandwich panels with trapezoidal corrugated cores and stated that front and back face sheet deflections could be decreased by using thicker sheets or cores [40]. Hua et al investigated the blast resistance of sandwich panels with carbon fiber front and back sheets and Rohacell 71 IG polyurethane (PMI) rigid foam core. They stated that increasing face sheets and core thicknesses increased the blast resistance of the panel. An increase in face sheet thicknesses from 0.381 mm to 0.762 mm and 1.524 mm decreased back face sheet deflection by 21.3% and 54.9%, respectively. On the other hand, an increase in core thickness from 3.175 mm to 6.35 mm and 12.7 mm decreased back face sheet deflection by 36.9% and 64.0%, respectively [41]. Zhang et al investigated the blast response of sandwich panels with 304 stainless steel front and back face sheets and triangular corrugated cores. They stated that sandwich panels showed lower back face sheet deflection than equivalent solid plate and an increase in front and back face sheet thicknesses and core thickness increased the blast resistance of sandwich panel [42]. Fan et al investigated the blast response of sandwich panels with Al-5052 front and back face sheets and hexagonal honeycomb core. They stated that increasing face sheets and core thicknesses increased the blast response of the sandwich panel and decreased the back face sheet displacement [43]. Santosa et al's study revealed that an increase in back plate thickness decreased central node displacement, therefore increased blast resistance [12]. Liang et al investigated the blast response of cylindrical shells with Voronoi core and stated that displacement of the outer face sheet decreased with increasing outer and inner sheet thicknesses and core thickness. On the other hand, energy dissipation increased with increasing core thickness or decreasing outer and inner sheet thicknesses [44]. Jamil et al investigated the blast response of sandwich panels with 1.2 mm 2024-T3 Al face sheets and polyether grade thermoplastic polyurethane core both experimentally and numerically. They stated that the core had very high blast resistance and an increase in the thickness of the core increased the blast resistance of the structure. Compared to the 5 mm only core geometry (without face sheets), sandwich panels with 1.2 mm thick face sheets and 5 mm, 10 mm and 20 mm cores showed 14.0, 23.8 and 71.2% higher blast resistance [45]. Abada and Ibrahim investigated the blast response of sandwich panels with trapezoidal and triangular ribbon type corrugated cores and stated that increasing front and back face sheet thicknesses decreased back face sheet deflection, on the other hand, back face sheet thickness did not have a considerable effect on front face sheet deflection. Numerical results showed that decreasing front face sheet thickness increased energy absorption capability but also increased the tearing damage probability and increasing core thickness and corrugation angle by more than 45 • decreased blast resistance [46]. Some research focused on the effectiveness of front and back face sheets and core thicknesses on blast performance. For instance, Balkan and Mecitoglu stated that increasing the thickness of the core is more effective in the blast resistance of sandwich panels than increasing face sheet thicknesses [47]. Zhang et al investigated the blast response of sandwich panels with a trapezoidal corrugated core. They stated that the deflection of the sandwich panel due to blast load depended more on front face sheet thickness than on back face sheet thickness and blast resistance increased with an increase in core thickness [48]. Lan et al investigated the blast resistance of cylindrical sandwich panels with three different cores: aluminum foam core, hexagonal honeycomb core, and auxetic honeycomb core. They stated that increasing back face sheet thickness was more effective than increasing front face sheet thickness in panels with auxetic honeycomb cores in terms of blast resistance. This result came out to be the opposite for the other two core configurations [49].
Thickness ratio (ratio of front face sheet thickness to back face sheet thickness) is also important in blast resistance of sandwich panels. Wang et al investigated the blast response of sandwich panels with asymmetric face sheets (face sheets with different thicknesses). They used Al 2024 material for face sheets and Al 3104 material for honeycomb core and stated that when thickness ratio decreased, energy absorption of sandwich panel increased [50]. Thickness ratio is the dominating factor to determine the blast resistance of sandwich panels that needs to be optimized considering the weight of the sandwich panels.

The effect of core density
Density of foam cores in sandwich panels has considerable effect on blast response of the overall panel. In literature, different core densities were also investigated in terms of blast performance. Based on the available literature, some of the studies focusing on core density can be summarized as follows. Hassan et al investigated blast response of sandwich panels with Al 2024-T0 alloy face sheets and crosslinked PVC cores. Their results revealed that an increase in the density of foam core decreased blast resistance of panels [51]. Fatt and Surabhi investigated blast response of sandwich shells with E-Glass Vinyl Ester face sheets and Divinycell H30, H100, H200, Klegecell R300 and Divinycell HCP100 foam cores. They stated that Divinycell HCP100 foam core showed the highest blast resistance due to density increase but the higher the density, the higher the weight of sandwich shell [38]. Langdon et al investigated blast response of sandwich panels with glass fiber reinforced vinyl ester face sheets and PVC foam cores. They stated that equivalent mass composite only panels showed better blast performance due to larger deflection and stress on back face sheet of sandwich panels which have lower transverse stiffness in each individual component. They also stated that denser cores showed better blast resistance [52,53]. Liu et al investigated blast response of sandwich panels with mild steel front and back face sheets and aluminum foam core and stated that sandwich panels with aluminum foam core showed 61.54%-64.69% less peak load than mild steel plates without foam core. Also, an increase in peak load was observed with a decrease in foam core density [54]. Jing et al investigated blast response of cylindrical sandwich shells with closed-cell aluminum foam cores. Their numerical study revealed that an increase in core relative density decreased energy absorption capability of shells monotonically [55]. Santosa et al's study results revealed that increase in density of foam decreased central node displacement, therefore increased blast resistance [12]. Brekken et al investigated the blast resistance of sandwich panels with EN AW 1050A-H14 aluminum face sheets and extruded polystyrene (XPS) cores of different densities. They stated that sandwich panels with XPS core showed higher blast performance than panels with skins only and XPS core with lower density gave a higher displacement of the back skin [56]. Chen et al investigated dynamic response of aluminum foam core under localized air blast and suggested that lighter front sheet and allocating mass from back sheet to foam core improves anti-blast abilities for mass allocation strategy [57]. Sun et al introduced a novel hierarchical hexagonal core structure which was constituted by placing smaller regular hexagonal structures to the vertex of the main hexagonal structure. The proposed structure improved the maximum deflection at the back sheet and specific energy absorption (SEA) value under impulses greater than 200 Ns [58].
The core density is the driving factor for increasing the blast performance of sandwich structures; thus, parametric optimization of core structure and other geometrical features of sandwich structures creates additional benefits in terms of dynamic responses. In addition, theoretical models provide additional benefits in computational time and accuracy. Rong et al investigated numerically the failure of sandwich structures formed from aluminum alloy corrugated cored and carbon fibre reinforced polymer (CFRP) face sheet. For the failure of fiber tensile, fiber compression and matrix tensile, Hashin criteria was adopted, and Yeh criteria was utilized in order to determine the delamination failure. In addition to criteria that were implemented the numerical analysis, SAM (short for simplified analytical method) was performed to rapid estimation of the ultimate strength of the sandwich structures [59]. Icardi and Sola proposed a new optimization technique deriving curvilinear fiber paths over the faces of sandwiches by solving the Euler-Lagrange equations. The optimization technique and computation response were utilized in analytical form by the implementation of zig-zag model with hierarchic representation of displacements across the thickness [60]. Wang et al [61] used parametric optimization methods based on multi-objective particle swarm optimization algorithm, Latin hypercube sampling method, and Gaussian process metamodel in order to reduce the dynamic response under air blast loading and mass of the structure. Qin et al [62] and Wang et al [63] developed an analytical model to predict dynamic response of symmetric and asymmetric sandwich structures with a metal foam. Fleck and Deshpande [64] constituted an analytical model for fully clamped metallic sandwich beams. Zhang et al [65] showed that analytical models are in good agreement with numerical results.

The effect of core grading
In some sandwich panels, core section was arranged with different grades and in all of these studies, it was concluded that core grading affected the blast resistance. However, graded core is not always beneficial for the energy absorption or deformation, the grade section number, grade sections thickness and sequence are the important parameters besides the grade section material properties. Zhou et al [66] experimentally investigated sandwich structures formed from metallic face-sheets and PVC foam ungraded/graded cores under blast loading. Results suggested that the placement of the high-density material at the second core layer and the low-density material at the third core layer for three layered core provides the reduced momentum transmission to the rear face and increasing in the crushing deformation of graded core. Thus, the blast resistance of the sandwich structure was enhanced. However, the blast performance comparison of ungraded and graded sandwich structures revealed that the graded sandwich structures do not experience better performance in comparison to ungraded ones.
Liu et al studied the blast resistance of metallic sandwich-walled hollow cylinders [67] and metallic sandwich plates [68] with graded aluminum foam cores and stated that graded cylinders or plates showed higher air blast resistance than ungraded ones. Raissi [69] showed that the geometrical features of the cylindrical sandwich structure; thickness, length, diameter and angle of the sandwich structure have dominating influence on the stress distribution in the sandwich cylindrical layers during the study that utilized layer wise theory along with higher-order shear deformation to determine the stress distribution in the three-layer simply supported sector of the cylindrical sandwich structure with piezoelectric face sheets and functionally graded carbon nanotube core subjected to blast load. Wang et al investigated the blast response of sandwich panels with E-Glass Vinyl Ester face sheets and stepwise graded styrene foam cores of two different layer arrangements: low/middle/high density foams and middle/low/high density foams. Their results revealed that large compression was observed in low density portion of low/middle/high density foams which reduced the deflection and deformation on the back face sheet. Therefore, low/middle/high density foams configuration showed higher blast resistance than middle/low/high density foams configuration [70]. Zhang et al investigated the blast response of sandwich panels with Steel 1018 front and back face sheets and Steel 1008 corrugated cores of uniform and non-uniform thicknesses and in the shape of half-sine curve. Four corrugated layers were arranged with different configurations: BBBB, AACC and ABBC where A referred to a 0.762 mm thick layer, B referred to a 0.508 mm thick layer and C referred to a 0.254 mm thick layer. Results revealed that the ABBC arrangement showed the smallest maximum back face sheet deflection [71]. Li et al investigated the blast response of sandwich spherical shells with graded aluminum foam core and stated that grading affected the blast resistance of sandwich spherical shell and core layer arrangements with relative densities of 15%-20%-10% and 20%-15%-10% (from inside to outside) showed the highest blast resistance [72]. Jin et al investigated the blast resistance of sandwich structures with graded regular and cross-arranged auxetic re-entrant cell honeycomb cores (figure 3). They stated that, compared to ungraded and regular-arranged cores, cross-arranged structures showed higher resistance against blast loads and the highest blast resistance was observed in structures where cross-arranged graded honeycomb cores with a higher density of the upper layer were used [73]. Li et al investigated the blast response of metallic sandwich panels with stepwise graded aluminum honeycomb cores. They stated that graded panels, especially panels with relative density descending core arrangement, showed better blast resistance than ungraded panels for a given loading condition [74]. Liang et al investigated the blast response of cylindrical shells with Voronoi core and stated that displacement of the outer face sheet decreased with decreasing core gradient. On the other hand, energy dissipation increased with increasing core gradient [44]. Li et al investigated the blast response of sandwich panels with triple layered graded honeycomb cores and stated that graded panels with the largest relative density core showed higher blast resistance than panels with uniform core [75]. Rolfe et al stated that using a stepwise graded density foam core in a composite sandwich panel where density increased away from the blast source, increased the blast resistance of the panel [76]. Liang et al investigated the blast response of two-layer graded aluminum foam materials and stated that when the foam gradient increased, the energy dissipation and transmitted impulse also increased [77]. Liang et al investigated the internal air blast response of cylindrical sandwich panels with metal face sheets and a graded metal foam core. They stated that this configuration showed good blast resistance which depended on the core gradient, face sheet thickness and explosive charge [78]. Chen et al stated that sandwich panels with graded cores had higher blast resistance than panels with ungraded cores [79]. Kelly et al investigated the blast resistance of sandwich panels with homogeneous and graded foam cores with different materials. They stated that grading the core mitigated the crack propagation through thickness [80]. Liang et al the investigated internal air blast response of cylindrical sandwich rings with metal face sheets and graded metal foam core. They stated that the maximum radial deflection of the graded ring was smaller and the energy absorption of the graded ring was higher than those of the ungraded ring [81]. In addition to experimental and numerical methods, Zhou and Jing [82] proposed a new yield criterion for sandwich structures with three-layer metal foam core and analytical solutions for maximum deflection of the sandwich structure. As a result, the corresponding theoretical method showed a good correlation with the experimental and finite element analysis (FEA) results.
In literature, sandwich panels with double layer cores instead of monolayer cores were investigated and results revealed that double layer cores showed better blast resistance than monolayer cores at high impulses (Ī > 0.0017) and than solid monolithic plates at low impulses (Ī < 0.001 25) [83]. Wang et al investigated and optimized graded foam core configured sandwich structures and resulted that the foam core with decreasing density gradient across the thickness from front to back sheet direction ensured the best anti-blast ability and the optimization of sheets and core thickness, and the density of each core decreased the mass up to 24.58% [84]. Cai et al investigated sandwich structures with multi-layered aluminum foam and ultra-high molecular weight polyethylene (UHMWPE) cores and stated that foam core gradation had limited influence on the failure mode and deflection; however, the replacement of an equivalent foam layer with UHMWPE could prevent petalling failure mode and reduce the deflection [85,86]. Improvements in additive manufacturing technologies enables the production and tailoring of the graded lattice structures, and current studies showed that the implementation and optimizing the grading cores increases the blast resistance ability of the sandwich panels.

The effect of core and face sheet types
To increase the blast performance of sandwich panels, different face sheets and cores with different geometries have been investigated in the literature. Related with face sheet geometry, mostly plate or cylindrical sheets have been used in sandwich panel applications, but different face sheet geometries have also been tried. For instance, Li et al compared blast resistance of double V-shaped face plated sandwich panels (figure 4) with monolithic plate, flat sandwich panel and single V-shaped face plated sandwich panel. They stated that double V-shaped face plated sandwich panels outperformed in terms of blast performance, and it maintained energy absorption capability of core [87].
In sandwich structures, different core topologies can be used. Yuen et al classified these core topologies as cellular material cores (honeycombs, foams etc), micro-architectural cores (lattice structures) and macro-architectural cores (larger scale cores) [88]. In literature, these different core topologies have been applied and compared in terms of their blast resistance characteristics. Some of these core topologies are shown in figure 5.
The following studies focused on different core topologies in blast loading applications, and they are chronologically ordered in this review. Xue and Hutchinson investigated the blast resistance of metal sandwich plates with pyramidal truss, square honeycomb and folded plate core geometries. Their results revealed that these sandwich panels showed higher blast resistance than a solid plate of the same weight [93]. Liang et al investigated the blast response of sandwich panels with square honeycomb, I-core, and corrugated cores and stated that corrugated cores showed the best blast performance [78]. Rubino et al stated that sandwich panels with a Y-frame core or triangular/V-shape corrugated core showed higher resistance to dynamic loads than monolithic plates of equal mass [94]. McShane et al compared the blast response of sandwich panels with Al 6082-T6 front and back face sheets and AISI 304 stainless steel honeycomb and corrugated cores. Their experimental and numerical results revealed that honeycomb core showed higher blast resistance than corrugated core [95]. Alberdi et al investigated the blast response of sandwich panels with different types of the core design. They used diamond folded, Y-frame folded, triangular folded, hexagonal honeycomb, square honeycomb, triangular honeycomb, diamond orthotropic, Y-frame orthotropic, and triangular orthotropic core topologies and stated that folded cores showed lower back face sheet deflections than honeycomb cores due to the fact that honeycomb cores are stiffer and showed lower deformation in core and higher deformation at back face sheet. For 0.5 kg explosive mass, the diamond folded core showed higher blast performance and for 4 kg explosive mass, hexagonal honeycomb and square honeycomb cores showed better blast resistance. They also concluded that orthogonal folded cores showed the best blast performance among all core topologies due to the thickness of the core and middle plate [96]. Huang et al investigated the blast response of aluminum sandwich panels with a trapezoidal corrugated core. They stated that these panels showed smaller inner face deflections than solid plates with the same mass per area for the air-backed condition [97]. Zhang et al investigated the blast resistance of sandwich panels with I-core and found that they showed better performance than equivalent solid plates. They stated that charge mass, face sheet configuration and core configuration affected blast resistance and thick front face and thin back face configuration showed better damage response [91]. Rong et al compared the energy absorption capability of sandwich panels with different types of corrugated cores: sinusoidal, arc-shaped, rectangular, triangular and trapezoidal. Their results revealed that the trapezoidal corrugated sandwich panel showed the best performance [59]. Li et al used sandwich panels with square dome shaped steel cores for blast protection and concluded that this type of sandwich panel configuration outperformed in terms of blast resistance. It was also stated that a higher number of domes, stiffer domes and higher domes heights increased the blast resistance of the panel [98]. Ahmed and Galal investigated the blast resistance of sandwich panels with honeycomb, folded and woven core geometries. Their results revealed that woven shape cores showed 14.8% more energy dissipation than the folded core and 48% more energy dissipation than the honeycomb shape [99]. Feng et al compared the blast resistance of sandwich panels with hourglass lattice cores with a monolithic solid plate and sandwich panels with pyramidal lattice cores. Their results revealed that sandwich panels with hourglass lattice core showed 60% less back face sheet deflection than the monolithic solid plate and 22%-38% less front face sheet deflection than sandwich panels with pyramidal lattice core [92]. Kumar et al compared the air blast response of square and octagonal honeycomb sandwich panels and stated that sandwich panels with octagonal core showed 16.81%, 16.51% and 22.83% less front face and 23.9935%, 5.569% and 0.3108% less back face deflections for 3 kg, 2 kg and 1 kg explosive charges, respectively [100]. Abada and Ibrahim investigated the blast response of sandwich panels with trapezoidal and triangular corrugated cores and stated that trapezoidal corrugated core showed fewer front and back face sheet deflections than the triangular corrugated core. When they used trapezoidal and triangular ribbon type corrugated cores, their results revealed that front and back face deflections decreased by 45.3% and 76.5%, respectively, for trapezoidal corrugated ribbon core sandwich panels and 69.3% and 112.1%, respectively, for triangular corrugated ribbon core sandwich panels [46]. Lv et al investigated the blast resistance of sandwich panels with Voronoi core and stated that it had 1.5 times higher blast resistance than sandwich panels with re-entrant core [101]. Al-Rifaie et al investigated the blast response of sandwich panels with four different types of Al 6063-T4 corrugated cores: trapezoidal, triangular, sinusoidal and rectangular. They stated that the trapezoidal core showed the best performance in terms of blast loading [102]. Furthermore, a hybrid lattice core configuration is an option to improve the energy dissipation and deflection of the plates. Pydah and Batra [103] examined the different combinations of honeycomb and Miura-ori lattice core configurations. As a result, it was shown that the Miura-ori core replaced at the top of the honeycomb structure provide more energy absorption via plastic deformation; however, the opposite core replacement lowered the face sheet deflections. Imbalzone et al compared numerically the anti-blast behavior of sandwich structures with regular honeycomb and auxetic re-entrant cores and suggested an empirical model for estimating the crushing stress. Results show that the sandwich structure with a re-entrant core experienced lower back sheet stress due to the accumulated and densified material in the center of the sheets [104].
One of the core types used in sandwich panels to increase blast resistance is the auxetic core. When a part is subjected to a tensile loading, it extends in the longitudinal direction and contracts in the lateral direction. The ratio of contraction strain to extension strain is called Poisson's ratio which is close to 1/3 for most materials but in rubbery materials, it approaches 1/2. Apart from these materials, some materials show negative Poisson's ratio characteristics [105]. Negative Poisson's ratio, or auxetic, materials expand laterally when stretched and contract laterally when compressed [106].
In a blast loading, auxetic structures move toward the impacted area due to their unique negative Poisson's ratio characteristics causing more densification and larger energy absorption at the impacted area [107]. Due to these unique characteristics, different types of auxetic structures have been used as core structures in sandwich panels for blast loading applications. For instance, reentrant auxetic structures have been used for blast loading applications in literature [108,109]. Qi et al investigated the ballistic response of honeycomb sandwich panels with aluminum face sheets and aluminum regular, rectangular-shaped, and reentrant hexagons cores. They stated that sandwich panels with reentrant hexagons cores showed the highest blast resistance due to negative Poisson's ratio characteristics [110]. Imbalzano et al investigated the blast performance of sandwich panels with reentrant auxetic core and stated that re-entrant auxetic core increased the plastic energy dissipation by 50% and decreased back face sheet displacement by 30% when compared with equivalent monolithic steel plates [5]. Qi et al evaluated the blast performance of sandwich panels with honeycomb core and reentrant hexagonal cells both numerically and experimentally. They stated that these structures showed higher blast resistance than conventional honeycomb panels of the same size, areal density and material [111]. Yang et al stated that sandwich panels with auxetic core showed better blast performance than traditional panels and this performance can be increased by increasing the number of layers and Poisson's ratio of core [112]. Wang et al stated that sandwich panels with three-dimensional double V auxetic core showed higher blast resistance and less back face deflection than solid plates [61]. Imbalzano et al investigated the blast resistance of auxetic composite sandwich panels and equivalent honeycomb panels. They stated that in both panels, core and front face sheets completely absorbed the impact energy, but auxetic composite sandwich panels resulted in less stress on back face sheets. Energy dissipation increased and stress on the back face sheet reduced when the number of layers increased in auxetic composite sandwich panels [104]. Hajmohammad et al the investigated blast response of sandwich panels with nanocomposite face sheets reinforced by carbon nanotubes and auxetic honeycomb core. Their results revealed that reinforcing face sheets with 0.1% carbon nanotubes decreased the maximum dynamic deflection by 59% [113]. Lan et al investigated the blast resistance of cylindrical sandwich panels with three different cores: aluminum foam core, hexagonal honeycomb core, and auxetic honeycomb core. They stated that panels with auxetic honeycomb cores showed higher blast resistance than that with aluminum foam cores and hexagonal honeycomb cores [49]. Li et al [114] also studied the effect of cylindrical sandwich structures with different lattice topologies on blast performance, including square, hexagonal, semi-re-entrant, re-entrant, sinusoidal and Kagome honeycombs. Two different lattice orientations of axial arranged and circularly arranged were defined for composing cylindrical sandwich structures. In the axially arranged configuration, the edge-wise direction of the lattice topologies was the mating side for the front and back sheets; however, the out-of-plane side was the bonded part of the lattice structure within the circularly arranged one. The change in lattice orientation thoroughly alters the deformation behavior. Radial bucking deformation pattern was the dominating failure mode of the cylindrical sandwich structures with circularly arranged lattice cores but axially arranged lattice cores have great influence on the deformation mechanism. The SEA (SEA-absorbed energy per mass) of the axially arranged square, semi-re-entrant, hexagonal, sinusoidal, re-entrant and Kagome was listed from maximum to minimum in order. The changes in lattice topology orientation did not affect the SEA values inconsiderably, except for Kagome. The value declined nearly half with the axial arrangement. Xiao et al investigated the high velocity impact response of sandwich beams with auxetic reentrant hexagonal aluminum honeycomb core experimentally and numerically. They stated that during impact, local indentation with negative Poisson's ratio deformation and then global deformation were observed and when re-entrant wall thickness increased, negative Poisson's ratio deformation characteristics decreased [115]. Novak et al investigated the blast resistance of sandwich composite panels with a 3D chiral auxetic core. They tested the specimen quasi-statically (with a 0.002 s −1 strain rate) and dynamically (with a 5.28 s −1 strain rate). Experimental results revealed that sandwich composite panels with chiral auxetic core resulted in higher SEA than a core with a positive Poisson's ratio materials of the same porosity and mass [107]. Luo et al investigated the blast resistance of sandwich panels with composite face sheets and reentrant and honeycomb cores. Their results revealed that panels with honeycomb cores showed less stress at back face sheet. On the other hand, panels with reentrant cores showed the best anti-explosion performance at the front face sheet. Panel deformation from blast loading was due to crushable cells with auxetic behavior for panels with reentrant cores and to whole panel bending for panels with honeycomb cores [116]. Wang et al proposed a sandwich structure with an aluminum tubular circular tube cores riveted laterally to back and front sheets with varying space between tubes and the number of the tubes, and it was observed that the plastic deformation of the tubes mitigates the load considerably [117]. Guan et al investigated the effect of through thickness stitching of three-dimensional woven S-glass/epoxy sheets and results showed that stitching has no considerable effect on anti-blast properties [118]. Different geometric type of core structures and sheets response in different levels under blast loadings and enables the improvement of the blast resistance.

The effect of core filling and stiffening
Filling a sandwich panel with different materials affects blast performance significantly. Nurick et al investigated the blast response of plates with an air core and sandwich panels with mild steel front and back face sheets and Al 5052 honeycomb core and stated that above 20 Ns impulses, honeycomb core sandwich panels showed higher blast resistance than plates with air core since honeycomb core absorbed some amount of blast load. However, below 20 Ns impulses, the situation was the opposite since, at this time, the honeycomb core transferred the blast load to the back face sheet [119,120]. Zhang et al investigated the blast response of sandwich panels with stainless steel front and back face sheets and trapezoidal plate core. They used unfilled and metallic foam-filled cores and stated that the foam-filled configuration showed better air blast resistance than the unfilled configuration [121]. Schimizze et al stated that filling a sandwich panel made from a vinyl-nitrile foam shell with glass beads, water or glycerin reduced the peak pressure by 33%-48% [122]. Borbón and Ambrosini stated that sandwich panels with aluminum front and back face sheets and a core of epoxy resin matrix with 5 wt % carbon nanotube showed better blast performance than neat epoxy specimens [123]. Yazici et al investigated the blast response of foam filled and unfilled sandwich panels with low carbon steel face sheets and galvanized low carbon steel in the shape of sinusoidal corrugated cores. Their experimental results revealed that foam filling reduced front and back face sheet deflection by more than 50% [124]. Gozzani et al investigated the blast response of sandwich panels with S235JR steel face sheets and different layer configurations. They used expanded glass particles as filler material and stated that increasing the number of layers in sandwich panels increased the blast resistance [125]. Fahr et al investigated the blast response of corrugated steel sandwich panels with a silicone based syntactic foam at the core section. They tested the panels at room and high temperatures and stated that foam-filled panels showed higher blast resistance than unfilled panels at room temperature. However, increasing the temperature increased back face sheet deflections [126]. In some studies, the filling of foam core with different fluids has been investigated in terms of blast performance. In these studies, shear thickening fluids which consist of nanometric particles added in fluids were impregnated to foam cores and it was stated that these core-filled sandwich panels showed better energy absorption capability but reduced with an increase in the stand of distance [3]. Ahmed and Galal compared the blast resistance of sandwich panels with fiber reinforced polymer face sheets and honeycomb cores with three different filling materials: sand, dytherm foam and polyurethane foam. Their results revealed that filling materials provided a damping environment and with the addition of these materials, the deflection of panels and energy absorption of panels were reduced up to 28.8% and 59.7%, respectively. Sandwich panels with dytherm foam showed the best blast resistance [127]. In addition, Shirbate and Goel stated that the increase in the core thickness not only provides a reduction in the deflection of the sheets but it also generates extra damping to the sandwich composite during the research on the effect of Saffil foam core thickness effect [22]. Karagiozova et al examined the cylindrical hollow tubes with sandwich walls comprising lower and higher density foam cores and a single walled cylindrical tube. The equivalent structures showed that low density foam sandwich tubes outperformed, and higher core structure experienced the poorest results [128]. Karen et al investigated the optimization of foam placement in the corrugated steel plate slots under different boundary conditions and improved the shock absorption by up to 21% with a 52% less volume [129].
Cheng et al investigated the filling effect on the blast response of sandwich panels. They used stainless steel front and back face sheets and stainless steel corrugated empty core, aluminum foam core and stainless steel corrugated core with aluminum foam filler (figure 6). They stated that aluminum empty core showed serious tearing failure due to blast loading, on the other hand, foam core and foam filled corrugated core showed no failure. Among these three configurations, the foam filled corrugated core panel showed the best back face sheet deflection under low intensity blast loading [130]. Rahmani et al stated that using granular core with sawdust and pumice granules in sandwich panels with Al 3105 front and back face sheets could reduce shock waves due to a blast load up to 88% [131].
By using some optimization approaches, the filling of sandwich panel cores can be optimized. For instance, Karen et al optimized cell geometry in foam filled sandwich panels to get better blast performance. They implemented three different boundary conditions (simply supported case, clamped-clamped case and rigid base case) and stated that the comparison of the optimized foam filled sandwich panel with the original one provided a minimum 6% higher shock absorption with 52% less volume of foam [129].
The core filling strategy also affects the blast resistance of sandwich panels. For instance, in one of the studies, Zhang et al investigated blast resistance of sandwich structures with corrugated cores of polymeric foam with three different filling strategies: back side filling, front side filling and full filling strategies. Compared to unfilled panels, the back side filling strategy showed no advantage, but the front side filling and full filling strategies showed higher blast resistance [132].
Apart from filling a core with different materials to mitigate blast effects, some researchers investigated the effect of stiffening of core on blast resistance. Shirbhate and Goel revealed that the utilization of stiffener configurations enhances the performance of composite sandwich structures as compared to conventional ones. Different configurations as seen in figure 7 were deployed in the study and it was concluded that the configurations of P2 and P5 provided considerable effect in the deflection of the back plates for 150 mm thick foam core. P6 showed mid-level effect but P4 and P7 experienced inconsiderable influence [22]. Similar  study including different type of stiffeners was conducted by Goel et al and stated that the use of stiffeners improved displacement of back sheet under blast load [133]. Wijaya and Kim compared blast response of stiffened and unstiffened trapezoidal corrugated panels and stated that unstiffened panels showed localized buckling and larger permanent deformation than stiffened panels which suppressed the structural response [134]. Balkan et al investigated the effect of adding carbon/epoxy face sheets and polypropylene honeycomb core stiffeners on blast response of four layers carbon/epoxy plates. Their experimental results showed good agreement with numerical and theoretical analysis [135]. Additionally, Pydah and Batra [103] were presented that the use of material failure criterion and removing failed elements do not influence considerably the energy absorption of a sandwich plate.

The effect of shape and mass of explosive charge and standoff distance
In a blast analysis, standoff distance (the distance between blast source and target), quantity or weight of explosive charge and transfer medium affect pressure generated and deformation made on target. Different studies have been performed to investigate the effect of these parameters on blast performance. Xiang et al investigated blast performance of sandwich panels with three different types of thin-walled tubes as core structure: closely arranged identical circular tubes, spaced circular tubes, and spaced square tubes. They stated that explosive charge, standoff distance, tube diameter, tube thickness and number of tubes affected the blast resistance [136]. Wang et al investigated the blast response of sandwich panels with aluminum hexagonal honeycomb core. They stated that face sheet thickness and explosive (RDX) charge had considerable effect on deformation and damage [137].
In blast load analysis, standoff distance is a very important parameter. Zhang et al investigated the blast response of sandwich panels with trapezoidal corrugated core. They stated that a decrease in standoff distance increased the damage on panel [48]. In another study, it was revealed that the maximum lateral residual deformation was reduced by 75% when standoff distance increased from 5 m to 10 m [138].
Wang et al investigated blast response of sandwich panels with Al 2024 front and back face sheets and foam core and stated that decrease in mass of explosive charge decreased back face sheet deflection [37]. Liang et al investigated the blast response of cylindrical shells with Voronoi core and stated that displacement of outer face sheet decreased with decreasing mass of explosive charge. On the other hand, energy dissipation increased with increasing mass of explosive charge [44]. Li et al investigated blast resistance of sandwich panels with Al-2024 front and face sheets and aluminum foam core and stated that energy absorption of sandwich panel increased with increasing mass of explosive charge or decreasing standoff distance [139].
Apart from standoff distance and mass of explosive charge, cross section of explosive charge also affects the blast pressure generated. Choudha et al investigated the rectangular and V shape explosive charges in terms of blast pressure and target damage and stated that V shape charge made more severe damage to target than rectangular charge [140].

The effect of radius of curvature of sandwich panel
In some blast loading application, curved sandwich panels have been used. Qi et al investigated blast response of curved sandwich panels with an aluminum alloy outer face, a RHA steel inner face and a closed-cell aluminum foam core. They stated that this configuration of sandwich panel showed good energy absorption and maximum deflection characteristics against air blast loading [141].
For these types of panels, blast resistance is affected by radius of curvature of panels. Jing et al investigated blast response of cylindrical sandwich panels with aluminum face-sheets and an aluminum foam core. They stated that blast resistance of these panels depended on arrangement of foam core layers of different densities, relative density of aluminum foam core, face-sheet thickness, specimen curvature and mass of charge, and blast resistance increased with an increase in radius of curvature of panels [142]. In another study, Jing et al investigated cylindrical sandwich structures air blast response numerically. In the finite element model, finite shock conditions and nonlinear air compressibility are adopted according to Kambouchev-Noels-Radovitzky (KNR) theory, and weight optimization was conducted to redefine the face-sheet thickness, core thickness and core relative density [143]. A similar conclusion was stated by Li et al where they numerically investigated the blast performance of spherical sandwich panels and revealed that spherical sandwich panels showed better blast performance than cylindrical-shape panels [144]. Lan et al investigated the blast resistance of cylindrical sandwich panels with three different cores: aluminum foam core, hexagonal honeycomb core, and auxetic honeycomb core. Their numerical results revealed that blast performance of panels with all types of cores increased with an increase in curvature [49]. Lan et al investigated the blast response of a curved structure with three-dimensional double arrow auxetic core. They performed two case studies to optimize radius of curvature of the curved structure, height ratio (a ratio of three radiuses of curvature of double arrow auxetic), number of double arrows auxetic units in longitudinal and circumferential directions and maximum deflection. In case study one, they focused on minimizing deflection and mass, on the other hand, in case study two, their focus is on minimizing the deflection and maximizing the SEA. Their results showed that curvature played a very important role in blast resistance and increasing height ratio increased the blast resistance of structure when performing case study one (no significant effect on case study two) [145]. Moreover, it was stated in the literature that panel curvature is the most influential parameter on deformation mode such that when panel curvature decreases and the panel becomes flatter, then blast loading causes an indentation mode failure on the panel [146]. Flatter panels, on the other hand, show flexural deformation mode [147]. Another study conducted by Lin et al revealed that sandwich panels with curvature has higher blast resistance than flat panels [148]. However, it was also stated in the literature that curved sandwich panels with intermediate curvatures showed delamination and fiber failure after a time interval [149]. Hause and Librescu proposed a theoretical approach to predict the dynamic behavior of doubly curved sandwich structures, and the solution methodology is based on the extended Galerkin method in combined with the Laplace transform technique [150]. Studies on the curved sandwich structures showed that there are limited studies in doubly curved sandwich structures which are essential components for vehicles.

Conclusion
This review focused on blast resistance of sandwich panels and different factors that have effects on blast performance. The findings in the literature can be summarized as follows: • Material of front and back face sheets and core directly affects blast performance. Therefore, it is very important to properly select the material type in specific blast loading application. • An increase in front and back face sheets and core thicknesses increases blast performance, but it increases the weight of the sandwich panel as well. • Core thickness is more effective than sheet thicknesses in sandwich panels.
• The effectiveness of front and back face sheet thicknesses on blast response depends on core geometry. • In general, an increase in core density increased the blast resistance.
• Continuous or topology optimized grading can be used in core section to mitigate blast loading effects.
• Different filler materials (glass beads, water, glycerin, carbon nanotube, expanded glass particles, shear thickening fluids, sand, dytherm foam, polyurethane foam, aluminum foam, sawdust, pumice granules etc) can be used in sandwich panel cores which increase the blast performance. • An increase in standoff distance or a decrease in mass of explosive charge decrease front and back face sheets and core deflections in a blast scenario. • Curved sandwich panels show very good blast performance and increase in radius of curvature of panel increases the blast resistance.
Based on the findings in the literature, the following research gaps were identified: • Optimization of the parameters stated in this review to get sandwich panel configurations of better blast performance needs detail investigation. • In nearly all of the scientific studies in literature, conventional manufactured core topologies have been used. Since additive manufacturing technologies enables more freedom in design, they can be used in core manufacturing. • Different types of lattice structures (beam-based lattice structures such as face centered cubic, body centered cubic etc, triply periodic minimum surfaces lattice structures such as gyroid, diamond, primitive etc) can be used as core topology in sandwich panels for blast loading applications. • In literature, density graded cores have been used but no study has focused on material graded or multimaterial core topology.