Numerical predictions of intralaminar and interlaminar damage in thin composite shells subjected to impact loads

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published by Elsevier in ThinWalled Structures, Vol. 192, on November 2023, available at: https://doi.org/10.1016/j.tws.2023.111148 Copyright 2023 Elsevier. En idUS Licencia Creative Commons CC BY-NC-ND Highlights Numerical predictions of intralaminar and interlaminar damage in thin composite shells subjected to impact loads L.M. Ferreira, C.A.C.P. Coelho, P.N.B. Reis •Investigation of the impact dynamics on composite shells using the explicit finite element method. •Numerical predictions of intralaminar damage using a continuum damage mechanics model. •Numerical predictions of interlaminar damage using a surface-based cohesive model. •Prediction of energy dissipation forms for di↵erent thicknesses. Numerical predictions of intralaminar and interlaminar damage in thin composite shells subjected to impact loads L.M. Ferreiraa,b,⇤ , C.A.C.P. Coelhoc, P.N.B. Reisd aGrupo de Elasticidad y Resistencia de Materiales. Escuela T´ecnica Superior de Ingenier´ıa. Universidad de Sevilla. Camino Descubrimientos, S/N 41092 Sevilla. Espa˜na bEscuela Polit´ecnica Superior. Universidad de Sevilla. C/ Virgen de ´ Africa, 7, Sevilla, 41011. Espa˜na cUnidade Departamental de Engenharias. Escola Superior de Tecnologia de Abrantes. Instituto Polit´ecnico de Tomar. Rua 17 de Agosto de 1808 S/N 2200-370 Abrantes. Portugal dUniversity of Coimbra, CEMMPRE, ARISE, Department of Mechanical Engineering, 3030-194 Coimbra, Portugal Abstract This paper investigates the impact dynamics of thin semicylindrical woven composite laminate shells, with a particular focus on understanding the influence of thickness. Utilising the finite element (FE) method, the study evaluates both intralaminar and interlaminar damage associated with the impact response. The findings show that the implementation of the explicit FE method, along with a continuum damage mechanics model, for the intralaminar damage, and a surface-based cohesive model, for the interlaminar damage, may be used to correctly predict the load histories, as well as the maximum impact force, maximum displacement, contact time and impact bending sti↵ness (IBS). The numerical predictions reproduce well the linear response of the maximum impact force and maximum displacement to the thickness variation, as well as the 2nd order polynomial curve of the IBS, with errors ranging from 2.7% to 15.9%. Moreover, the damage areas and the e↵ect of thickness on the damage severity were accurately replicated. These results’ validation enables the prediction of the energy histories and the ensuing energy dissipation forms. According to the findings, the intralaminar damage is around 5 times more significant than the other energy dissipation forms. The accuracy of the simulation creates the possibility for more impact investigations using a similar numerical approach, reducing the expenditures of experimental testing. Keywords: Finite element method (FEM), Continuum damage mechanics (CDM), Cohesive behaviour, Low-velocity impact, Woven-fabric composites, Composite shells Preprint submitted to Thin-Walled Structures February 1, 2024 1. Introduction Composite materials have become increasingly popular due to their unique combination of high strength, low weight, and excellent fatigue resistance. However, they are susceptible to damage from low-velocity impacts that can occur during handling, transportation, maintenance, and service. These impacts can5 cause localised damage to the structure, which can result in reduced strength, sti↵ness, and durability of the composite material [1–5]. Therefore, understanding the damage mechanisms and behaviour of composite materials under lowvelocity impacts is of utmost importance to ensure the reliability and safety of composite structures. In this context, it is not surprising that literature presents10 several strategies to increase impact strength, such as the use of nanoparticles [6], multiaxial mesh fabrics [7], hybrid laminates [8], sandwich composites [9, 10] or simply changing the stacking sequence of the laminates [11]. Since the early 1990s, impact analysis on composite structures has been a subject of study. Thereafter, several numerical research studies have been done15 using di↵erent abstraction scales and applied methods. The finite element (FE) method has been used extensively to develop models of unidirectional composite plates and evaluate various parameters such as material characteristics, impact energy, and geometry. Yet, there are relatively few studies that analyse the impact dynamics on cylindrical shells, particularly when it comes to composites20 made of woven fabrics. The most relevant studies found in literature regarding low-velocity impact on cylindrical shells, are dedicated to analyse the e↵ect of curvature of the shell on the impact force, displacement (deflection) and contact time [12–15]. The findings of these studies are consistent and reveal that the impact force increases with the increase in curvature, while deflection and25 contact time decrease. Investigations have also been conducted to determine how thickness a↵ects the impact response of composite laminate plates and shells [16–21]. These studies have shown that increasing the thickness of the laminates leads to notable e↵ects on several impact-related parameters. It was found that increasing the thickness of the composite laminates results in in-30 creased sti↵ness. This higher sti↵ness imparts the laminates with the ability to withstand higher impact loads. As a result, the laminates exhibit smaller deflections and reduced contact times during impact events. Furthermore, the damage onset and damage evolution were studied in [22], and it was found that for unidirectional composite plates and shells, damage progresses di↵erently.35 Although the numerical approach utilizing FE models allows the simulation of complicated structures under ostensibly complex external loads and boundary conditions, from the numerical perspective, simulating impact is still a complex task. Moreover, achieving a suitable level of accuracy in a fair amount of time continues to be a challenge [23, 24].40 Composite materials experience several di↵erent damage modes under im- ⇤Corresponding author Email address: [email protected] (L.M. Ferreira) 2 pact loads such as matrix cracking, delamination, fibre failure and perforation, which can considerably lessen the material’s strength and sti↵ness [25]. It is then crucial to develop credible FE models capable of forecasting these damage modes. Focus is here on fabric-reinforced composite laminate shells with45 a semicylindrical cross-section. These composites have practical interest for impact-resistant constructions like wind turbine blades or aircraft structures. The built-in continuum damage mechanics model (CDM) for fabric reinforced composites available in ABAQUS [26] and developed by Johnson [27], is employed to model the intralaminar damage, while the interlaminar damage, know50 as delamination, is modelled using the surface-based cohesive damage model (S-BCM). The two-step homogenization method proposed by Liu et al. [28] is used to predict the laminas’ properties from the constituents properties. This study follows the experimental and numerical work previously developed by the authors [29–31]. Firstly, the e↵ect of thickness on the multi-impact response55 of semicylindrical composite laminated shells with 6-, 9-, and 12-layers was experimentally analysed in [29]. Subsequently, based on the experimental results obtained, a FE model for a single thickness was generated, and in which the physical intralaminar and interlaminar progressive damage models were introduced [30]. This work focused on e↵ect of the FE mesh discretization and60 mass-scaling on the load history predictions and in evaluating the efficiency and reliability of the numerical model. Afterwards, the influence of interlaminar properties on delamination predictions for a single thickness was studied in [31]. Finally, the present paper represents an expansion of the analysis and validation process to encompass di↵erent thicknesses, while striving to comprehend65 the underlying damage mechanisms at both the intralaminar and interlaminar levels. Therefore, to summarize, the current work serves as a continuation of the previous numerical investigation and complements the experimental findings. It introduces novel contributions, including the development and validation of FE70 models capable of investigating the impact dynamics of semicylindrical woven composite laminate shells with di↵erent thicknesses. Moreover, the study focuses on predicting and evaluating the intralaminar and interlaminar damage modes, as well as identifying the energy dissipation mechanisms that occur during low-velocity impact events. As far as the authors are aware, these topics75 in the domain of thin semicylindrical composite shells, are still lacking comprehensive understanding and research. 2. Damage models Low-velocity impacts on composite laminates can cause fibre failure and matrix cracking (intralaminar damage), as well separation of the interface regions,80 known as delamination (interlaminar damage) [32, 33]. To model these damage mechanisms in semicylindrical woven composite laminate shells, a CDM at the lamina level to address the intralaminar damage, and a S-BCM at the lamina’s interface to account for the interlaminar damage, were implemented. These 3 damage models are fully described in [26, 34, 35], thus only the main aspects of85 the CDM and S-BCM will be briefly described in the following subsections. 2.1. Intralaminar damage model To evaluate the complex damage evolution at the intralaminar level, the built-in constitutive model for fabric reinforced composites available in ABAQUS/Explicit [36], developed by Johnson [27] and based on Ladeveze and Ledantec work90 [37], was employed. This damage model is applied as a built-in VUMAT user subroutine and accessed by naming the user-defined material with the string “ABQ PLY FABRIC” [26]. This VUMAT subroutine is compatible only with plane-stress elements and considers each fabric reinforced lamina as a homogeneous orthotropic elastic material that withstands sti↵ness reduction due to95 fibre failure and/or matrix cracking and plastic deformation under shear loading. It uses the maximum stress failure criterion to determine the damage onset of the fibres, and a damage evolution model based on the fracture energies to control the sti↵ness reduction. The Hooke’s law for a degraded orthotropic material is expressed as,100 "=2 6 4 S1 (1d1)S12 0 S21 S2 (1d2)0 00S6 (1d12) 3 7 5(1) where Sij are the components of the compliance matrix of the undamaged orthotropic material, is the nominal Cauchy stress tensor, "is the elastic strain tensor, and d1,d2and d12 are the damage coefficients. Notice that the damage coefficients d1and d2are associated with fibre fracture along directions 1 and 2, respectively, and d12 is associated with the matrix micro-cracking due to shear105 deformation. As mentioned before, the CDM uses the maximum stress criterion to determine the damage onset of the fibres, and to simulate the two failure modes (fibre tension and fibre compression). Therefore, the elastic domain, at any given time, is calculated in terms of the damage activation functions, F↵, as110 F↵=˜↵ X↵ r↵0with↵=1±,2±,12 (2) where ˜↵and X↵are the tensile/compressive/shear e↵ective stresses and strengths, respectively, and r↵are the damage thresholds, which are initially defined with a value of 1. After reaching the damage onset, that is, when ˜↵ X↵= 1, the evolution the damage coefficients, d1and d2, associated with the tensile and compressive loading, are obtained using equations 3 and 4, while the damage115 coefficient d12 associated with shear loading, is obtained by equation 5, d1,2=11 r1,2 eA1,2(r1,21) (3) A1,2=2g1,2 0Lch G1,2 fg1,2 0Lch with g1,2 0=X2 1,2 2E1,2 (4) 4 d12 =min [↵12 ln (r12),d max 12 ] (5) where r1,2and r12 correspond to the damage thresholds for the tensile/compressive and shear loading, respectively, G1,2 fto the fracture energies per unit area, g1,2 0 to the elastic energy density at the damage onset, and Lch to the characteristic length of the element. The shear damage parameter ↵12 is obtained through a120 calibration procedure detailed in [26]. At the intralaminar level, the shear damage response is driven by the matrix’s nonlinear behavior caused by the matrix microcracking, and it involves both sti↵ness loss and plasticity. The yield and hardening functions represented in equations 6 and 7, respectively, are used by the VUMAT subroutine to define125 the plasticity response of the matrix, Fpl =|˜12|˜0(¯"pl)0 (6) ˜0(¯"pl)=˜y0+C(¯"pl)p(7) where ˜12 is the e↵ective shear stress, ˜y0is the initial e↵ective shear stress, and ¯"pl is plastic strain due shear deformation. The hardening function’s coefficient and power term are denoted by Cand the superscript p, respectively. To be able to validate the numerical models based on the experimental ev-130 idence presented in [29], the sti↵ness properties of the woven fabric composite laminas were estimated from the constituents’ properties of the tested specimens, using the two-step homogenization methodology presented by Liu et al. [28]. The obtained elastic properties are consistent with those reported in literature for plain weave E-glass woven fabric composites [38–40]. This multiscale135 approach involves first estimating the e↵ective properties of the tows from the fibre and matrix properties and then predicting the lamina properties from the properties of the tows and the matrix. This methodology was implemented using the software TexGen4SC [41, 42]. Each lamina is composed of a polyester resin matrix (AROPOL FS 1963 with MEKP-50 hardener) reinforced with a140 bi-axial E-glass plain weave fabric (EC9 68×2). The lamina’s sti↵ness properties were estimated from the elastic constants extracted from [43–46]. The remaining properties and coefficients required to implement the VUMAT subroutine, such as the strength properties, fracture toughness and shear plasticity, were taken from literature [38, 47–51]. The lamina’s intralaminar properties145 are shown in Table 1. Notice that a good agreement between the experimental results and the numerical predictions was attained in previous work developed by the authors, and in which the same properties and coefficients were employed [30, 31]. The transverse shear sti↵ness of the laminas must be defined for the VUMAT150 subroutine [26] because it cannot be calculated by ABAQUS/Explicit [36] for composite shell elements. Considering that each lamina can be thought of as a homogeneous shell with orthotropic elastic properties, equations 8 were used to calculate the transverse shear sti↵ness, 5 Table 1: Intralaminar properties defined for each lamina [30]. Property Symbol Units Value Density ⇢kg/m31900 Sti↵ness properties E+, 1=E+, 2GPa 21.9 E3GPa 8.6 G12 GPa 3.4 G13 GPa 2.4 ⌫12 - 0.14 Strength properties X+ 1=X+ 2MPa 250 X 1=X 2MPa 200 X12 MPa 40 Fracture toughness G1,2 fJ/m24500 Shear plasticity dmax 12 -1 ˜y0MPa 25 C800 p0.552 kts 1=5 6G13t, kts 2=5 6G23t, kts 12 = 0 (8) where G13 and G23 are the out-of-plane shear moduli of the lamina, tis the155 thickness of the lamina, and 5/6 is a shear correction coefficient that is obtained by comparing the transverse shear energy to that for an 3D structure in pure bending, as suggested in [36]. Considering the out-of-plane shear moduli calculated by the homogenization process, the following values were used in the definition of the intralaminar properties: kts 1=kts 2=3.5⇥105N/m and160 kts 12 = 0. 2.2. Interlaminar damage model To account for the interlaminar damage, i.e. delamination, the bond between the laminas of the composite laminate was modelled using a S-BCM. This model is primarily intended for negligible small interface thicknesses and o↵ers very165 similar capabilities to cohesive elements. The cohesive behaviour is defined as a surface interaction property, and identically to the cohesive elements it is governed by a traction-separation constitutive model. Hence, the interlaminar fracture behaviour (delamination) is defined as a constitutive relation between the traction ⌧and the separation , see Fig. 1.170 The initial linear response until the damage onset it reached is controlled by the value defined for the normal knand tangential ks,k tcohesive sti↵nesses. These parameters influence the performance of the FE model and for which there are di↵erent approaches available in literature to obtain its value [52–55]. For instance, Daudeville et al. [52] determined the cohesive sti↵ness as a function175 6 Figure 1: Bilinear traction-separation response of the cohesive surface. of the interface’s thickness and the elastic modulus of the resin-rich layer, while Zou et al. [53] suggested the use of interface sti↵ness values between 105and 107times the interface strength divided by length unit. Another approach was presented by Turon et al. [55], in which the interface sti↵ness is calculated as function of the elastic properties of the laminate. The cohesive sti↵ness in this180 study is set at 106N/mm3, as suggested by Camanho et al. [54]. Also, it is considered that its value is the same for all directions, that is, kn=ks=kt, as used in [30, 31, 55–57] with satisfactory results. It is noteworthy that considering high values for the cohesive sti↵ness potentially leads to convergence problems, on the other hand, the use of low values may a↵ect the global sti↵ness and thus185 compromise the validation of the FE model [56]. The following stress-based quadratic failure criterion was employed to predict the damage initiation, ✓h⌧ni ⌧0 n◆2 +✓⌧s ⌧0 s◆2 +✓⌧t ⌧0 t◆2 = 1 (9) where ⌧n,⌧ sand ⌧trepresent the interface normal and shear contact stresses, and ⌧0 n,⌧0 sand ⌧0 trepresent the corresponding interface strengths. The Macaulay190 brackets hiindicate that the compressive stress doesn’t contribute to damage. The following interlaminar strengths were used in the S-BCM: ⌧0 n= 15 MPa and ⌧0 s=⌧0 t= 30 MPa [30]. Once the onset of damage is reached, that is, when the quadratic interaction function of the stress ratios reaches 1, the cohe7 Figure 7: E↵ect of thickness on the numerical and experimental [29] maximum displacement results. 4.2. Deformation histories The deformation histories of the 6-, 9and 12-layer composite laminates at di↵erent step times are shown in Fig. 8. The selected time steps for analysis are represented in Fig. 4, denoted as Ai,B iand Ci, which correspond to the following contact times: Aito half of the peak force time; Bito the peak force340 time; Cito half of the time between the peak force and the total contact time. Here, the subscript i=6,9,12, identifies the configuration of the laminate. A notable trend can be observed wherein an increase in thickness results in a corresponding increase in the sti↵ness of the composite laminate. Among the laminates studied, the 6-layer laminate exhibits the highest degree of de-345 formation, followed by the 9-layer and 12-layer laminates. As anticipated, the deformation steadily intensifies until it reaches the peak force, at which point the impactor rebounds and the specimen commences its elastic recovery. 4.3. Impact bending sti↵ness The studies developed by Liu [64] and David-West et al. [65] suggest that350 the impact bending sti↵ness is an important parameter to evaluate the damage resistance of a composite, in particular delaminations. According to these authors, the slope of the ascending branch of the load-displacement curve defines the IBS, because the plate is under bending at the beginning of the impact 14 Figure 8: Deformation histories for the 6-, 9and 12-layer composite laminates. 15 Figure 9: E↵ect of thickness on the numerical and experimental [29] IBS results. regime [65]. In this study, the IBS is calculated from the experimental and nu-355 merical curves depicted in Fig. 5, and Table 2 presents and compares the values obtained. It should be noted that the IBS predictions for the 6-layer FE model had the largest percentage of error. This is most likely because damage begins to appear at slightly di↵erent loads than simulated. Actually, until reaching the peak force, the experiments shown a smoother damage growth than the360 simulations. This di↵erence in the initial behaviour can be attributed to the use of the semi-automatic mass scaling technique in the numerical models [30]. Nevertheless, all the predicted IBS values are within the limits of the experimental evidence. The evolution of the IBS with thickness is shown in Fig. 9. The figure outlines the FE models capability to accurately reproduce the 2nd 365 order polynomial curve followed by the experiments, and which are represented by the plotted trend lines. 4.4. Damage The numerical predictions for the intralaminar damage (output variables SDV1 to SDV5) and the interlaminar damage (output variable CSDMG>0.6)370 were overlapped to allow a complete representation of the damage severity for the di↵erent laminate thicknesses, see Figs. 10, 11 and 12. Notice that the output identifier CSDMG, represents the scalar sti↵ness degradation for cohesive surfaces, and measures delamination after damage initiation. When it reaches 16 Figure 10: Numerically predicted tensile and compressive damage along the fibre directions and delaminated area for the 6-layer laminate. the value of 1, the interface is considered to be fully delaminated. Moreover, the375 CDM for fabric reinforced composites used in this study does not di↵erentiate between fibre and matrix damage at the intralaminar level, it includes only the outputs variables of tensile/compressive damage along the fibre directions and the shear damage. Therefore, it limits a more detailed identification of the damage modes at the intralaminar level.380 The simulations show that laminate’s thickness a↵ects how severe the damage is. The 6-layer FE model sustained damage commencing at the point of impact and extending the full length of the shell. The 9-layer FE model predicted a less severe damage but quite similar to the one obtained with the thinner laminate. On the other hand, damage is restricted to the impact location for385 the 12-layer FE model. This response can be explained by the fact that more interfaces are available to dissipate the impact energy as thickness increases and consequently, there is less energy available to increase damage. These results are consistent with the experimental findings, which showed that the damaged severity increases with decreasing thickness [29]. Moreover, it correlates with390 the larger displacements observed in thinner laminates, see Fig. 5. Moreover, it is also possible to appreciate in Figs. 10 to 12, that regardless of the thickness, the damaged incurred in the bottom layers of the shell is more severe in comparison to the top layers. It is known that during a lowvelocity impact event, the bottom layers of the shell, located opposite to the395 impact side, experience tensile stresses resulting in material (fibre and matrix) elongation. Conversely, the top layer of the shell, which comes into direct contact 17 Figure 11: Numerically predicted tensile and compressive damage along the fibre directions and delaminated area for the 9-layer laminate. Figure 12: Numerically predicted tensile and compressive damage along the fibre directions and delaminated area for the 12-layer laminate. 18 Figure 13: Delamination predictions along the di↵erent interfaces of the 6-, 9-, and 12-layer composite laminates. with the impactor, experiences compression forces. These compression forces induce localized deformation in the impacted region which undergoes plastic deformation and compression. Although the CDM does not provide specific400 identification of the various damage modes, the numerical predictions suggest that at the intralaminar level, the most prominent damage mechanisms are fibre breakage and/or matrix cracking. These damage modes are closely associated with the tensile stresses developed in the bottom layers during the impact event. The delamination areas predicted for each interface of the laminates are il-405 lustrated in Fig. 13. Once again, it is evident that delamination primarily occurs within the impact region. However, as previously observed, the delamination in the 6and 9-layer laminates propagates along the length of the shell. Regarding the interfaces, it is noteworthy that for the same laminate thickness, they generally exhibit similar delamination areas in terms of size and severity. However,410 there is an exception observed for interface 7 of the 12-layer laminate. This particular interface is located approximately in the middle of the laminate’s thickness, between layer 7 and layer 8. The predicted delamination region for this interface is slightly larger and more severe compared to the other interfaces. Nevertheless, the overall results have a good correlation with the experimental415 evidence presented in Fig. 14. The predicted impact footprints, resulting from the overlapping of the intralaminar and interlaminar damage modes are compared with the actual impact footprints obtained experimentally, in Fig. 14. Notice that the damage on the tested specimens was captured through photography using intense backlight,420 19 Figure 14: Numerical and experimental [29] impact footprints for the 6-, 9and 12-layer composite laminates. taking advantage of the translucent characteristic of the laminates. Despite the limitations on the accuracy of the non-destructive testing technique employed to assess the damage extension, the projected damage areas are generally well predicted by the FE models. The uniform FE mesh size used, contributed for the correct predictions of the damaged areas that can be seen along the length425 of the laminates. However, it should be noted that they tend to be slightly overestimated around the impact location. The scattered points that can be appreciated in the simulations of the 6and 9-layer laminates outside the concentrated damaged areas, correspond to isolated nodes which have experienced delamination.430 4.5. Energy histories In the loading stage of a low-velocity impact test, a sizeable portion of the kinetic energy that is transferred from the impactor to the laminate is converted into elastic energy. The remaining energy is dissipated owing to friction and to the di↵erent failure modes that occur at the intralaminar and interlaminar lev-435 els. The elastic energy that the specimen stores is released during the unloading stage, causing the impactor to rebound. As the impactor loses contact with the specimen, the energy stabilizes [66, 67]. Since in the experimental setup the impactor’s mass and the drop height remained consistent across di↵erent thickness variations, the peak values observed on the energy-time curves remained identi-440 cal. This behaviour can be appreciated in the energy histories of the 6-, 9and 12-layer laminates shown in Fig. 15. Overall, a good numerical-experimental correlation can be appreciated. Notice that the numerical predicted impact energy curves for the 6and 9-layer laminates present a rugged behaviour during 20 Figure 15: E↵ect of thickness on the numerical and experimental [29] energy-time results. the unloading stage, which is due to the vibrations of the FE model. On the445 other hand, given its higher sti↵ness, the 12-layer laminate presents a smoother behaviour. The validation of simulations of the energy and load histories, along with the well predicted damage areas, opens the possibility of identifying the amount of energy that is dissipated through intralaminar damage, delamination and fric-450 tion. The experimentally measured impact energy converted from the impactor, and the numerical predictions for the impact energy and the subsequent dissipated energy forms obtained with 6-, 9and 12-layers FE models, are shown in Figs. 16, 17 and 18, respectively. Regardless of the thickness under consideration, the intralaminar damage455 outweighs the other energy dissipation forms by about 5 times, confirming that it is the primary damage mode. The energy dissipation due to delamination and friction is negligible, however, a slight increase as thickness increases can be observed. The larger number of interfaces may explain this behaviour. Moreover, the high interlaminar fracture toughness and low in-plane strength of the460 woven fabric composites may justify the propensity for intralaminar damage propagation rather than delamination. The total transferred energy curve’s peak, which corresponds to the instance of maximum displacement, is correctly predicted, and the energy balance is accurately reproduced. It is noteworthy to mention that the total energy (output465 ETOTAL), remains stable, which indicates a correct definition of the step time 21 Figure 16: Numerical and experimental [29] energy history for the 6-layer laminate. Figure 17: Numerical and experimental [29] energy history for the 9-layer laminate. 22 Figure 18: Numerical and experimental [29] energy history for the 12-layer laminate. increments. Also, the external energy (ALLAE output), is a small fraction of the internal energy (ALLIE output), meaning the hourglass control method is adequate. 5. Conclusions470 The intralaminar and interlaminar damage and the impact response of thin semicylindrical woven composite laminate shells under low-velocity impact loads was simulated using the finite element method, with particular focus on evaluating the e↵ect of thickness. The numerical predictions were compared with the findings of the previous experimental work conducted by the authors.475 The results obtained in this study, demonstrate that the low-velocity impact response of thin semicylindrical woven composite laminate shells can be reliably simulated using the explicit FE method together with a CDM, to account for intralaminar damage, and a S-BCM, to account for interlaminar damage. The numerical models were able to satisfactory predict the load histories, as480 well as the maximum impact force, maximum displacement, contact time, and IBS. 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