Blast Performance of Polyurea-Coated Modular Structure Composed of Fiber-Reinforced Polymer and Foam Sandwich Panels

Abstract

Lightweight modular structures have become a requirement in today’s world, especially for areas that are prone to occurrence of extreme events, such as earthquakes and blasts, and are situated in difficult terrains with challenging accessibility. Sandwiched composites can be one of the most suitable building units for construction of these structures due to their engineered mechanical and physical properties. Therefore, in this numerical study, performance assessment of a sandwich modular structure in the shape of a truncated cylinder is conducted under blast load. The sandwich modular structure is composed of flat and curved carbon fiber-reinforced polymer (CFRP) and extruded polystyrene (XPS) foam sandwich panels. A three-dimensional (3D) finite element (FE) model of the sandwich modular structure is developed considering the orthotropic behavior of CFRP facesheets and the crushing foam behavior is accounted for the XPS foam core in the FE modeling. The damage assessment in the CFRP facesheet is performed using Hashin’s damage criterion. Furthermore, the effect of polyurea with varying thicknesses on the blast-resistance of the structure is investigated. The polyurea is modeled as hyperelastic material using the Mooney-Rivlin model. The influence of polyurea positioning is studied when (a) applied externally to flat and curved walls of the structure directly exposed to the blast and (b) applied internally to flat and curved walls of the structure opposite to the exposure of the blast (rear face). It is observed that the flat walls of the structure are more vulnerable to the blast load than the curved walls of the structure. Moreover, a quadratic and linear reduction in the deflection of flat and curved walls with increasing thickness of polyurea coating is obtained, respectively. In addition, with increasing thickness of the additional polyurea coating, a logarithmic reduction in the kinetic energy of the sandwich modular structure is reported.

Keywords

Blast composite fiber-reinforced polymer modular structure polyurea sandwich panel

Introduction

Modular structures have become a necessity for rapid developments in civil infrastructures. The advantage of the reusability of their building components makes them preferable for reducing construction waste. It also has a potential to help in contributing towards reducing greenhouse gas emissions induced by the production of the building units for civil infrastructures. Steel (ASCE, 2008; Summers, 2008) and aluminum-based (Sharma et al., 2023) building units are commonly used for structures in petrochemical and nuclear industries as much in defense field. These structures are generally subjected to extreme loads, such as blast-induced loading caused due to accidental explosions and terrorist activities. Therefore, understanding the behavior of such structures under blast-induced loading and further enhancing its performance using various blast mitigation strategies are essential. The dynamic behavior of a steel shell or cylindrical structure under blast load has been studied by some researchers (Su and Zhai, 2018; Wei et al., 2022; Yin et al., 2023). The effective use of construction materials for achieving enhanced blast protection (Matsagar, 2013), using an additional protection wall around the structure (Su and Zhai, 2018), and the importance of the shape of the structure (Wei et al., 2022; Yin et al., 2023) have been reported as efficient blast mitigation strategies for these structures. The effectiveness of steel and aluminum sandwich panels for cubical industrial room was studied to sustain the applied blast load in different scenarios (Sharma et al., 2023). It is apparent from the literature that the behavior of metallic building units under blast load helps in dissipating/absorbing the energy induced by shock significantly; hence preferred for such structures. However, due to advanced requirements of the important structures, i.e., safety, lightweight, sustainability in extreme loadings and weather, transportation to complex/ difficult geographical conditions, and insulation, fiber-reinforced polymer (FRP) with foam sandwich composite panels are gaining more attention as recommended building units. Therefore, it is essential to assess the behavior of FRP and foam sandwich composite and further enhance their performance in such extreme loading scenarios. Some researchers (Arora et al., 2011; Gabriel et al., 2021) have reported the blast performance of glass fiber-reinforced polymer (GFRP) and foam sandwich panels. Arora et al. (2011, 2012) reported the effective blast mitigation by GFRP and styrene acrylonitrile (SAN) foam sandwich panels with various boundary conditions experimentally and numerically. Effectiveness of aluminum sheets and extruded polystyrene (XPS) core with different densities has been observed in terms of a significant energy absorption under blast load (Brekken et al., 2020). However, various blast mitigation strategies to further improve the blast-resistance performance of the sandwich structures are required to be investigated. Various methods are recommended by researchers, to enhance the blast-resistance of sandwich structures, for example, using high-strength materials, stiffeners (Goel et al., 2011; Morin et al., 2017; Sharma et al., 2023), and providing additional protective coating to such structures, for example, polyurea.

In this study, the effect of additional polyurea coating on the behavior and resistance of a full-scale sandwich structure subjected to blast load has been investigated. Polyurea is made from the polymerization of diamines and isocyanates. The composition of hard and soft links in the polyurea gives the advantages of high strength and resisting extensive damage simultaneously (Zhang et al., 2022). Additionally, the properties of polyurea, such as flexibility to be applied to different surfaces, water resistance, and thermal resistance, make it an excellent strengthening/ blast-retrofitting solution to be applied under extreme loads. The use of additional polyurea coating has been proven effective due to its advanced properties (Leite et al., 2022) in enhancing the performance of concrete (Rizwan et al., 2021; Saini and Matsagar, 2024), aluminum (Mohotti et al., 2015), and steel panels (Ackland et al., 2013; Chen et al., 2020; Chu et al., 2022; El Sayed et al., 2008; Li et al., 2023a, 2023b) under blast and impact loads. However, there are very few studies (Bahei-El-Din and Dvorak, 2007a, 2007b; Gauch et al., 2018; Grujicic et al., 2010; Liu et al., 2022; Saini et al., 2023; Tekalur et al., 2008), in which the effectiveness of polyurea coating on FRP structures under blast load is presented. A significant reduction in the blast response of a CFRP and H100 divinycell foam core sandwich panel has been reported due to polyurea application when applied in between facesheet and foam (Bahei-El-Din and Dvorak, 2007a, 2007b). Tekalur et al. (2008) have also shown the enhanced blast performance of GFRP composite panels due to polyurea applied in between the layers of laminate. Similarly, for Kevlar FRP composite helmets, an additional polyurea padding helped in the mitigation of blast effect on the helmets used for army personnel (Grujicic et al., 2010). Moreover, the advantages of polyurea padding over conventional ethylene-vinyl-acetate foam padding have been highlighted under varying blast pressures (Grujicic et al., 2010). Also, in the case of underwater explosions, the addition of polyurea resulted in enhanced blast-resistance of a GFRP composite-wrapped cylinder (Gauch et al., 2018).

The position of the polyurea application on a structure and its thickness also plays a significant role in the blast response mitigation of the structure. Some researchers (Liu et al., 2022; Saini et al., 2023) have investigated the influence of polyurea positionings, i.e., applied to the blast-exposed face and/or rear face, on the blast-resistance of carbon fiber-reinforced polymer (CFRP) and GFRP with divinycell foam sandwich panels, respectively. The polyurea at the rear face of the panel resulted in a higher reduction in deformation (measured at the opposite face to the blast) than when polyurea was applied to the exposed face of the sandwich panels. However, there is no study that investigates the effect of an additional polyurea coating on the performance of a truncated cylindrical shaped FRP and foam sandwich modular structure under blast load. Therefore, the objectives of this study are, (a) to investigate the behavior of a modular structure composed of CFRP and XPS foam sandwich flat (MS-F) and curved (MS-C) panels subjected to blast load, (b) to assess the effect of different positioning of polyurea, i.e., applied to external (PUE) and internal (PUI) faces of the flat and curved walls of the modular structure, on the blast-resistance of the structures, and (c) to present the influence of polyurea thicknesses on the blast response of the structures. Accordingly, the different configurations of the sandwich modular structure are considered in this study, as presented in Table 1.

Table 1.

Different configurations of sandwich modular structures without and with polyurea considered in this study.

S. N	Configuration of structure	Positions of blast and polyurea	Thickness of polyurea
1	MS-F	Blast applied on the flat wall with no polyurea	0
2	MS-C	Blast applied on the curved wall with no polyurea	0
3	MS-PUE5-F	Blast applied on the flat wall with polyurea applied externally to the same wall	5 mm
4	MS-PUI5-F	Blast applied on the flat wall with polyurea applied internally to the same wall	5 mm
5	MS-PUE5-C	Blast applied on the curved wall with polyurea applied externally to the same wall	5 mm
6	MS-PUI5-C	Blast applied on the curved wall with polyurea applied internally to the same wall	5 mm
7	MS-PUE10-F	Blast applied on the flat wall with polyurea applied externally to the same wall	10 mm
8	MS-PUI10-F	Blast applied on the flat wall with polyurea applied internally to the same wall	10 mm
9	MS-PUE10-C	Blast applied on the curved wall with polyurea applied externally to the same wall	10 mm
10	MS-PUI10-C	Blast applied on the curved wall with polyurea applied internally to the same wall	10 mm

In Table 1, the modular structure (MS) is considered composed of carbon fiber-reinforced polymer (CFRP), and extruded polystyrene (XPS) foam sandwich is represented with MS-F and MS-C, when the blast load is applied on the flat wall (F) and curved wall (C) of the structure, respectively. If additional layer of polyurea (PU) (with 5 mm thickness) is applied to the external face (E) of the structure, the abbreviations for the configurations are used as MS-PUE5-F and MS-PUE5-C, when the blast load is applied to the flat wall and curved wall of the structure, respectively. Similarly, for MS with additional layer of the polyurea (with 5 mm thickness) is applied to the internal face (I) of the structure, the abbreviations for the configurations are used as MS-PUI5-F and MS-PUI5-C under blast load applied on the flat and curved walls, respectively. The same nomenclature is followed for MS with an additional layer of polyurea with 10 mm thickness applied to external and internal faces of the flat and curved walls of the structure.

Finite element modeling

In this study, the behavior of a truncated cylindrical shaped modular structure composed of flat and curved panels of CFRP and XPS sandwich composite building units is assessed under blast load. The length and width (diameter) of the structure respectively are 4 m and 3.5 m, as illustrated in Figure 1. The dimensions are taken such that the structure can accommodate two to three personnel. The thickness of commercially available CFRP facesheets and XPS foam core are taken as 2.7 mm and 80 mm, respectively. Furthermore, the effect of polyurea on the blast-resistance of the structure is investigated numerically. The three-dimensional (3D) finite element (FE) model of the sandwich modular structure made from individual CFRP and XPS flat and curved panels under blast load is developed (see Figure 1). In the study, the unidirectional CFRP facesheets are modeled with a shell (SC8R) element, and foam core and polyurea are modeled with a solid element (C3D8R) (ABAQUS, 2014). The mesh size adopted in the study is 40 mm for the building panels based on a convergence study performed. The bond/interaction between facesheets and foam core are modeled with a tie contact. The bond between different building units to combine the structure are also modeled with the tie contact applied on the sharing surfaces of the units. Delamination is not considered as a part of this study, which can be suitably developed using traction-separation law in a cohesive zone model. The modular structure is considered supported using fixed boundary conditions at the base.

The free air blast load corresponding to explosive weight (W), 0.45 kg (approximately 1 lb) at a radial distance (R), 0.5 m or scaled distance 0.652 m/kg^1/3 on the modular structure is applied using CONWEP blast loading. The blast loading depends on the angle of incidence of shock wave, scaled distance (from the structure), and weight of explosive. The loading represents an exponential decaying pressure time history with approximately 4.55 MPa peak positive pressure and negligible negative pressure. In this study, the blast behavior of the sandwich structure without and with polyurea applied externally (directly exposed to the blast) and internally (at the rear face opposite to the direct blast) with 5 mm and 10 mm thicknesses is investigated. The study is performed for two blast cases, (a) Case 1: blast pressure applied on the flat wall of the sandwich structure, and (b) Case 2: blast pressure applied on the curved wall of the sandwich structure. Accordingly, different configurations of the modular structure without and with polyurea applied either on external or internal faces of the structure are listed in Table 1.

Material properties

The CFRP material behavior is modeled with orthotropic elastic constants, presented in Table 2. Generally, the FRP laminates, which have length to thickness ratio higher than 20 are considered as thin laminates (Bathe, 2006). These laminates have insignificant influence of out of the plane shear stresses and can be represented as orthotropic material using nine independent elastic constants (Daniel and Ishai, 2006). Hashin’s damage criterion is implemented to assess the damage induced in CFRP, which has four types of failures with corresponding damage indices: fiber and matrix failures in tension and compression. These damage indices are dependent on normal stresses,

σ_{11}

and

σ_{22}

in local longitudinal and transverse directions of the CFRP facesheet, respectively, and in-plane shear stress in the facesheet,

τ_{12}

, as follows.

Table 2.

Material properties of CFRP considered in the study.

Elastic property		Strength
$E_{11}$ (GPa)	170	$F_{xT}$ (MPa)	2200
$E_{22}$ (GPa)	15	$F_{xC}$ (MPa)	800
$G_{12} = G_{13}$ (GPa)	10	$F_{yT}$ (MPa)	75
$G_{23}$ (GPa)	8	$F_{yC}$ (MPa)	145
$ν_{12}$	0.29	$F_{s}$ (MPa)	50

(a) Fiber damage in tension ( $σ_{11} \geq 0$ )

{({d_{f}}^{T})}^{2} = {(\frac{σ_{11}}{F_{xT}})}^{2} + α {(\frac{τ_{12}}{F_{s}})}^{2},

(1)

(b) Fiber damage in compression ( $σ_{11} < 0$ )

{({d_{f}}^{C})}^{2} = {(\frac{σ_{11}}{F_{xC}})}^{2},

(2)

{({d_{m}}^{T})}^{2} = {(\frac{σ_{22}}{F_{yT}})}^{2} + {(\frac{τ_{12}}{F_{s}})}^{2},

(3)

(d) Matrix damage in compression ( $σ_{22} < 0$ )

{({d_{m}}^{C})}^{2} = {(\frac{σ_{22}}{2 F_{s}})}^{2} + [{(\frac{F_{yC}}{2 F_{s}})}^{2} - 1] (\frac{σ_{22}}{F_{yC}}) + {(\frac{τ_{12}}{F_{s}})}^{2},

(4)

where

F_{xT}

F_{yT}

F_{xC}

, and

F_{yC}

are tensile and compressive strengths along the axes 1 and 2 of the lamina, respectively; the shear strength of the lamina is presented as

F_{s}

; and

α

is the coefficient to consider the contribution of shear in tensile failure of fiber. The magnitude of the strengths of CFRP and elastic properties are shown in Table 2. The exceedance of these damage indices beyond 1 shows the corresponding damage in the laminate.

Here,

E_{11}

and

E_{22}

are elastic moduli in longitudinal and transverse directions, respectively;

G_{12}

G_{13}

, and

G_{23}

are shear moduli in different planes 12, 13, and 23; and

ν_{12}

is Poisson’s ratio. The XPS foam is modeled as crushable foam, using the parameters shown in Table 3.

Table 3.

Material properties of XPS foam considered in the study.

Density (kg/m³)	Elastic modulus (MPa)	Poisson’s ratio	Compression yield stress ratio	Hydrostatic yield stress ratio	Yield stress (MPa)
36	45.8	0.1	1.1	0.3	0.5

The polyurea coating can be modeled as viscoelastic or hyperelastic materials. There are many studies that have shown different modeling methods for polyurea (Bai et al., 2016; El Sayed et al., 2008; Leite et al., 2022; Wang et al., 2022). In this study, polyurea is modeled as hyperelastic material using the Mooney-Rivlin model, the parameters required for the model are listed in Table 4 (Ackland et al., 2013).

Table 4.

The parameters of the Mooney-Rivlin hyperelastic material model for polyurea.

Density (kg/m³)	D₁ (kPa⁻¹)	C₀₁ (kPa)	C₁₀ (kPa)
1000	4 × 10⁻⁷	6321.3	875.2

Here, D₁ represents the compressibility of a material, whereas C₀₁ and C₁₀ are polynomial constants. The considered hyperelastic properties, as per the Mooney-Rivlin model, make the polyurea close to an incompressible material. The deviatoric strain energy of the material can be represented as,

U = C_{10} (I_{1} - 3) + C_{01} (I_{2} - 3) + \frac{1}{D_{1}} {(J_{el} - 1)}^{2},

(5)

where J_el is elastic volume strain, whereas I₁ and I₂ are the first and second strain invariants. The validation of the finite element (FE) model for FRP and foam sandwich panel, material behavior, and blast load are performed in the next section.

Validation of numerical model

The validation of the detailed finite element model, material behaviors, and blast load applied is performed with respect to past studies (Ackland et al., 2013; Goel et al., 2013) to ensure the accuracy of the present 3D-FE model developed. Goel et al. (2013) have investigated the behavior of sandwich panels with fixed boundary conditions under pulse type blast load with peak pressure 0.7 MPa and duration 15 ms [refer Figure 2(a)]. The blast behavior of a steel facesheet has been modeled with an elastic-plastic material model and the dytherm foam core has been modeled using a crushable foam material model (Goel et al., 2013). It is observed that, the comparison between the results of Goel et al. (2013) and the present study shows good agreement. A small difference in the response is observed due to the difference in element type used for the facesheet, i.e., the S4R element in the literature (obsolete in the newer version of the software Abaqus^®) and SC8R in the present study.

Ackland et al. (2013) investigated the response of a fixed steel panel with polyurea under blast load induced by the explosive weight of Pentolite 0.5 kg at 51.5 mm radial distance. The steel panel has been modeled using shell elements and polyurea as per the Mooney-Rivlin hyperelastic material model. Also, the material behavior and modeling of polyurea under blast load are validated by Ackland et al. (2013), as illustrated in Figure 2(b). A small difference between the response obtained and reported in the literature (Ackland et al., 2013) and the present study is observed due to the difference in the modeling of the blast load. The air between explosion and structure has also been modeled in the literature; however, in the present 3D-FE model, the blast event is modeled as pressure loading using CONWEP model (ABAQUS, 2014). It is observed that, the current numerical model shows good agreement with that presented in the literature. Therefore, the same modeling method is adopted for the complete sandwich modular structure.

Performance of sandwich modular structure without and with polyurea under blast

A model analysis of the CFRP and XPS foam sandwich modular structure is performed, and different mode shapes of the structure are obtained in free vibration condition (illustrated in Figure 3). The sandwich structure has a fundamental time period of 0.0121 s. The first two modes (Mode 1 and Mode 2) show the major deformation and vibration of curved walls, followed by two modes (Mode 3 and Mode 4) with the deformation and vibration of flat walls of the structure. On the other hand, Mode 5 and Mode 6 represent the combined deformation and vibration of curved walls and flat walls of the structure, respectively.

An explicit dynamic analysis is performed to assess the behavior of the structure under blast load. The behavior is observed in both cases, when the blast load is applied on the flat and curved walls of the structure. The effectiveness of two positionings of polyurea, i.e., applied to the external face exposed to the blast and applied to the internal face (rear face) opposite to the exposed face of the modular structure, are compared. Generally, whenever shock waves interact with a material, results in propagation of elastic waves followed by plastic waves (if stresses increase beyond yield), which shows the nature of stresses induced in the material. Here, the elastic wave velocity through each layer is calculated based on the elastic modulus and density of the material. The highest elastic wave velocity is observed in CFRP, 10645.81 m/s, followed by XPS, 1127.93 m/s, and polyurea, 79.5 m/s, respectively. Based on wave impedance, the reflection and transmission coefficients are estimated, which further show the nature of reflection and transmission waves at the interface of the two materials (Hetherington and Smith, 2014). In the case of polyurea placed at the external face, the reflecting wave is a compression wave at both the interfaces of polyurea and external CFRP sheet, and XPS foam and internal CFRP sheet. However, at the interface of the external CFRP sheet and XPS foam, the reflecting wave shows tensile nature. In the case of polyurea at the internal surface of the structure, the reflecting wave has tensile nature at the interface of external CFRP sheet and XPS foam and at the interface of internal CFRP sheet and polyurea. On the other hand, the reflecting wave shows the nature of a compression wave at the interface of XPS foam and internal CFRP sheet. The transmitting waves have a compression wave nature in both cases, same as the incident wave. The wave transfers from a medium with a higher density to a medium with a lower density, resulting in the tensile nature of the reflection wave. When the equilibrium of stresses is established at the interfaces, the compressive nature of the reflection wave results in increasing compression stresses at the surface.

Blast load applied on the flat wall

In the first case, the blast pressure is applied at the flat wall of the sandwich modular structure (at the center of the surface area) without and with 5 mm and 10 mm thick polyurea applied to the external (MS-PUE5-F and MS-PUE10-F) and internal (MS-PUI5-F and MS-PUI10-F) faces of the structure. Accordingly, the deformation shapes and response (average response at Point A and Point B) time histories under the blast load are presented in Figures 4 and 6 at 3 ms and 6 ms time instants of the load, and Figures 5 and 7, respectively. As the peak deflection of the structure is obtained at a time instant close to 6 ms, the deformed shapes of the structures are presented at this maximum response point, i.e., 6 ms and an intermediate point, i.e., 3 ms. It is observed that for MS-F, the peak deflection of the external face (at Point A) is obtained as 176.46 mm, which is reduced to 136.10 mm at the midpoint of the internal face (at Point B). Whilst, with additional polyurea coating, the peak deflections, 112.66 mm, 87.04 mm, 128.62 mm, and 108.04 mm (at Point A) are reduced by 14.5 %, 10.92 %, 37.49 %, and 45.19 % at the internal face for MS-PUE5-F, MS-PUE10-F, MS-PUI5-F, and MS-PUI10-F structures, respectively. Figures 4 –9 show a clear reduction in the response of the structure under blast load with an additional layer of polyurea coating applied, convincingly establishing the effectiveness of applying polyurea for blast response mitigation.

Polyurea with 5 mm and 10 mm thicknesses applied to the external face of the flat wall under blast results 33.14 % and 47.35 % reduction in average peak deflection, respectively, as compared to that of the MS-F structure. On the other hand, when polyurea with 5 mm and 10 mm thicknesses is applied to the internal face of the flat wall resulting 33.12 % and 46.49 % reduction in average peak deflection, respectively, as compared to that of MS-F. Polyurea with 5 mm thickness applied to the flat wall on external and internal surfaces reduces the peak kinetic energy of the structure by 32.11 % and 2.76. %, respectively. Similarly, polyurea with 10 mm thickness applied to the external and internal faces of the flat wall leads to reduction in peak kinetic energy by 49.76 % and 5.56 %, respectively.

The reduction and increment in the plastic dissipation energy are obtained for the cases when polyurea is applied to the external and internal faces of the structure as compared to that of MS-F, respectively. In the case of polyurea applied to the external face, when the shock wave passes through the layers, and the energy is dissipated by polyurea and followed by CFRP, before it reaches to XPS foam, results in lesser deformation of the foam. In this case, polyurea provides additional protection to foam core crushing (Bahei-El-Din and Dvorak, 2007a, 2007b). When polyurea is applied to the internal face, the CFRP facesheet interacts with the shock wave first, followed by XPS foam, CFRP facesheet, and then polyurea. In this case, higher deformation in the foam layer is observed resulting in higher stresses and plastic dissipation energy. Moreover, a reduction of 22.87 % in effective von-Mises stress at the internal face is observed as compared to that of the external face of MS-F structure. The application of polyurea on the external face (exposed to the blast pressure) of the flat wall of the sandwich modular structure results in approximately 10 to 20 % increment in effective von-Mises stress depending upon thickness of polyurea due (measured at internal face) to the initial shock effect (Amini et al., 2010). However, when polyurea is applied to the internal face of the flat wall of the sandwich modular structure, it helps in reducing the effective von-Mises stress by approximately 99.8 % (measured at internal face).

The flat walls are found to be more vulnerable to blast loading as compared to the curved walls of the sandwich modular structures. Therefore, the damage assessment is carried out in the CFRP sheet of the flat wall using Hashin’s damage criterion, as described in Material properties Section. The tensile failure of the matrix is found to be the most predominant failure on the flat wall of the structure. It is observed that the damage in CFRP reduces due to an additional polyurea coating applied in both cases. In the case where polyurea is applied to the internal face of the structure, the damage in CFRP observed is higher than in the case of polyurea applied to the external face of the structure (see Figures 8 and 9) due to the direct exposure of the facesheet to the blast. Moreover, higher thickness of polyurea coating on the sandwich modular structure leads to increased damage reduction in the CFRP facesheet of the structure. The highest strain or damage occurs at the height of the explosion and near to the restrained regions (i.e., base and top).

Blast load applied on the curved wall

In the second case, the blast pressure is applied at the curved wall of the sandwich structure without polyurea (MS-C), and with polyurea thicknesses of 5 mm and 10 mm applied to the external face (MS-PUE5-C and MS-PUE10-C) and internal face (MS-PUI5-C and MS-PUI10-C). The deformation shape and average response time histories obtained are presented in Figures 10 and 12, and Figures 11 and 13, respectively. It is observed that for MS-C, the peak deflection at the midpoint of the external face (at Point A) is 121.08 mm, which is reduced to 82.44 mm (reduced by 31.92 %) at the midpoint of the internal face (at Point B). Additional polyurea coatings applied on the curved walls of the structure results in the reduction of the peak deflections, 88.33 mm, 70.99 mm, 101.76 mm, and 97.52 mm (at Point A), by 25.31 %, 17.56 %, 40.49 %, and 52.51 % at internal face for MS-PUE5-C, MS-PUE10-C, MS-PUI5-C, and MS-PUI10-C structures, respectively. A significant reduction in the response of the structure with an additional layer of polyurea is observed under the applied blast load in Figures 10 to 13.

The structure with additional polyurea layers of 5 mm and 10 mm thicknesses applied to the external surface, results in reduction of the average peak deflection by 24.17 % and 36.36 %, respectively at the curved wall as compared to that of the MS-C. On the other hand, when an additional polyurea layer is applied to the internal surface of the curved wall (opposite to the direct blast exposure), the average peak deflection reduces by 20.21 % and 29.91 %, respectively with polyurea thicknesses of 5 mm and 10 mm, as compared to that of MS-C. Moreover, the polyurea with 5 mm thickness applied at the curved walls on external and internal surfaces results in reduction of the peak kinetic energies by 46.33 % and 16.16 %, respectively, as compared to that of the MS-C. In comparison, 10 mm polyurea thickness applied to the external and internal surfaces on the curved walls results in reduction of peak kinetic energy by 61.53 % and 18.14 %, respectively.

It is observed that the curved wall exposed to the blast load results in lesser deformation than the flat wall, which was expected. Langdon et al. (2023) also reported higher blast-resistance of a curved FRP and foam sandwich panel than the flat panel under blast. Also, as the thickness of polyurea applied to the external or internal face on the flat and curved walls increases, a higher response reduction in the structure has resulted. The curved wall of the structure without polyurea deforms approximately 34.92 % lesser and shows 3.94 % lesser kinetic energy as compared to the flat wall of the structure under the blast load. Further, MS-PUE5-C and MS-PUI5-C show 26.19 % and 22.35 % lesser average peak deformation and 24.07 % and 17.18 % lesser kinetic energy as compared to that of the MS-PUE5-F and MS-PUI5-F. Similarly, MS-PUE10-C and MS-PUI10-C show 21.34 % and 14.75 % lesser average peak deformation, and 26.44 % and 16.74 % lesser kinetic energy as compared to that of the MS-PUE10-F and MS-PUI10-F. A reduction of 39.62 % is observed in the effective von-Mises stress at internal face induced in the MS-C as compared to the MS-F. The application of polyurea on the curved walls of the sandwich structure results in reduction of effective von-Mises stress at internal face induced by 13.6 % (with thickness 5 mm applied externally), 21 % (with thickness 10 mm applied externally), and approximately 99.0 % (for both thicknesses applied internally) as compared to that of the MS-C.

Response with varying thicknesses of polyurea

Assessment of the influence of the thickness of polyurea (t_p) on the response of the structure when applied to the external surface is helpful in the design of blast-resistant structure. A higher reduction in the average response of the structure is obtained for the case when polyurea is applied to the external surface of the structure. The reduction pattern of the response with polyurea thickness is obtained using a fitted curve equation with the coefficient of determination (r²). For the flat wall, the percentage reduction in the peak deflection with respect to that of the MS-F follows the quadratic behavior with increasing thickness of polyurea (−0.0841 t_p² + 4.2067 t_p + 13.035, with r² = 0.99). On the contrary, for the curved wall, the percentage reduction in the peak deflection with respect to that of the MS-C can be represented with both quadratic and linear behavior with the thickness of polyurea (−0.0299 t_p² + 2.3504 t_p + 38.417, with r² = 0.99 and 1.5697 t_p + 41.382, with r² = 0.98) (see Figure 14). Moreover, a logarithmic reduction in the kinetic energy of the sandwich structure is obtained for both the cases when blast load is applied on the flat [19.308 ln (t_p) + 5.3011, with r² = 0.98] and curved [20.576 ln (t_p) + 12.476, with r² = 0.99] walls. A possible reduction in the deflection and kinetic energy of the sandwich modular structure for a given thickness of additional polyurea coating can be predicted based on the estimated equations.

Such lightweight sandwich modular structures have potential to be used for various structures subjected to extreme loads, such as emergency shelters, temporary and permanent housings at complex geographical locations, high altitude areas, where transporting heavy construction materials is a challenge, in areas of different nuclear industries, petrochemical industries, and defense field. Therefore, design of polyurea-coated modular structure composed of the FRP and foam sandwich panels for improved blast-resistance performance has been established through this 3D-FE-based study. Optimized design parameters for the sandwiched modular structure will be required to be obtained on case-to-case basis for scenario-specific design.

Conclusions

In this study, the behavior of a truncated cylindrical shaped modular sandwich structure composed of flat and curved carbon fiber-reinforced polymer (CFRP) and extruded polystyrene (XPS) sandwich panels is investigated under blast loading. Moreover, the effect of polyurea (with varying thicknesses) on the blast-resistance of the sandwich structure is evaluated when applied to the internal and external faces of the flat and curved walls of the structure. A three-dimensional (3D) finite element (FE) model of the structure exposed to the blast loading is developed, where CFRP is modeled with Hashin’s damage criterion, XPS foam is modeled as crushing foam, and polyurea is modeled as hyperelastic material using the Mooney-Rivlin model. Based on the findings of the study, following major conclusions are drawn.

1. The flat walls of the truncated cylindrical shaped sandwich modular structure is more vulnerable to blast load than the curved walls of the structure. The curved wall shows 20 % to 40 % lesser deformation than the flat wall of the structure without and with additional polyurea coating to the walls.

2. As the polyurea thickness increases, the response of the sandwich modular structure reduces. A higher reduction in the average deflection and kinetic energy of the sandwich structure response is obtained for the case when polyurea is applied to the external face of the structure.

3. A higher reduction in the equivalent von-Mises stresses occurs if the polyurea layer is applied to the internal face of the flat and curved walls of the sandwich structure.

4. A quadratic and linear reduction in the deflection of the sandwich modular structure occurs with increasing polyurea thickness when the blast load is applied on the flat and curved walls, respectively.

5. A logarithmic reduction in kinetic energies of the sandwich modular structure occurs with increasing polyurea thickness for both the cases where the blast load is applied on the flat and curved walls.

Furthermore, as a future scope of study, (a) delamination between facesheet and core, (b) bond and connections between individual building units of the modular structure, and (c) effect of the different material properties of the polyurea coating under different blast scenarios can be investigated to further contribute towards blast mitigation strategies from the sandwich structures.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Aeronautics Research and Development Board (AR&DB), Defence Research and Development Organisation (DRDO); ARDB/01//1082030/M/I, 2030.

ORCID iDs

Kusum Saini

Vasant Annasaheb Matsagar

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