Experimental and Numerical Analysis of Nonlinear Flexural Behaviour of Lattice-Web Reinforced Foam Core Composite Sandwich Panels

,is paper conducted experimental and numerical analysis of the nonlinear flexural behaviour of lattice-web reinforced foam core composite sandwich panels. Composite sandwich panels composed of a polyurethane (PU) foam core with glass fibre-reinforced polymer (GFRP) composites as the face sheets and lattice webs were fabricated through the vacuum infusion moulding process (VIMP). ,e flexural behaviour of these composite sandwich panels were experimentally investigated under both uniformly distributed and concentrated loading scenarios. ,e results showed that reinforced lattice webs can significantly increase the flexural stiffness and load-carrying capacity of sandwich panels and effectively postpone the onset of interfacial debonding failure between the face sheets and core. ,e effects of the lattice-web height and spacing on the ductility and load-carrying capacities of the sandwich panels were also analysed. Several numerical simulations on lattice-web reinforced foam core composite sandwich panels under concentrated loadings were also conducted. ,e effectiveness of the finite element (FE) model was validated by the experimental work. Parametric studies indicated that thicker face sheets and lattice webs can remarkably increase the loadcarrying capacity. Moreover, the load-carrying capacity and midspan deflection were hardly affected by the foam density.


Introduction
Composite sandwich structures have been widely employed in aviation, military, transport, and civil applications as a result of their unique characteristics, including their high strength, high stiffness-to-weight ratio, structural designability, and excellent corrosion resistance [1][2][3].Lowdensity materials such as foam, honeycomb cells, and balsa wood are usually adopted as the core of composite sandwich structures, thereby contributing to a high stiffness along the face sheets to resist loadings.e face sheets are generally made of various fibre (e.g., glass, aramid, or carbon) reinforced polymer composites.From a structural perspective, the face sheets provide a major contribution to the bending stiffness, while the core provides a major component of the shear stiffness of a sandwich structure [1].
A large number of experimental and analytical studies on sandwich structures with different types of cores have been carried out over the past three decades [4][5][6][7][8][9].Sharaf et al. [10] studied the uniaxial bending behaviour of ten foamfilled sandwich panels experimentally.
e test results demonstrated that the bending strength and stiffness of sandwich panels increased significantly with an increase in the foam density; meanwhile, a considerable horizontal slip occurred between the top face sheet and the core due to the low toughness of the foam core.Prakash et al. [11] investigated the maximum impact load, energy absorption, and failure modes of honeycomb sandwich panels with various cells through low-velocity impact tests.eir test results showed that the core buckled at relatively low energy levels but crushed at higher levels.Steeves and Fleck [12,13] conducted experimental and analytical investigations on the collapse mechanisms of simply supported sandwich beams composed of glass fibre-reinforced polymer (GFRP) face sheets and a polyvinyl chloride (PVC) foam core that were loaded under three-point bending.e experimental results demonstrated that the failure mode was dependent on the beam geometry and the density of the foam core.Moreover, they found that the ultimate bending strength and initial stiffness of the sandwich panels were relatively small because no lattice web or fibre insertions were utilized to improve the core stiffness.Keller et al. [14] manufactured a low-storey building in Lausanne, Switzerland, using pultruded GFRP profiles as structural members, e.g., beam and columns, and GFRP/foam sandwich panels as the roof structure.Manalo et al. [15] fabricated GFRP sandwich beams by using an adhesive to bond the GFRP skins to the phenolic foam cores.Interfacial debonding was found to be the main failure mode when such beams were subjected to flexural loading.Based on the above mentioned studies, it seems that the weakness of the interfacial debonding between the face sheets and the core within a traditional sandwich structure reduces its load-carrying capacity and therefore limits its structural application.
A lattice-web reinforced composite sandwich structure was proposed to overcome this weakness; the insertion of GFRP into the lattice web prevents debonding between the face sheets and core and enhances the compressive strength of the sandwich structure [16][17][18][19].James et al. [20] investigated the flexural performance of one-way lattice-web reinforced GFRP composite sandwich structures; the typical failure modes included core shear failure, local indentation, and debonding or delamination between the core and face sheets.To achieve a better mechanical performance than those of one-way lattice-web reinforced structures, two-way lattice-web reinforced composite sandwich structures with lattice-web reinforcements in both the longitudinal direction and the transverse direction were fabricated through the vacuum infusion moulding process (VIMP) technique and studied.Such lattice-web reinforced sandwich panels [21,22] showed a significant increase in the load-carrying capacity under compression and bending due to the improved resistance to interfacial debonding between the face sheets and the core.Moreover, this kind of composite sandwich panel has been applied in some construction projects, as shown in Figure 1. Figure 1(a) shows a footbridge using two-way lattice-web reinforced foam core composite sandwich panels as bridge decks, which can sustain a crowd.Figure 1(b) shows a temporary house using two-way lattice-web reinforced foam core composite sandwich panels as roof panels and wall panels.Nevertheless, to understand the mechanical behaviour of the components of sandwich panels, the bending behaviour of such panels must be investigated.
e present study investigated the flexural behaviour of two-way lattice-web reinforced foam core composite sandwich panels under both uniformly distributed and concentrated loading through experimental and numerical studies.Uniformly distributed and concentrated loading tests were carried out on square composite sandwich panels with four simply supported edges as the boundary conditions.e load-deflection relationships and failure modes of the sandwich panels with different lattice-web geometries were reported.Numerical simulations using finite element (FE) modelling were also carried out and compared with the experimental results.Furthermore, parametric studies on the effects of the face-sheet thickness, lattice-web thickness, and foam density were analysed and discussed in this paper.

Test Specimens and Material Properties.
e proposed lattice-web reinforced foam core composite sandwich panels are illustrated in Figure 2, in which the core is composed of small sliced foam blocks wrapped with glass fibre fabrics as reinforcing webs in both the longitudinal and the transverse directions.ese composite sandwich panels were manufactured through the VIMP process.Different series of specimens were prepared to investigate the performance of the composite sandwich panels, as listed in Table 1, where the label OS represents sandwich panels without lattice web, and the label TS represents sandwich panels reinforced with lattice webs.Specimens with different core heights (50 mm, 75 mm, and 100 mm) and lattice-web spacing values (75 mm, 125 mm, and 175 mm) and the same face-sheet thickness (1.6 mm) were prepared as described in Table 1.
e material properties were determined through coupon tests.For the GFRP face sheets composed of unsaturated polyester resin and biaxial [0 °/90 °] glass fibre fabrics, the   Advances in Civil Engineering tensile strength and elastic modulus are 322.9MPa and 20.95 GPa, respectively, according to standard ASTM D3039 [23].For the GFRP lattice web composed of unsaturated polyester resin and biaxial [−45 °/45 °] glass bre fabrics, the tensile strength and elastic modulus are 296.3MPa and 6.41 GPa, respectively, and the shear modulus is 5.82 GPa according to standard ASTM D2344 [24].Polyurethane (PU) foam with a density of 60 kg/m 3 was used to form the core.e stress-strain curve of the PU foam is shown in Figure 3; according to standard ASTM D1621 [25], the initial elastic modulus and the compressive strength of the PU foam are 7.17 MPa and 0.28 MPa, respectively, whereas the shear modulus and strength (ASTM C273 [26]) are 2.08 MPa and 0.29 MPa, respectively, and Poisson's ratio is 0.3.

Experimental Setup.
e lattice-web reinforced foam core sandwich panels were simply supported on a 1 m × 1 m square steel frame that was composed of four I-section steel beams welded together.e sandwich panels were tested under two loading scenarios: (1) uniformly distributed loading (UDL), which was applied by the gravity of accumulated balance weights, as shown in Figure 4 and (2) concentrated loading, which was applied to the centre of the face sheet by a hydraulic jack at a rate of 2 mm per min, as shown in Figure 5.

Uniformly Distributed Loading (UDL).
e aim of a UDL test is to evaluate the exural sti ness of a specimen; thus, specimens are loaded within the elastic region, and they do not reach ultimate failure.Figure 6(a) presents the loadmidspan de ection curves of the lattice-web reinforced foam core sandwich panels with di erent web heights; the bending  OS represents ordinary sandwich panels (PU core) without lattice-web reinforcements, and the following number (e.g., 50, 75, and 100) represents the height of the core. 2 TS represents lattice-web reinforced sandwich panels; the rst number (e.g., 75, 125, and 175) represents the spacing between the lattice webs, and the following number (e.g., 50, 75, and 100) represents the web height.sti ness is calculated according to the slope of the loadde ection curve.e sti nesses of the sandwich panels with web heights of 75 mm (specimen TS75-75) and 100 mm (specimen TS75-100) increased by 100% and 88.8%, respectively, relative to specimen TS75-50 with a web height of 50 mm.erefore, an increment in the web height can signi cantly increase the exural sti ness of sandwich panels.Similarly, the in uence of the lattice spacing on the exural sti ness of sandwich panels with the same web height is presented in Figure 6(b), which demonstrates that increments in the web spacing from an initial value of 75 mm to 125 mm and 175 mm caused the exural sti ness to decrease by 12.1% and 18.2%, respectively.erefore, an increment in the web spacing can decrease the exural sti ness of composite sandwich panels; however, the magnitude of the sti ness reduction is small.e e ects of the reinforcement, height, and spacing of the lattice web on the failure modes and load-carrying capacities were investigated.
(1) E ect of the Lattice-Web Height.For specimens TS75-50, TS75-75, and TS75-100, all of which have the same web spacing (75 mm) but di erent web heights (50 mm, 75 mm, and 100 mm), the failure modes were similar.For specimen TS75-50, local debonding between the top face sheet and the core was rst observed when the applied load reached 36.2 kN, and several perpendicular cracks initiated alongside the loading jack.When the applied load reached 53.2 kN, a loud noise was heard, and the top face sheet exhibited buckling failure, while the glass bres failed by cracking.e corresponding maximum midspan de ection was 40.5 mm.Specimens TS75-75 and TS75-100 followed similar failure processes, and the corresponding ultimate loads at failure were 83.3 kN and 108.8 kN, respectively.Figure 7 shows the failure mode on TS75-75 at the ultimate load.e maximum midspan de ections for TS75-75 and TS75-100 were 27.6 mm and 25.7 mm, respectively.
(2) E ect of the Lattice-Web Spacing.Interfacial debonding between the top face sheet and core was the dominant failure mode for specimens TS75-75, TS125-75, and TS175-75, all of which have the same lattice-web height (75 mm) but di erent lattice-web spacing values (75 mm, 125 mm, and 175 mm).However, the interfacial debonding observed in specimen TS175-75 was more severe than that observed in specimens TS75-75 and TS125-75.During the loading, slight local debonding was initially observed in specimen TS175-75 between the top face sheet and core along with several cracks when the load reached 38.2 kN. is local debonding that initiated on the top face sheet gradually propagated to the four edges of the sandwich panel with an increasing load, leading to interfacial debonding failure between the top face sheet and the core, as shown in Figure 8. e ultimate loads for specimens TS125-75 and TS175-75 were 65 kN and 49.8 kN, respectively, and the corresponding maximum midspan de ections were 29.1 mm and 31.2 mm.
(3) E ect of the Lattice-Web Reinforcement.For specimen OS50, which does not have a reinforced lattice web, a slight splitting sound was heard that originated from the top face sheet at an applied load of 11.5 kN.When the load reached 27.2 kN, an abrupt and loud sound was heard coincident

Load-Displacement Curves.
e load-midspan deection curves are shown in Figure 9, and the results are analysed below.Advances in Civil Engineering panels increased signi cantly, i.e., the ultimate loads of lattice-web sandwich panel specimens TS75-75 and TS125-75 were 83.3 kN and 65.0 kN, but sandwich panel specimen OS75 without lattice-web reinforcements had an ultimate load of only 18.3 kN. e unreinforced sandwich panel specimen experienced brittle failure, and the large-scale interfacial debonding between the top face sheet and the core constituted the nal failure mode.In contrast, ductile failure was observed during the exural testing of the lattice-web reinforced sandwich panels.(4) Although composite face sheets and shear cores are brittle materials, the sandwich panel specimens exhibited ductility after implementing lattice-web reinforcements between the two types of materials; therefore, the nonlinearity was sustained during the failure process.Such ductility can be called "pseudoductility" [14] because it is not caused by the materials themselves but by the gradual debonding along the interfaces between the GFRP members and core materials.e ductility coe cient μ, which is expressed as Formula (1), can be used to examine such pseudoductility [27].
where D u is the maximum displacement of a structural member under the ultimate load and D y is the maximum displacement of the structural member under the elastic yielding load.
e elastic yielding point can be determined using the method from [28], i.e., the yielding point is the point on the curve with a tangent slope that is identical to the slope of the straight line connecting the origin point to the peak point; if there are two or more points, the yielding point can be determined from the projection of the average load values.e load capacity and displacement at the elastic limit, the ultimate load capacity, the ultimate displacement, and the ductility coe cient are listed in Table 2. e testing results obtained from specimens TS75-75, TS125-75, and TS175-75 (with the same core height of 75 mm) showed that their ductility coe cients increased with an increase in the web spacing.However, for the specimen with no lattice web, which corresponds to an in nite web spacing, the ductility coe cient was a minimum (equal to 1).Hence, this analysis is e ective only when the web spacing exceeds a certain value.e initial ductility coe cient of specimen TS75-75 is 1.7; the ductility coe cients corresponding to increases in the web spacing from 75 mm to 125 mm and 175 mm were 2.0 and 2.6, e.g., the ductility coe cient increased by 17.6% and 30.0%. is pseudoductility is attributed to the interfacial debonding between the core materials and face sheets, as shown in Figure 8 for specimen TS175-75.Specimens TS75-50, TS75-75, and TS75-100 (with the same web spacing of 75 mm) showed similar ductility coe cients, e.g., 2.0, 1.7, and 1.9, respectively, with increases in the web height from 50 mm to 75 mm and 100 mm.e three specimens showed similar failure modes, e.g., buckling failure on the top face sheet, as shown in Figure 7 for specimen TS75-75.6

Finite Element Analysis
Advances in Civil Engineering along the interface are merged assuming that sliding does not occur between the composite materials and the foam core.

Element Type.
e GFRP face sheets and lattice webs were simulated with Belytschko-Tsay shell elements [29].
e shell element is widely used during research on thinwalled structures because of its remarkable e ciency arising from adopting a reduced integration technique.e rigid loading cell and PU foam core were modelled using solid elements, which were also formulated with the reduced integration method.e mesh size was successively re ned until an optimum result was achieved.

Material Model.
e GFRP face sheets and lattice webs were modelled using an available material model MAT 54 (enhanced composite damage), which was utilized with optional brittle failure formulated by Chang [30,31].e Chang-Chang failure criterion is given as Formulas ( 2)- (5).* PART_COMPOSITE was used to de ne the thickness and material angle for each composite layer.Tables 3 and 4 list the mechanical properties of the GFRP face sheets and lattice webs, respectively, obtained from the experiments.e PU foam was modelled using MAT 63 (crushable foam), which is expert at modelling crushable foam with optional tension cuto and damping.In this work, the tensile stress cuto and damping coe cient were set to 1 MPa and 0.5, respectively.Figure 3 shows the trilinear equivalent stress-strain curve of the PU foam.e data points of the curve were used to put into the simulation.In addition, a failure criterion was used for MAT 63, and once the maximum principal strain reaches 0.1, the element is deleted from the calculation [32].
For the tensile bre mode, where σ aa > 0: where E a E b G ab ] ab ] ba 0 upon failure, β is a weighting factor for the shear term with a range of 0-1, σ aa is the stress in the bre direction, σ ab is the transverse shear stress, X t is the tensile strength in the bre direction, and S c is the shear strength.In this work, the weighting factor β is set to 0.5.
For the compressive bre mode, where σ aa < 0: where E a ] ab ] ba 0 upon failure and X c is the compressive strength in the bre direction.

Advances in Civil Engineering
For the tensile matrix mode, where σ bb > 0: where E b � ] ba � G ab � 0 upon failure, σ bb is the stress normal to the fibre direction, Y t is the tensile strength normal to the fibre direction, and Y c is the compressive strength normal to the fibre direction.

Loading and Contact Conditions.
e concentrated loading was achieved by moving the rigid loading cell with a constant velocity.e vertical displacements of the nodes on all four sides of the bottom of the panel were constrained.
e rigid loading cell was constrained in all degrees of freedom apart from the vertical displacement.A rate of 2 mm/min was applied to the loading cell in the direction of the vertical displacement.In order to model the interaction between the rigid loading cell and the specimen, an "automatic surface to surface" contact was defined following the suggestion of Yin [33] and Zhang [34].

Concentrated Loading Simulation.
To obtain numerical stability in an explicit simulation, the time step is usually small.However, a small time step is not suitable for concentrated loading simulation because an enormous amount of steps are required for the concentrated loading simulation.Two approaches have been commonly used to minimize the computational time: (1) scaling up the loading cell velocity and/or (2) scaling up the mass density [35].In this work, the real rate of 2 mm/min is replaced by 50 mm/s.Such an approach attains a concentrated loading process, for the ratio of the kinetic energy to the internal energy is less than 1.5% during the loading process, as shown in Figure 11.

Validation of the Finite Element Model.
Validation of the FE model is one of the most important steps in the model building process.e FE model for concentrated loading is validated by comparing the load-displacement curve with the experimental results.
Figure 12 shows a comparison of the load-displacement curves between the experimental results and numerical simulations.During the initial loading step, the loaddisplacement curve behaves linearly with a high slope, and the slope gradually decreases with an increase in the load until reaching ultimate failure.e ultimate load from the FE analysis is 116.5 kN, which is 7.5% higher than the experimental result of 108.4 kN, and the ultimate displacement from the FE analysis is 23.3 mm, which is 9.3% less than the experimental result of 25.7 mm. e numerical simulation accurately predicts the crushing behaviour, although there is a small difference between the experimental results and the predicted loads.Considering the complexity of the model, this comparison shows that the proposed FE model can greatly predict the responses of the test specimens.

Parametric Studies
e previous section proved the reliability of the FE modelling approach; therefore, additional parametric studies were carried out on the effects of the face-sheet thickness, lattice-web thickness, and foam density on the flexural performance of the composite sandwich panels using FE modelling, the results of which are discussed in this section.

Effect of the Face-Sheet ickness.
Figure 13 shows the effect of the face-sheet thickness on the load-carrying capacity and midspan deflection under the same lattice-web height (h � 100 mm), lattice-web spacing (s � 75 mm), lattice-web thickness (t w � 1.6 mm), and foam density (ρ � 60 kg/m 3 ).When the face-sheet thicknesses were 1.6 mm, 2.4 mm, 3.2 mm, and 4.0 mm, the load-carrying capacities

E ect of the Lattice-Web ickness.
Figure 14 shows the e ect of the lattice-web thickness on the load-carrying capacity and midspan de ection under the same lattice-web height (h 100 mm), lattice-web spacing (s 75 mm), facesheet thickness (t w 1.6 mm), and foam density (ρ 60 kg/m 3 ).When the lattice-web thicknesses were 1.6 mm, 2.4 mm, 3.2 mm, and 4.0 mm, the load-carrying capacities were 116.5 kN, 134.0 kN, 142.8 kN, and 150.9 kN, respectively, and the corresponding midspan de ections were 23.3 mm, 22.7 mm, 22.3 mm, and 22.0 mm.erefore, increasing the lattice-web thickness can result in a larger load-carrying capacity.However, the di erences in the midspan deections among these four panels were negligible.

E ect of the Foam Density.
Figure 15 shows the e ect of the foam density on the load-carrying capacity and midspan de ection under the same lattice-web height (h 100 mm), lattice-web spacing (s 75 mm), face-sheet thickness (t s 1.6 mm), and lattice-web thickness (t w 1.6 mm).e stressstrain data points of the PU foam with di erent foam densities are listed in  e di erences in the load-carrying capacities and midspan de ections among these four panels were negligible.Hence, the load-carrying capacity and midspan de ection were hardly a ected by the foam density.

Conclusions
is paper investigated the nonlinear exural behaviours of foam core composite sandwich panels with and without lattice-web reinforcements through UDL and concentrated loading tests.e e ects of various geometric parameters on the exural performance of the sandwich panels were analysed and discussed through nonlinear experimental and numerical modelling.
e following conclusions can be drawn from this work: (1) e failure mode of ordinary composite sandwich panels without lattice-web reinforcements under compression is interfacial debonding between the core and face sheets.However, the onset of interfacial debonding failure can be delayed for sandwich panels with two-way lattice-web reinforcements.e introduction of lattice webs can improve the composite action between the core and the face sheets and substantially increase both the exural sti ness and the ultimate load capacity of composite sandwich panels.(2) e main failure mode for composite sandwich panels with lattice-web reinforcements is buckling failure together with the breakage of glass bres on the face sheets.e failure modes are similar for sandwich panel specimens with di erent web heights; however, local interfacial debonding occurred between the core and the face sheets, and this local interfacial debonding failure mode became more evident as the lattice web spacing increased.(3) An FE model was developed, and simulations of the concentrated loading showed good agreement with the experimental results.Parametric studies based on the veri ed model demonstrated that thicker face sheets and lattice webs can remarkably increase the load-carrying capacity.However, the load-carrying capacity and midspan de ection were hardly a ected by the foam density.
Data Availability e data used to support the ndings of this study are available from the corresponding author upon request.

Figure 1 :
Figure1: Practical constructions using two-way lattice-web reinforced foam core composite sandwich panels as the main loading-bearing components: (a) a footbridge using sandwich panels as bridge decks and (b) a temporary house using sandwich panels as roof panels and wall panels.

Figure 3 :
Figure 3: e trilinear equivalent stress-strain curve of the PU foam core.

3. 2 .
Concentrated Loading 3.2.1.Failure Modes.Concentrated loading tests were performed on the composite sandwich panels with four simply supported edges until they reached ultimate failure.

4. 1 .Figure 9 :
Figure 9: Load-midspan de ection curves of specimens (a) with di erent web heights and (b) with di erent web spacing values.

Figure 11 :Figure 12 :Figure 13 :Figure 14 :
Figure 11: Ratio of the kinetic energy to the internal energy of specimen TS75-100.

Figure 15 :
Figure 15: E ect of the foam density (h 100 mm, s 75 mm, t s 1.6 mm, and t w 1.6 mm).

Table 1 :
Description of the specimens.
Specimen L x (mm) L y (mm) s (mm) h (mm) H (mm) t w (mm) t s (mm) Specimen length

Table 2 :
Experimental results of the ultimate load capacity, displacement, and ductility coe cient.

Table 3 :
Material parameters of the GFRP face sheets.

Table 4 :
Material parameters of GFRP lattice webs.