Experimental and numerical investigation on the low-velocity high-energy impact response of thick steel-viscoelastic composite metal laminate with different viscoelastic layer configurations and impact energies

Abstract

This study aims to investigate the effects of viscoelastic layer configurations and impact energy on the low-velocity, high-energy impact response of thick steel-viscoelastic Composite Metal Laminate (TSV-CML). A combined approach of low-velocity drop-weight impact testing and LS-DYNA finite element simulation was employed to analyze the force-time, energy-time, force-displacement, displacement-time, and velocity-time responses of a five-layer TSV-CML configuration, denoted as SNCNS (where “S” represents steel layer, “N” represents natural viscoelastic layers, and “C” denotes carbon fiber-reinforced polymer layers), under an impact energy of 500 J. The simulation results demonstrated high consistency with experimental data in terms of key parameters and damage morphology, validating the reliability of the numerical model. Based on this, a systematic comparison was conducted on different viscoelastic layer arrangements (impact side, non-impact side, and symmetrical distribution) and their influence on impact response. The results indicate that the SNCNS configuration, with symmetrically arranged viscoelastic layers on both sides of the carbon fiber-reinforced polymer (CFRP) layer, exhibits the highest energy absorption efficiency, lowest damage level, and superior impact resistance and toughness under identical impact energy. Furthermore, it was observed that the impact response of TSV-CML structures exhibits a monotonic trend with increasing impact energy. These findings provide theoretical guidance for the optimized design of TSV-CML and offer important insights for understanding and predicting their mechanical behavior under varying energy levels.

Introduction

In recent years, composite structures have achieved significant advancements in aerospace and mechanical engineering due to their high ductility, low weight and excellent structural stability. ¹ To improve their impact resistance, researchers have explored various strategies, particularly focusing on the incorporation of hard material layers into the composite design.^2,3 Fiber metal laminates (FMLs) are a representative example, exhibiting superior low-velocity impact performance owing to the alternating stacking of metal and composite layers.^4–6 This hybrid configuration combines the isotropy, durability, plasticity, and reparability of metals with the high strength, stiffness, and fatigue resistance of composites. ⁷ As a result, FMLs are widely used in aerospace, automotive, and architectural applications, including protective structures such as rocket fuselages, vehicle chassis, and explosion-proof building façades, as illustrated in Figure 1.

Figure 1.

(a) Vehicle chassis, (b) explosion-proof building façades.

In practical applications, conventional fiber metal laminates (FMLs) are often exposed to a range of impact loads,^8,9 including collisions with debris during rocket transport, shocks from uneven terrain in engineering vehicles, and extreme events such as earthquakes or building explosions. Studies have shown that under such loading, FMLs are susceptible to stress concentrations that can trigger interlayer delamination, intralaminar cracking, and even complete fracture of the composite layers. These failure modes compromise structural integrity and safety, potentially resulting in damage to protected components and harm to vehicle operators.^10,11 Furthermore, the limited toughness of traditional FMLs makes them vulnerable to interfacial debonding, fatigue cracking, and structural failure under high load conditions, thereby reducing their effectiveness and reliability in harsh environments and demanding applications.^12–14 To overcome these limitations, recent studies have investigated the integration of viscoelastic materials into FMLs, such as interlayer thermoplastic films, polyurea coatings, and rubber layers, to enhance impact resistance and damage tolerance.^15–17 Viscoelastic layers offer excellent elastic recovery and toughness, enabling them to mitigate stress concentrations during impact and improve overall structural ductility.^18–20 Their presence also extends fatigue life and enhances stability under cyclic loading. ²¹ Furthermore, viscoelastic layers help reduce thermal expansion mismatch and suppress galvanic corrosion between dissimilar materials in FMLs.^22,23 This integration significantly improves damping capacity, delamination resistance, and corrosion resistance, thereby expanding the potential applications of FMLs in more demanding and diverse environments.^24–26

With ongoing advancements in engineering technology, composite structures incorporating viscoelastic layers are being increasingly adopted across a wide range of applications. Khodadadi et al. ²⁷ examined the mechanical response of rubber sheets with varying hardness under high-velocity impact. The results demonstrated that rubber hardness and filler content significantly influenced the energy absorption capacity, with higher hardness leading to a notable increase in the ballistic limit and energy mainly dissipated through damage mechanisms. Verma et al. ²⁸ proposed an anchoring design by embedding shape memory alloy (SMA) wires into a glass fiber-reinforced polymer (GFRP) matrix, which exhibited the smallest pull-out displacement and markedly enhanced impact resistance. Falaschetti et al. ²⁹ and Povolo et al. ³⁰ further reported that the incorporation of electrospun nitrile butadiene rubber/poly (ε-caprolactone) (NBR/PCL) nanofiber mats into composites significantly improved interlaminar fracture toughness and damping performance without compromising stiffness.

From a structural perspective, many researchers have focused on optimizing the thickness of viscoelastic layers to improve the impact performance of composite laminates. Sarlin et al. ²⁵ and Li et al. ³¹ revealed that an appropriate rubber-layer thickness can effectively suppress damage propagation and enhance energy dissipation efficiency. Mohotti et al. ³² and Li et al. ³³ further demonstrated that viscoelastic coatings or hybrid viscoelastic-metal laminates reduce permanent deformation and promote more uniform stress distribution under impact loading, thereby improving overall structural integrity.

In addition to improving impact resistance and damage tolerance, the integration of viscoelastic layers in laminated structures has been shown to provide additional engineering benefits. Stoll et al. ²³ found that incorporating a viscoelastic interlayer in carbon fiber-reinforced aluminum laminates effectively mitigated thermal expansion mismatch and suppressed galvanic corrosion. Subsequent studies further demonstrated that viscoelastic interlayers can significantly enhance fatigue endurance and vibration damping.^21,26 and adjust the stiffness-ductility balance depending on their thickness. ³⁴

Most current studies on the impact response of composite structures focus on low-energy collision scenarios involving thin-layer composites subjected to low or high-velocity impacts by low-mass projectiles. In contrast, research on the high-energy impact behavior of thick-layer composites under low-velocity, high-mass loading remains limited. Existing work primarily investigates the role of viscoelastic layers in enhancing impact resistance or examines how variations in viscoelastic layers type and thickness influence impact response characteristics. However, in practical engineering applications, structures are frequently subjected to high-energy impacts caused by low-velocity collisions with heavy equipment or engineering vehicles, such as falling machinery. Moreover, the mechanical response of composite structures depends not only on the thickness and material properties of the viscoelastic layers but also on their specific placement within the laminate. To address these gaps, this study systematically explores the influence of viscoelastic layer arrangement on the impact response of thick-layer composite structures under low-velocity, high-energy impact conditions. The aim is to provide new insights and a technical foundation for improving the impact resistance and toughness of fiber metal laminates in complex loading environments.

This study investigates a custom-designed thick steel-viscoelastic composite metal laminate (TSV-CML) and systematically examines the influence of viscoelastic layer placement and impact energy on its response under low-velocity, high-energy impact conditions. Low-velocity drop-weight impact tests, combined with finite element simulations, are used to analyze the force-time, energy-time, displacement-time, and velocity-time response curves, along with corresponding damage cross-sections under various parameter configurations. These analyses characterize the impact response behavior of TSV-CML structures. The findings provide theoretical guidance for the optimized design of viscoelastic layers in thick-layer composite structures and offer practical insights for the engineering implementation of high-energy impact protection structures. To present the technical route and analysis logic of this study more intuitively, a research idea diagram is attached to this paper, as shown in Figure 2.

Figure 2.

Research procedure of TSV-CML impact response study.

The rest of this paper is organized as follows: the experimental procedure about TSV-CML is described in Experimental procedure. Finite element simulation and verification gives finite element simulation and verification of a five-layer TSV-CML configuration. In Results and discussion, the typical impact response characteristics are carried out on different viscoelastic layer arrangements and varying impact energy levels. Conclusion gives the results.

Experimental procedure

Materials

TSV-CML structure comprises three components: (1) the metal layer (2) carbon fiber-reinforced polymer (CFRP) layer, and (3) viscoelastic layer.

The metal layer is made of 45 steel, with a nominal thickness of 3 mm. This steel grade is commonly used in applications subjected to heavy loads and impacts. Before the curing process, the metal layers are cleaned with acetone and subsequently surface-treated by sanding to improve adhesion to the viscoelastic layer.

This study developed a novel viscoelastic material using natural rubber as the base matrix, modified with calcium carbonate, carbon black, and other additives to enhance its mechanical performance. The natural rubber, with a nominal thickness of 10 mm, Owing to its biodegradability, environmental sustainability, high flexibility, elasticity, and outstanding impact resistance,^35,36 natural rubber was chosen as the viscoelastic matrix material. The novel viscoelastic material was incorporated as the intermediate layer in the TSV-CML structure to enhance energy dissipation and improve impact response.

In addition to these material characteristics, the viscoelastic layer exhibits typical nonlinear elastic behavior, including large deformation capability, strain-dependent stiffness, and significant energy dissipation under compressive loading. These mechanical features are essential for its role as an impact-mitigating interlayer within the TSV-CML structure. The detailed constitutive representation and the calibrated Mooney-Rivlin parameters for this viscoelastic material are provided later in Viscoelastomer.

The CFRP laminate used in this study consists of unidirectional T700 carbon fibers and epoxy resin, with a fiber volume fraction of approximately 60% and a total thickness of 1 mm. To obtain the orthotropic elastic constants and strength parameters required for finite element modeling, tensile, shear, and compressive tests were conducted in accordance with ASTM D3039, ASTM D3518, and ASTM D3410 standards, respectively. These parameters represent the initial undamaged stiffness and strength of the laminate and serve as input for the progressive damage model employed in Material models. The detailed material properties are summarized in Table 1.

Table 1.

Mechanical properties of the CFRP composite laminate.

Mechanical property	Value
Matrix type	Epoxy resin
Fiber volume fraction	0.60
Densities (kg/m3)	$1871.00$
Young’s moduli $E_1,E_2,E_3$ (Pa)	$1.15\times {10}^{11},8.50\times {10}^9,8.50\times {10}^9$
Poisson’s rations $v_{12},v_{13},v_{23}$	$0.32,0.32,0.46$
Shear modulus $G_{12},G_{13},G_{23}$ (Pa)	$4.20\times {10}^9,4.20\times {10}^9,2.70\times {10}^9$
Tensile strengths $S_1,S_2$ (Pa)	$2.30\times {10}^9,5.50\times {10}^7$
Compressive strengths $C_1,C_2$ (Pa)	$1.05\times {10}^9,1.90\times {10}^8$
Shear strength $S_{12},S_{13},S_{23}$ (Pa)	$9.00\times {10}^7$

Specimen preparation

The TSV-CML was fabricated by curing the stacked laminate layers in a thermal mold. The curing process was conducted at 160°C under a pressure of 23 bar for 300 s. The final laminate measures 150 × 150 mm. A schematic of the TSV-CML structure is shown in Figure 3(a), with a cross-sectional view illustrating the actual layer thicknesses in Figure 3(b). The thickness of each steel layer is 3 mm; the thickness of both the upper and lower viscoelastic layers is 10 mm; and the thickness of CFRP layer is 1 mm, resulting in a total laminate thickness of 27 mm. Test specimens were prepared by cutting the cured laminate into 150 × 150 mm squares using waterjet cutting.

Figure 3.

(a) Schematic diagram of the TSV-CML structure, (b) cross-sectional view of the specimen.

Manufacturability

The manufacturability of the proposed TSV-CML structures is an essential factor for their engineering application. From a fabrication perspective, the multi-layer laminate consisting of steel sheets, natural-rubber viscoelastic layers, and CFRP laminates can be manufactured using existing metal-composite bonding technologies, which ensures practical feasibility. The steel layers can be cut and shaped using conventional machining processes, while the CFRP layer is fabricated through standard prepreg lay-up and autoclave curing.

A key manufacturing challenge lies in achieving stable bonding at the steel-rubber and rubber-CFRP interfaces. Natural rubber exhibits low shear stiffness, making the interface prone to local sliding or debonding if the bonding process is not well controlled. In practice, surface roughening and applying a primer or coupling agent are effective in improving interfacial adhesion. In addition, hot-press molding can be used to ensure uniform pressure distribution and eliminate voids in the viscoelastic layers.

Another important consideration is thickness accuracy. The impact response of the TSV-CML structures is highly sensitive to the rubber layer thickness, particularly for asymmetric configurations. Therefore, the rubber sheets must be precision-cut, and the stacking process must minimize geometric tolerance. Modern compression-molding and CNC cutting techniques can achieve thickness deviations of less than ±0.1 mm, which is sufficient for the present structural design.

With regard to mass production, the proposed laminate does not rely on sophisticated or uncommon materials. Steel and natural rubber are cost-effective, and CFRP is widely available in aerospace-grade supply chains. The manufacturing steps—surface pretreatment, adhesive bonding, and hot-pressing—are compatible with common composite-metal hybrid structures. Therefore, scaling the TSV-CML configuration to larger components or panels is feasible without requiring substantial modification to current industrial processes.

When scaling the TSV-CML structures from laboratory-scale specimens to full-size engineering components, several additional practical considerations must be acknowledged. As the overall panel size increases, achieving uniform curing pressure across large areas becomes more challenging, which may introduce residual stresses or local debonding due to the thermal-expansion mismatch among steel, rubber, and CFRP. These issues can be mitigated by employing step-wise pressurization or segmented curing to maintain consistent adhesive consolidation. Moreover, small thickness deviations in the rubber layers—which are already critical at small scale—can accumulate in large components, potentially altering the global impact response. To address this, precision cutting, rigid external fixtures, and in-process thickness monitoring are recommended. In addition, viscoelastic relaxation of the rubber during curing or service loading may become more pronounced in large structures, and selecting rubber compounds with controlled relaxation behavior or applying post-curing stabilization can help maintain long-term structural integrity.

Low-velocity impact test

As illustrated in Figure 4, low-velocity impact tests were carried out using a DHR-9401 drop-weight impact testing machine. A No. 4 weight block with a mass of 79.92 kg was used, and when combined with the impactor and other components, the total impact mass reached 90.44 kg. The impactor featured a hemispherical steel striker with a diameter of 10 mm, allowing for the application of localized and repeatable impact loads to the specimen surface. Based on potential energy calculations derived from the impact mass and drop height, the impact energy was set to 500 J. Multiple repeated tests were conducted at this energy level across different specimen configurations to ensure the repeatability and reliability of the data.

Figure 4.

(a) Drop-weight impact testing machine, (b) experimental platform.

The drop-weight fixture consisted of upper and lower clamping plates, each with a central square opening measuring 125 mm × 125 mm. The plates were bolted together using high-strength fasteners to secure the specimen and limit boundary movement. A high-frequency force sensor was integrated into the system to capture real-time contact force signals during the impact event. By integrating the raw force-time data and conducting post-processing, a complete set of impact response curves was obtained, including force-time, displacement-time, velocity-time, and energy-time profiles.

Finite element simulation and verification

Geometric modeling

In this study, LS-DYNA was employed to perform explicit dynamic simulations owing to its capability of capturing severe geometric, material, and contact nonlinearities typically observed in low-velocity impact problems.^37,38 To improve computational efficiency while retaining structural symmetry, a quarter-symmetry (1/4) finite element model was established.

For the discretization, all structural components—including the steel layers, viscoelastic layers, and the CFRP laminate—were modeled using eight-node hexahedral solid elements with one-point reduced integration. This element type is widely adopted in impact simulations because of its high numerical stability and low susceptibility to volumetric locking. Stiffness-based hourglass control was activated to suppress zero-energy deformation modes, and a fully Lagrangian formulation was used for all components.

The clamping frame used in the experiments was explicitly modeled to reproduce the actual boundary conditions. Two orthogonal symmetry planes were defined in the 1/4 model, where normal displacements were constrained by enforcing Ux = 0 and Uy = 0, respectively. In addition, to represent the fully fixed clamping condition, four corner nodes located on the upper and lower fixture plates (two on each side) were fully constrained in all translational and rotational degrees of freedom. These constraints effectively prevented rigid-body motion while avoiding excessive restraint on the specimen, thereby ensuring consistency between the numerical and experimental setups.

A systematic mesh convergence study was carried out to determine the optimal element size. The mesh was uniformly refined from an initial size of 2.5 mm to 1.5 mm and finally to 1.0 mm. Convergence was assessed based on peak impact force, absorbed energy, and maximum displacement. Differences between the 1.5 mm and 1.0 mm meshes were within 3%, indicating mesh convergence. Therefore, an element size of 1.5 mm was selected for the final simulations to balance accuracy and computational cost. The resulting finite element model is shown in Figure 5.

Figure 5.

Geometric modeling (a) isometric view, (b) cross-sectional view.

Material models

Four material models were used in the simulation to represent the different components: the rigid material model (RIGID), the Cowper-Symonds model for the steel layer, the Chang-Chang composite failure model for the CFRP layer, and the incompressible Mooney-Rivlin model for the viscoelastic layers. Each model was selected to accurately capture the mechanical behavior of its corresponding material under impact loading.

Rigid materials

To reduce computational time, the hammerhead was modeled as a rigid body in the simulation using the LS-DYNA keyword *MAT_RIGID. As part of the model simplification, components such as the force sensor mounted on the experimental impactor were excluded. Instead, the density of the hammerhead was adjusted to ensure that its total mass in the simulation matched the actual mass used in the experiment. The parameters defining the rigid material model for the hammerhead are listed in Table 2.

Table 2.

Material model parameters of the hammer.

Mechanical property	Value
Densities (kg/m3)	$5.10\times {10}^3$
Poisson ratio	$0.29$
Modulus (Pa)	$2.06\times {10}^{11}$

Steel

The Cowper-Symonds model is a classical constitutive formulation used to characterize the dynamic mechanical behavior of steel. By accounting for strain rate hardening, it effectively captures the increase in yield strength from quasi-static to high strain rate conditions. This model is commonly applied in dynamic loading scenarios, including steel layer collisions and ballistic impacts. In this study, the Cowper-Symonds model was employed to simulate the dynamic response of the steel layer, and its strain rate-dependent behavior is described as follows:

${\sigma }_{\mathrm{Y}}=\left({\sigma }_0+\beta E_P{\epsilon }_{\mathrm{p}}^{\text{eff}}\right)\left[1+{\left(\dot{\epsilon }/C\right)}^{\frac{1}{P}}\right]$

(1)

$E_{\mathrm{p}}=E{E}_{\mathrm{t}}/E‐E_{\mathrm{t}}$

(2)

Where ${\sigma }_0$ , $\dot{\mathrm{\epsilon }}$ and ${\epsilon }_{\mathrm{p}}^{\text{eff}}$ represent the initial yield stress, strain rate, and effective plastic strain, respectively; $\beta$ is the hardening parameter; $E_P$ denotes the plastic hardening modulus; $E$ and $E_{\mathrm{t}}$ correspond to the elastic modulus and tangent modulus, respectively; and $C$ and $P$ are the strain rate sensitivity parameters. To illustrate the strain-rate dependence considered in this model, Figure 6 presents the engineering stress-strain curves of the steel measured at strain rates of 1 s⁻¹, 10 s⁻¹, and 100 s⁻¹. These curves clearly demonstrate the rate-sensitive hardening behavior of the steel used in this study. The fitted values of these parameters are presented in Table 3.

Figure 6.

Stress-strain curves for the steel at different strain rates.

Table 3.

Material modeling parameters for steel layers.

Mechanical property	Value
Densities (kg/m3)	$7.83\times {10}^3$
Poisson ratio	$0.3$
Modulus (Pa)	$2.10\times {10}^{11}$
Yield stress (Pa)	$3.55\times {10}^8$
Plastic hardening modulus (Pa)	$1.00\times {10}^{10}$

Carbon fiber/epoxy composites

To describe the intra-laminar failure behavior of the CFRP layers under impact loading, a progressive damage model based on the Chang-Chang failure theory was employed. This model is specifically formulated for in-plane orthotropic plies and distinguishes between four failure modes, namely fiber tension, fiber compression, matrix tension, and matrix compression. It allows the simulation of stiffness degradation and progressive damage evolution within each ply, thereby capturing the intra-laminar nonlinear stress-strain responses of composite laminates subjected to dynamic loading. ³⁹ The Chang-Chang model has been extensively applied and validated in low-velocity impact simulations of laminated composites,^40,41 demonstrating reliable capability for modeling fiber- and matrix-related intra-laminar damage. Based on these considerations, material model No. 22, MAT_COMPOSITE_DAMAGE, commonly referred to as the Chang-Chang composite failure model, was employed in LS-DYNA. In its LS-DYNA implementation, the four theoretical failure modes are represented by three corresponding failure criteria, which account for matrix cracking (tension), matrix compression, and fiber breakage (tension/compression), as shown below:

Failure criterion for matrix cracking damage:

$F_{\text{matrix}}={\left({\sigma }_2/S_2\right)}^2+\overline{\tau }>1$

(3)

Where ${\sigma }_2$ , $S_2$ as well as $\overline{\tau }$ are the transverse stress, transverse tensile strength and fiber matrix shear terms, respectively.

Compression failure criteria is given as:

$F_{\text{comp}}={\left({\sigma }_2/2S_{12}\right)}^2+\left[{\left(C_2/2S_{12}\right)}^2‐1\right]{\sigma }_2/S_2+\overline{\tau }>1$

(4)

where $S_{12}$ and $C_2$ are shear and transverse compressive strengths.

Fiber breakage mode which is represented as:

$F_{\text{fiber}}={\left({\sigma }_1/S_1\right)}^2+\overline{\tau }>1$

(5)

in which ${\sigma }_1$ and $S_1$ are longitudinal stress and strength, respectively.

When any of the failure criteria are satisfied and the progressive damage formulation has already reduced the relevant stiffness components to a negligible level, the *MAT_ADD_EROSION option is subsequently activated to remove elements that no longer possess load-carrying capacity. In the present study, element deletion is employed solely as a post-failure numerical treatment to eliminate severely distorted elements according to predefined strain limits, thereby preventing mesh entanglement and ensuring computational stability. Importantly, erosion is invoked only after the constitutive model has fully degraded the material stiffness; thus, it does not influence the physical damage evolution, which is governed entirely by the underlying progressive damage model.

Viscoelastomer

In this study, the viscoelastic material is assumed to be isotropic and incompressible. Under this assumption, its hyperelastic behavior is described using the Mooney-Rivlin constitutive model. The strain energy density function is expressed as:

$\mathrm{W}={\displaystyle \sum }_{i+j=1}^N{C}_{ij}{\left(I_1-3\right)}^i{\left(I_2-3\right)}^j+{\displaystyle \sum }_{i=1}^N\left[1/D_i{\left(J-1\right)}^{2i}\right]$

(6)

where $I_1$ and $I_2$ are the principal invariants of the left Cauchy-Green deformation tensor, defined as follows:

$I_1=trC={\lambda }_1^2+{\lambda }_2^2+{\lambda }_3^2$

(7)

$I_2=1/2\left[{\left(trC\right)}^2-tr{C}^2\right]={\left({\lambda }_1{\lambda }_2\right)}^2+{\left({\lambda }_2{\lambda }_3\right)}^2+{\left({\lambda }_1{\lambda }_3\right)}^2$

(8)

Where ${\lambda }_1$ , ${\lambda }_2$ and ${\lambda }_3$ are the principal elongations in the three deformation directions.

Under the given assumptions, the elastic strain energy density function is defined as follows. Based on equations (4)–(6), it can be expressed as:

$\mathrm{W}={\mathrm{C}}_{10}\left(I_1-3\right)+{\mathrm{C}}_{01}\left(I_2-3\right)+1/D_1{\left(J-1\right)}^2$

(9)

where $D_1$ is a material constant related to the compressibility of the viscoelastic material, while $C_{10}$ and $C_{01}$ are viscoelastic material constants determined from experimental data.

The Mooney–Rivlin (MR) model is employed in this study to characterize the nonlinear hyperelastic behavior of the viscoelastic material under large deformation. This model captures the elastic response of the material but does not include any time-dependent viscoelastic terms. For the TSV-CML structure examined here, the selected viscoelastic material is relatively soft, the viscoelastic layer is comparatively thick, and its deformation is strongly constrained by the steel face sheets, leading to a deformation state closer to a quasi-static strain-rate regime where high-rate viscoelastic effects are diminished. Accordingly, quasi-static uniaxial tension tests were conducted at loading rates of 5 mm/min, 50 mm/min, and 500 mm/min, and the stress–strain curves obtained at each rate were individually fitted using the MR formulation to determine the material parameters $C_{10}$ and $C_{01}$ . The fitted parameters are listed in Table 4, and the corresponding fitted curves are presented in Figure 7. Future work will further incorporate a Prony-series-based viscoelastic model to explicitly describe the relaxation behavior and rate-dependent mechanical response of the viscoelastic layer under dynamic loading conditions.

Table 4.

Material parameters of the viscoelastic rubber.

Mechanical property	Value
Densities (kg/m3)	$9.80\times {10}^2$
Poisson ratio	$0.49$
Modulus (Pa)	$7.59\times {10}^6$
$C_{10}$ (Pa)	$4.43\times {10}^5$
$C_{01}$ (Pa)	$5.16\times {10}^4$

Figure 7.

Mooney-Rivlin fitted stress-strain curves for the rubber at different strain rates.

Consistent with the treatment of composite materials, failed elements are removed based on defined strain limit criteria using the *MAT_ADD_EROSION failure model. This approach prevents numerical instability during the simulation by eliminating elements that no longer contribute to structural response.

Contact settings

The CONTACT_AUTOMATIC_SURFACE_TO_SURFACE_TIEBREAK contact algorithm was applied to all potential interfaces in the hybrid laminate, including those between the steel and viscoelastic layers, between the steel and CFRP layers, between the CFRP and viscoelastic layers, and between adjacent CFRP plies. This cohesive contact model can effectively transfer normal and shear stresses at the interfaces, allowing accurate characterization of the interlaminar shear behavior under low-velocity transverse impact. Once the combined shear and normal stresses at an interface reach the specified failure criterion, the contact is released, allowing delamination or interfacial debonding to occur. Such a formulation has been widely adopted in composite mechanics to simulate the initiation and propagation of delamination in layered or hybrid laminate structures.^16,42–44

${\left({\sigma }_n/\text{NFLS}\right)}^2+{\left({\sigma }_s/\text{SFLS}\right)}^2\ge 1$

(10)

In the contact simulation, ${\sigma }_n$ and ${\sigma }_s$ represent the current normal and shear stresses, respectively, while NFLS and SFLS denote the normal and shear failure strengths of the interface. This contact formulation is effective for capturing interfacial delamination behavior between layers in the composite structure. To specify these failure strengths for each interface, the corresponding material definitions were established as follows.

The interfaces between the steel, viscoelastic, and CFRP layers were modeled using a cohesive traction-separation law. The interface strengths in equation (10) were determined from the specifications provided by the adhesive manufacturer and calibrated using the interfacial behavior observed during testing. Independent interfacial measurements were not performed. For the steel-rubber interface, both the normal and shear strengths were set to 120 MPa. Before bonding, the steel surfaces were mechanically abraded and cleaned with acetone to promote adhesion. Only minor localized debonding was observed near the impact region, while the remainder of the steel-rubber interface remained well bonded. The steel-CFRP interface was assigned a cohesive strength of 20 MPa according to the properties of the structural adhesive used during fabrication. The viscoelastic-CFRP interface exhibited comparatively stronger bonding. Therefore, the same cohesive formulation was adopted, but the interface strength was increased to 200 MPa to reflect the experimentally observed behavior.

The interaction between the impactor and the structure was modeled using the *CONTACT_ERODING_SURFACE_TO_SURFACE contact type, which employed a segment-based algorithm. To account for sliding behavior between different materials, static friction coefficients of 0.2 and 0.1 were assigned, respectively.

Low-velocity impact response

The typical low-velocity impact response of the TSV-CML structure is illustrated in Figure 8. Figure 8(a) and (b) show the load-time and energy-time curves, respectively. The impact process is divided into three stages: stiffness degradation, impact loading, and impact unloading.

Figure 8.

Typical impact response of the five-layer TSV-CML structure under 500 J impact energy. (a) force-time curve, (b) absorbed energy-time curve, (c) displacement-time curve, (d) velocity-time curve (impactor), (e) force-displacement curve.

In the first stage, stiffness degradation, multiple inflection points appear on the force-time curve, indicating a progressive reduction in stiffness within the composite structure. These fluctuations are associated with the early onset of local plastic indentation in the upper steel layer, the initiation of matrix micro-cracks in the CFRP, and the accumulation of shear deformation within the viscoelastic core. Such incipient damage mechanisms reduce the effective stiffness, leading to the nonlinear response observed in this stage.

In the second stage, impact loading, the load increases with time until it reaches its peak. This stage corresponds to continuous indentation of the steel layer and significant compression of the viscoelastic layer. As the structure approaches peak load, high through-thickness shear stresses develop near the CFRP layer, which may promote limited interfacial debonding between the steel-rubber and rubber-CFRP interfaces. The gradual deviation from linearity before the peak load is consistent with the initiation of these interlaminar and intralaminar damage processes. The energy absorption curve similarly shows three stages. During the compression phase, absorbed energy increases steadily, reflecting the accumulation of deformation energy in the metal, viscoelastic, and CFRP layers.

In the third stage, impact unloading, the load gradually decreases to zero as the impactor rebounds. During this period, partial elastic recovery occurs in the steel and viscoelastic layers; however, the plastic indentation of the steel sheet and the unrecovered compression of the viscoelastic core result in observable permanent deformation. This is reflected in Figure 8(c), where the displacement stabilizes at a value between zero and the peak. Such residual displacement corresponds to the permanent dent and localized irreversible indentation formed under low-velocity impact conditions. In the rebound phase, the absorbed energy decreases as the impactor separates from the specimen and eventually stabilizes.

To further describe the damage mechanisms induced by low-velocity impact, Figure 8(e) presents the force-displacement response. During the loading stage, the curve exhibits an approximately linear increase with slight oscillations, which is consistent with progressive stiffness degradation caused by local indentation of the upper steel layer, the initiation of matrix micro-cracks in the CFRP, and shear deformation within the viscoelastic core. As the displacement approaches its maximum value, the slope of the curve decreases slightly, indicating intensified viscoelastic compression and the possible onset of interfacial debonding. During the unloading stage, the force drops rapidly while the displacement remains at a nonzero residual level, clearly demonstrating significant plastic deformation in the steel layer and incomplete recovery of the viscoelastic core. The dent depth marked in Figure 8(e) agrees well with the permanent indentation observed on the impacted specimen.

Figure 8(d) shows the velocity-time curve. During impact loading, the velocity decreases steadily to zero as kinetic energy is absorbed by the structure, demonstrating an inverse relationship between velocity and energy absorption. In the subsequent unloading stage, the release of elastic energy causes the impactor to rebound, initiating a reverse acceleration. The limited rebound velocity reflects the substantial permanent deformation accumulated in the steel and viscoelastic layers.

Finite element model validation

Data validation

Figure 9 presents a comparison between the simulation and experimental results for the five-layer TSV-CML structure under the first 500 J impact. The simulation accurately reproduces the experimental trends in the force-time, absorbed energy-time, displacement-time, velocity-time, and force-displacement curves. The discrepancies in key parameters—including peak force, absorbed energy, displacement, rebound velocity, and the overall shape of the force-displacement curve—are all within 10%, demonstrating the high reliability and accuracy of the numerical model in capturing the impact response of the structure.

Figure 9.

Comparison between experimental and simulation results of the five-layer structure under the first 500 J impact: (a) force-time curve, (b) absorbed energy-time curve, (c) displacement-time curve, (d) velocity-time curve (impactor), (e) lode-displacement curve.

In addition, the comparisons for the second and third 500 J impacts, presented in Figures 10 and 11, also show consistent agreement between simulation and experiment, further verifying the validity of the numerical model.

Figure 10.

Comparison between experimental and simulation results of the five-layer structure under the second 500 J impact: (a) force-time curve, (b) absorbed energy-time curve, (c) displacement-time curve, (d) velocity-time curve (impactor), (e) lode-displacement curve.

Figure 11.

Comparison between experimental and simulation results of the five-layer structure under the third 500 J impact: (a) force-time curve, (b) absorbed energy-time curve, (c) displacement-time curve, (d) velocity-time curve (impactor), (e) lode-displacement curve.

Damage validation and failure mechanism

The damage morphology of the five-layer TSV-CML structure under impact loading is simulated using finite element analysis, in parallel with physical experiments to validate the model’s predictive accuracy. Figure 12 shows the damage cross-section after the third impact at an energy level of 500 J. The comparison indicates strong agreement between the simulated damage patterns and experimental observations, demonstrating the model’s effectiveness in capturing the structural response and failure characteristics.

Figure 12.

Comparison of results during the third impact at 500 J: (a) experimental result and (b) finite element simulation result.

Figure 13 illustrates the cross-sectional interface and associated failure mechanisms of the TSV-CML structure. Region A represents interfacial delamination between the steel layer and the viscoelastic layer, primarily induced by stress wave propagation. When the impactor contacts the laminate surface, compressive waves travel laterally and reflect at material interfaces, producing tensile waves that lead to interfacial separation. Region B corresponds to fracture damage in the carbon fiber-reinforced polymer, resulting from tensile stresses generated as the impactor penetrates through the laminate thickness during impact. Region C indicates rupture of the steel layer, caused by severe plastic bending and localized shear stress concentration at the impact site, leading to fracture. Region D shows tearing of the viscoelastic layer, classified as puncture failure, which arises from high-strain tensile deformation of the viscoelastic under impact loading.

Figure 13.

Schematic diagram of failure mechanisms.

Results and discussion

This study first examines the typical impact response characteristics of the TSV-CML structure. It then compares the differences in impact behavior among various configurations under identical impact energy, and subsequently investigates the dynamic response evolution of a specific configuration subjected to varying impact energy levels. To clearly identify the simulated specimens, a naming convention is adopted: the steel layer is denoted as S, the viscoelastic layer as N, and the CFRP layer as C. For instance, a five-layer structure is labeled as SNCNS. The specific configurations of the three structures are illustrated in Figure 14.

Figure 14.

Configurations of the specimens: (a) SNCNS, (b) SCNS, and (c) SNCS.

Typical dynamic response of TSV-CML (SNCNS configuration)

The SNCNS specimen is selected to analyze the typical impact response of the TSV-CML structure. Three repeated impacts at an energy level of 500 J are applied, resulting in two distinct structural states: non-failure and failure. The corresponding post-impact deformation patterns are presented in Figures 15–17.

Figure 15.

Damage cross-section after the first impact.

Figure 16.

Damage cross-section after the second impact.

Figure 17.

Damage cross-section after the third impact.

As shown in Figure 15, during the initial stage of impact, the impactor first makes contact with the outer steel layer surface of the structure, and the impact force is transmitted through the steel layer to the inner layers. The central impact region experiences a combination of stresses, primarily dominated by compressive stress. Following the first 500 J impact, the specimen exhibits no significant damage. Only localized plastic deformation in the impact zone, slight compression of the viscoelastic layer, and early signs of interlaminar delamination in the carbon fiber layer are observed. At this stage, the viscoelastic layer effectively acts as a cushion, delaying the inward propagation of stress concentration.

In terms of energy dissipation, the majority of the impact energy is absorbed by the top steel layer through plastic deformation, while the CFRP and the bottom steel layer carry only minimal deformation and contribute very little to energy absorption. The viscoelastic layer mainly serves to redistribute load, moderate stress wave transmission, and suppress premature damage rather than absorbing a substantial amount of energy.

As shown in Figure 16, after the second impact, the localized yielding within the internal structure progressively evolves into more pronounced damage. Cracking occurs in the steel layer beneath the impact point, and the viscoelastic layer, having undergone repeated compression, exhibits a reduced elastic modulus, leading to a diminished energy dissipation capacity. Within the impact zone, the viscoelastic layer is almost completely torn and fails. The underlying CFRP layer begins to experience the combined effects of shear stress and interlaminar tensile stress, resulting in the initiation of interlaminar delamination. Although full penetration does not occur on the non-impact side, more pronounced denting is observed, along with interfacial debonding between the viscoelastic layer and the steel layer.

From an energy perspective, as the stiffness of the top steel sheet decreases after the first impact, part of the impact energy is redistributed to the other structural layers. Although the top steel sheet still absorbs a considerable portion of energy, its contribution is lower than that during the first impact due to material softening and cracking. Most of the remaining energy is dissipated through tearing of the viscoelastic layer on the impact side.

As shown in Figure 17, following the third 500 J impact, damage propagation enters a rapid growth stage, resulting in severe localized failure in the central region of the specimen. All internal layers are penetrated except for the bottom steel sheet. Under the combined effects of radial compressive stress and in-plane shear stress, fiber fracture occurs in the CFRP layer beneath the impactor. The viscoelastic layer undergoes extensive tensile tearing, and the bottom steel sheet exhibits significant bending deformation. A complex failure mode develops throughout the entire impact region, involving multiple mechanisms including metal shear plugging, CFRP fiber breakage, tensile tearing of the viscoelastic layer, and interfacial delamination. This compound damage pattern is mainly driven by strongly fluctuating radial and circumferential tensile stresses during impact, ultimately leading to the collapse of the structure’s overall load-bearing capacity.

In terms of energy absorption, the fractured upper layers contribute little during the third impact. Most of the impact energy is transferred to the bottom steel sheet, which undergoes significant plastic deformation and becomes the primary absorber, while a smaller portion is dissipated through CFRP fiber fracture and tearing of the viscoelastic layer.

The overall failure process of the structure proceeds as follows: during the first impact, the applied load is absorbed primarily by the top steel layer, which undergoes noticeable plastic deformation without fracturing. The second impact causes rupture of the upper steel layer and tearing of the upper viscoelastic layer. During the third impact, the CFRP layer fractures, leading to additional tearing of the lower viscoelastic layer. The impact force is eventually transmitted to the bottom steel layer, which exhibits a certain degree of plastic deformation.

Correspondingly, the energy absorption transitions from being dominated by the top steel layer during the first impact, to a more distributed pattern during the second impact, and finally to being dominated by the bottom steel layer after severe structural degradation in the third impact.

Figure 18 presents the force-time and energy-time responses of the specimen under the first (SNCNS-1), second (SNCNS-2), and third (SNCNS-3) impacts. In all three cases, the force curves remain relatively smooth during the initial loading stage. This behavior can be attributed to the viscoelastic layer, which enlarges the effective contact area, reduces the propagation speed and amplitude of the impact load, and consequently produces a more gradual load transfer. Quantitatively, the first impact yields a peak force of 55 kN and an absorbed energy of 459 J. These values increase to 65 kN and 488 J in the second impact. In contrast, the third impact shows a pronounced reduction in peak force and absorbed energy, decreasing to 36 kN and 421 J, respectively. The peak force in the third impact occurs as the impactor contacts the bottom steel layer, which undergoes significant plastic deformation and transmits the remaining load directly to the underlying components. Additionally, almost no rebound is observed during the second impact, indicating that most of the kinetic energy is dissipated through internal damage. These trends suggest that structural failure initiates during the second impact. The increase in peak force and absorbed energy from the first to the second impact further reflects the structure’s capacity to sustain and dissipate energy before collapse.

Figure 18.

Comparison of the TSV-CML structure under three impacts, showing (a) force-time curves, (b) absorbed energy-time curve, (c) displacement-time curves, (d) velocity-time curves, and (e) force-displacement curves.

Additional insights into damage progression are provided by the displacement-time, velocity-time, and force-displacement curves. In the first impact, the specimen reaches a peak displacement of 19.09 mm and exhibits a residual displacement of 14.50 mm, consistent with plastic denting of the upper steel layer and partial compression of the viscoelastic core. During the second impact, the peak displacement decreases to 12.53 mm and the residual displacement to 10.26 mm. Despite the higher peak force, the premature tearing of the upper steel layer induces an early load drop that limits further deformation. By the third impact, the peak and residual displacements increase substantially to 21.30 mm and 16.09 mm, respectively, reflecting severe stiffness degradation that allows deeper penetration of the impactor.

The velocity-time responses reinforce this interpretation. The rebound velocity after the first impact is 1.09 mm/ms. In the second impact, it decreases to 0.68 mm/ms, demonstrating that most of the input energy is dissipated irreversibly. In the third impact, the rebound velocity increases to 1.44 mm/ms, corresponding to the reduced energy absorption capability of the severely weakened structure and the larger elastic release associated with extensive softening.

The force-displacement curves provide further evidence of progressive stiffness loss. The first impact shows a smooth and continuous increase in force with displacement. In the second impact, however, an abrupt force drop occurs at approximately 10 mm displacement due to tearing of the upper steel layer. By the third impact, the curve becomes substantially flatter, with a much lower peak force for a comparable displacement, indicating severe stiffness deterioration.

Overall, the SNCNS specimen evolves from a non-failure state in the first impact—characterized by an intact upper steel layer and only partial compression of the viscoelastic core-to a failure state in the second impact, where steel rupture and extensive tearing of the viscoelastic layer occur. The third impact acts on a severely degraded laminate, as evidenced by CFRP fracture, tearing of the lower viscoelastic layer, and additional plastic deformation of the bottom steel layer. Under repeated impacts, the absorbed energy is increasingly dissipated through progressive damage mechanisms, including metal plasticity, fracture, viscoelastic tearing, and interlaminar delamination of the composite, ultimately resulting in significant structural degradation.

Impact response of TSV-CML with different viscoelastic layer arrangements under the same impact energy

To examine the influence of different viscoelastic layer arrangements on the structural impact response, three configurations are designed, as shown in Figure 19. In the first configuration (SNCS), a 20 mm viscoelastic layer is placed above the CFRP layer, on the impact-facing side. In the second configuration (SCNS), a 20 mm viscoelastic layer is positioned beneath the CFRP layer, on the rear (non-impact) side. In the third configuration (SNCNS), viscoelastic layers with a thickness of 10 mm are symmetrically arranged on both sides of the CFRP layer. Finite element simulations are performed under identical impact energy conditions to evaluate the effect of these configurations. Figure 15 presents the post-impact cross-sectional views of all three arrangements following a 500 J impact.

Figure 19.

Comparison of damage cross-sections for different TSV-CML configurations, including (a) SNCNS, (b) SNCS, and (c) SCNS.

The analysis focuses on the damage performance of the TSV-CML structure under three different viscoelastic layer arrangements: on the impact side (SNCS), on the non-impact side (SCNS), and symmetrically on both sides of the CFRP layer (SNCNS). 1.5 1.6 As shown in Figure 19(a), the symmetric arrangement (SNCNS) provides substantial cushioning and energy dissipation during impact. The specimen exhibits a maximum dent depth of 18.9 mm and a residual indentation of 15.66 mm, indicating that the deformation is well controlled and the structure has a strong ability to resist permanent indentation. The absorbed energy (422 J) and a rebound velocity of 1.15 mm/ms confirm that the impact energy is largely dissipated through viscoelastic deformation rather than structural damage. Only a small delamination zone (∼8% of the total interface area) appears at the bottom steel/viscoelastic interface, with no fiber breakage observed. This behavior demonstrates that the symmetric viscoelastic layers form a coordinated upper-lower damping interface that effectively suppresses shear concentration and interfacial delamination during through-thickness stress transmission. The configuration promotes a more uniform distribution of impact-induced stress within the CFRP layer, reduces localized tensile and shear stress concentrations, and thereby preserves overall structural integrity.

As shown in Figure 19(b), when the viscoelastic layer is placed only on the impact side (SNCS configuration), the structure does not exhibit through-thickness fracture, but localized deformation becomes deeper and more concentrated in the central region (maximum dent depth = 19.09 mm). The residual indentation (15.4 mm) and rebound velocity (1.29 mm/ms) indicate overall recovery comparable to the symmetric configuration, though local damage is more pronounced. The impact force is initially transmitted from the upper steel layer to the viscoelastic layer, which undergoes significant deformation and delays stress transmission to the underlying layers, thereby protecting the CFRP layer to some extent. At the macroscopic level, no severe fiber fracture is observed. However, delamination occurs at both the fiber interface and the lower steel-rubber interface, with a total delaminated area of approximately 35%. This debonding is attributed to the asymmetric placement of the viscoelastic layer: the absence of damping on the non-impact side allows stronger tensile-wave reflection from the rigid steel layer, causing the CFRP laminate to experience a more complex tensile-shear stress state that facilitates delamination initiation. In contrast, the SNCNS configuration, featuring symmetric viscoelastic layers, provides balanced damping on both sides, equalizes the impact load, mitigates stress gradients during transmission, and significantly reduces the risk of interlaminar delamination within the CFRP layer.

As shown in Figure 19(c), when the viscoelastic layer is positioned only on the non-impact side (SCNS configuration), the viscoelastic layer does not participate in energy absorption during the initial phase of impact. The load is transmitted directly from the rigid steel layer to the CFRP laminate, forcing it to withstand a sudden surge of kinetic energy, which leads to a through-thickness crack and evident fiber fracture. The maximum dent depth (18.7 mm) and residual indentation (15.4 mm) are comparable to those of other configurations, but the internal damage is significantly more severe. Once the CFRP layer fails, the bottom viscoelastic layer begins to respond during the later stage of impact, resulting in radial tearing and interfacial delamination (∼20%) between the rubber and steel layers. This indicates that, although the viscoelastic layer contributes to energy dissipation in the later stage, its passive engagement is insufficient to effectively mitigate the initial stress concentration. Consequently, the SCNS specimen exhibits the most severe overall damage, including a complete through-thickness fracture of the CFRP layer and severe tearing of the viscoelastic layer. In comparison, placing the viscoelastic layer on the impact side—particularly in a symmetric or thicker configuration such as SNCS and SNCNS—more effectively attenuates impact loads, delays structural failure, and reduces the overall extent of damage.

Figure 20 presents the time histories of force, energy absorption, central displacement, and impactor velocity, as well as the corresponding force-displacement curves, for the SNCNS, SCNS, and SNCS specimens following impact.

Figure 20.

Comparison of impact responses for different TSV-CML configurations, showing (a) force-time curves, (b) absorbed energy-time curve, (c) displacement-time curves, (d) velocity-time curves (impactor), and (e) force-displacement curves.

Analysis of the impact response of the TSV-CML structure under different viscoelastic layer placements reveals that when the viscoelastic layer is positioned on the non-impact side (SCNS), its cushioning effect is not activated during the critical initial phase of impact. As a result, the upper steel layer and CFRP layer are exposed directly to the incoming load without adequate buffering, leading to rapid stress concentration and early fracture of the CFRP layer. Although the viscoelastic layer eventually undergoes tearing, its energy absorption occurs at a delayed stage, primarily as a passive response following structural damage. Consequently, it contributes more to secondary damage during structural instability than to effective energy dissipation, resulting in the lowest energy absorption efficiency among the three configurations. This trend is also reflected in the force-displacement curves in Figure 20(e), where the three configurations exhibit very similar initial stiffness, but the SCNS curve shows a slightly earlier deviation from linearity, consistent with its earlier damage initiation and lower load-bearing stability. In contrast, when the viscoelastic layer is placed on the impact side (SNCS), the peak force increases by 2.3 kN and the energy absorption efficiency improves by 1.8% compared to the SCNS configuration. This improvement is attributed to the viscoelastic layer’s ability to deform significantly and immediately upon receiving the impact through the upper steel layer. Due to its thickness and high compressibility, the viscoelastic layer efficiently absorbs kinetic energy in the early stages and delays the transmission of stress waves to the underlying layers. This buffering effect not only reduces stress concentration in the region behind the upper steel layer but also delays loading on the more brittle and rigid components, namely the CFRP layer and bottom steel layer, allowing the stress to spread more uniformly. As a result, the structure achieves a higher load-bearing capacity, and the early-stage deformation of the viscoelastic layer ensures continuous energy dissipation throughout the impact event, thereby enhancing the structure’s overall energy absorption capacity. When viscoelastic layers are symmetrically arranged on both sides of the CFRP layer (SNCNS), the structural stiffness and energy absorption performance are further optimized, with the energy absorption efficiency reaching 84.4%. In this configuration, the upper viscoelastic layer undergoes large deformation immediately upon impact, attenuating the load and absorbing energy, while the lower viscoelastic layer continues to dissipate the transmitted stress as it propagates through the CFRP layer. This alternating soft-hard layering allows both viscoelastic layers to deform cooperatively under the constraint of the steel layers, significantly enhancing energy absorption efficiency and minimizing damage to the CFRP layer.

As shown in the energy-time curve in Figure 20(b), all three configurations reach their peak energy absorption within approximately 9 ms. Among them, the SNCS configuration exhibits the highest peak energy absorption, reaching approximately 490 J, indicating efficient energy dissipation through the large deformation of the viscoelastic layer. The SNCNS configuration follows closely, while the SCNS configuration shows the lowest peak value, around 470 J. In terms of final absorbed energy, the SNCNS, SNCS, and SCNS configurations achieve 422 J, 412 J, and 403 J, respectively. When the viscoelastic layer is placed on the impact side (SNCS), the absorbed energy is 412 J, corresponding to an energy absorption efficiency of 82.4%. With viscoelastic layers symmetrically arranged on both sides of the CFRP layer (SNCNS), the absorbed energy increases to 422 J, raising the efficiency to 84.2%. This represents a 1.8% improvement in energy absorption efficiency compared to the SNCS configuration. As shown in Figure 15, the SCNS configuration primarily dissipates energy through plastic deformation of the steel layer and fracture and delamination of the CFRP layer, resulting in significant structural damage. In contrast, the SNCNS and SNCS configurations dissipate energy more effectively through plastic deformation of the steel and large, controlled deformation of the viscoelastic layers. The SNCS configuration also shows slight interlaminar delamination in the CFRP layer. Additionally, the peak and final absorbed energy values for SCNS (470 J and 403 J, respectively) are both lower than those for SNCNS and SNCS, confirming that the symmetric viscoelastic layer arrangement in the SNCNS configuration is more effective than single-sided configurations in enhancing energy absorption while maintaining structural integrity. The maximum rebound velocities of the impactor are 1.15 m/s for SNCNS, 1.28 m/s for SNCS, and 1.25 m/s for SCNS. These results indicate a trend in which larger deformation areas are associated with lower rebound velocities, reflecting more effective energy dissipation during impact.

As shown in Figure 20(c), the displacement variations among the three configurations during the initial phase of impact are relatively small, indicating that the position of the viscoelastic layer has minimal influence on the early-stage dynamic response of the TSV-CML structure. As deformation progresses, each structure reaches its respective peak displacement: 19.09 mm for SNCNS, 18.90 mm for SNCS, and 18.70 mm for SCNS. These results suggest that the symmetric viscoelastic layer arrangement in the SNCNS configuration provides enhanced resistance to deformation, demonstrates higher overall stiffness, and offers more effective control of structural deflection under impact loading.

By evaluating the impact performance of various TSV-CML configurations under a 500 J impact, this study investigates the effect of viscoelastic layer placement on the structure’s energy absorption characteristics and dynamic response. The key findings are as follows: When viscoelastic layers are symmetrically arranged on both sides of the CFRP layer (SNCNS), the structure exhibits the highest energy absorption efficiency and peak force. The upper and lower viscoelastic layers act in coordination to provide effective cushioning, resulting in improved structural integrity and minimal damage. When the viscoelastic layer is placed on the impact side (SNCS), the structure undergoes significant deformation during the early stage of impact. While the energy absorption capacity is slightly reduced compared to the symmetric configuration, partial interlaminar delamination is observed in the CFRP layer. When the viscoelastic layer is located on the non-impact side (SCNS), the impact energy is primarily absorbed by the upper steel layer and the CFRP layer. This leads to fiber fracture and tearing of the viscoelastic layer, causing the most severe structural damage and the lowest energy absorption efficiency among the three configurations. Overall, the results demonstrate that a symmetrically distributed viscoelastic layer layout is more effective than a concentrated configuration in enhancing energy absorption and maintaining structural integrity under high-energy impact conditions. Therefore, the SNCNS configuration is selected as the representative model for subsequent analyses under varying impact energy levels.

Influence of impact energy on the impact response of TSV-CML structures

In this section, all specimens adopt the SNCNS configuration to investigate the effect of varying impact energy levels—500 J, 600 J, and 700 J—on the impact response of TSV-CML structures. The selected impact energy range of 500-700 J was primarily determined by the deformation characteristics of the TSV-CML specimens. Energies below 500 J produced only minor bending deformation and were insufficient to activate the full damage mechanisms of interest, while preliminary tests indicated that when the energy exceeded 700 J, the specimens experienced near-perforation, rendering further investigation at higher energies of limited significance. Within this defined range, response curves and post-impact damage are analyzed to evaluate how increasing energy influences deformation, energy absorption, peak force, and residual displacement, thereby providing insights for optimizing impact-resistant design.

As shown in Figure 21, under a 500 J impact, the impactor first contacts the upper steel layer, causing plastic deformation and a pronounced dent in the central region, with a maximum dent depth of 18.9 mm and a residual indentation of 15.66 mm. The underlying viscoelastic layer exhibits significant compression but remains largely intact, with only minor shear strain observed near the carbon fiber layer. The absorbed energy reaches 422 J, and the rebound velocity is 1.15 mm/ms, indicating that most of the impact energy is primarily absorbed by the upper steel layer through plastic bending, while the viscoelastic layer plays an important role in cushioning and delaying load transfer, effectively attenuating the transmitted energy before it reaches the CFRP laminate. The CFRP layer shows only localized compressive deformation without visible fracture, and the interlaminar delamination area is limited to approximately 8%, demonstrating that the overall structural integrity is well preserved.

Figure 21.

Comparison of damage cross-sections of TSV-CML (SNCNS) under different impact energy levels: (a) 500 J, (b) 600 J, (c) 700 J.

Based on the observed deformation pattern, the energy-absorption ranking at 500 J can be inferred as follows: steel layer (highest, dominated by plastic bending), viscoelastic layer (moderate, mainly due to compression and shear), and CFRP layer (lowest, with minimal damage-induced dissipation).

At an impact energy of 600 J, the damage zone expands. The impact-side steel layer exhibits a deeper indentation (20.4 mm) and signs of localized shear instability. Compression in the viscoelastic layer intensifies, and tearing begins to appear in some regions. The absorbed energy increases to 504 J, accompanied by a residual indentation of 17 mm and a rebound velocity of 1.21 mm/ms. The CFRP layer displays clear interlaminar delamination near the impact center, with the delaminated area expanding to approximately 20%, indicating that higher impact energy accelerates the initiation and propagation of interfacial failure.

The steel layer remains the primary energy-absorbing component as plastic deformation deepens. The viscoelastic layer ranks second, and the CFRP laminate—despite the onset of delamination—remains the smallest contributor.

When the impact energy further increases to 700 J, the structural damage becomes markedly more severe. The upper steel layer fractures at the impact site, leading to a significant reduction in load-bearing capacity. The maximum dent depth reaches 23 mm, and the residual displacement equals the total indentation, indicating complete plastic deformation and loss of recovery capability (rebound velocity = 0 mm/ms). The adjacent viscoelastic layer undergoes through-thickness tearing, and the deformation region expands outward. The absorbed energy rises to 684 J, meaning that nearly all the impact energy is dissipated through structural damage. The CFRP layer exhibits pronounced interlaminar delamination, and delamination also occurs at the steel-viscoelastic interface due to increasing in-plane tensile stress. As the impact energy continues to increase, the delamination at the steel-viscoelastic interface intensifies, overall structural damage deteriorates, and the SNCNS configuration experiences a substantial decline in load-bearing capacity.

At 700 J, fracture of the steel layer results in the largest energy absorption by a wide margin. The viscoelastic tearing provides the second-highest contribution, whereas the CFRP laminate, although severely delaminated, contributes the least.

As shown in Figure 22(a), under an impact energy of 500 J, the structure exhibits a peak force of approximately 59 kN. The force-time curve is smooth, with both the loading and unloading phases progress steadily, indicating that the structure remains within the elastic-plastic range and experiences only limited damage. When the impact energy increases to 600 J, the peak force rises to approximately 65 kN, and slight fluctuations begin to appear on the curve. These fluctuations reflect the initiation of early damage mechanisms, such as local cracking in the carbon fiber layer, the onset of delamination, and microscale shear damage within the viscoelastic layer. Despite these phenomena, the curve retains a relatively stable single-peak profile, suggesting that the structure maintains its primary load-bearing capacity. At 700 J impact energy, the peak force approaches 70 kN; however, the curve exhibits repeated and pronounced instabilities and oscillations. These reflect severe structural failure, including fracture of the steel layer, extensive delamination in the CFRP layer, interfacial separation, and tearing of the viscoelastic layer. As a result, the structure rapidly loses its primary load-bearing path. Qualitatively, at the 700 J impact level, the SNCNS structure experiences intensified plastic deformation, interlaminar delamination, and interface debonding. The energy absorption capacity of the viscoelastic layers may reach saturation, limiting their ability to effectively buffer further impact loads. This reduction in damping capability contributes to instability in the structural response, as evidenced by the irregular and oscillatory behavior of the force-time curve. These coupled damage mechanisms ultimately lead to a significant degradation in structural performance. A similar trend can be observed in the force-displacement curves shown in Figure 22(e). As the impact energy increases from 500 J to 700 J, the peak load rises accordingly, and the corresponding peak displacement shifts toward a larger deformation range, further confirming the intensified damage under higher-energy impacts. As shown in Figure 22(b), increasing the impact energy results in a substantial rise in the energy absorption rate of the material. The steadily increasing slope of the energy-time curve indicates that the failure process accelerates under higher energy impacts. At the 700 J impact level, the energy absorption curve reaches a plateau after its peak, suggesting that nearly all of the impact energy is dissipated through internal damage within the specimen. Figure 22(c) further demonstrates that both the peak impact displacement and the residual displacement of the laminate increase with rising impact energy. These findings collectively confirm that the deformation behavior of a single-type TSV-CML exhibits a clear monotonic relationship with increasing impact energy, reflecting progressively greater structural degradation and energy dissipation.

Figure 22.

Comparison of impact responses of the TSV-CML (SNCNS) configuration under different impact energy levels, showing (a) force-time curves, (b) absorbed energy-time curve, (c) displacement-time curves, (d) velocity-time curves (impactor), and (e) force-displacement curves.

In summary, as the impact energy increases from 500 J to 700 J, the failure mode of the TSV-CML structure evolves from localized elastic-plastic deformation to more severe damage, including fracture and delamination. At impact energies of 600 J and above, the structure exhibits combined failure mechanisms, such as interlaminar delamination and shear failure of the viscoelastic layer. Under 700 J impact loading, damage becomes critical, involving fracture of the steel layer, delamination within the CFRP layer, and interfacial separation between material layers. These failures lead to the collapse of the primary load-bearing path, resulting in pronounced oscillations and instability in the load-time response. Concurrently, structural response parameters, including peak force, energy absorption rate, peak displacement, and residual displacement, exhibit a clear monotonic increase as the impact energy rises. This trend indicates that the energy absorption capacity of the viscoelastic layer approaches saturation at higher energy levels. The synergistic interaction of multiple damage mechanisms under such conditions further amplifies the nonlinearity and instability of the structural response.

Based on these observations, several strategies for improving the impact-energy tolerance of TSV-CML structures can be inferred. These include optimizing the modulus and thickness of the viscoelastic layer to delay shear failure, enhancing interface strength to mitigate early debonding, and adopting more symmetric layer configurations to achieve a more balanced and stable load-transfer path under high-energy impacts.

Conclusion

In this study, low-velocity impact tests are conducted on TSV-CML structures using a drop-weight impact testing machine. Combined with finite element simulations, the investigation focuses on two scenarios: (1) analyzing the impact response of three different viscoelastic layer configurations (SNCNS, SCNS, and SNCS) under identical energy input (500 J), and (2) examining the same configuration (SNCNS) under varying impact energies (500 J-700 J). Based on the force-time, energy-time, displacement-time, and velocity-time, and force-displacement response curves, as well as corresponding damage cross-sections obtained from both experimental and simulation results, the effects of viscoelastic layer placement and impact energy on the impact response of TSV-CML structures are systematically analyzed. The following conclusions are drawn.

Under identical impact energy, the impact responses of TSV-CML structures are analyzed by comparing three viscoelastic layer configurations: placement on the impact side, the non-impact side, and symmetrically on both sides of the CFRP layer. When the viscoelastic layers are symmetrically arranged on both sides of the CFRP (SNCNS), the structure exhibits the highest peak force and the highest energy absorption efficiency (84.4%), with both upper and lower viscoelastic layers jointly contributing to impact mitigation, thereby maintaining structural integrity. In contrast, when the viscoelastic layer is positioned on the impact side (SNCS), the structure experiences large deformations at the early stage of impact, resulting in slightly reduced energy absorption and noticeable interlayer delamination of the CFRP. When the viscoelastic layer is located on the non-impact side (SCNS), the impact energy is primarily borne by the upper steel layer and the CFRP, leading to CFRP fracture, viscoelastic layer rupture, and the most severe structural damage, along with the lowest energy absorption efficiency. These findings indicate that greater viscoelastic layer thickness on the impact side enhances initial buffering performance, improves energy absorption, and helps preserve structural integrity. Furthermore, symmetric and dispersed placement of viscoelastic layers proves more effective in improving energy absorption and maintaining structural completeness compared to concentrated configurations.

At an impact energy of 500 J, the absorbed energies for the SNCNS, SNCS, and SCNS configurations are 422 J, 412 J, and 403 J, respectively, following the order: SNCNS > SNCS > SCNS. The SNCS configuration absorbs energy primarily through plastic deformation of the steel layer, large deformation of the viscoelastic layer, and interlaminar delamination of the CFRP. In the SNCNS configuration, energy absorption occurs mainly via plastic deformation of the steel layer and large deformation of the symmetrically placed viscoelastic layers. For the SCNS configuration, the energy is mainly absorbed through plastic deformation of the steel layer and fracture of the CFRP. These results further confirm that the symmetric and dispersed arrangement of viscoelastic layers significantly enhances the impact resistance and toughness of TSV-CML structures.

Under varying impact energies, the single-configuration TSV-CML exhibits the following trends: as the impact energy increases, the degree of damage intensifies and the deformation area expands accordingly. Both the peak impact force and the fluctuation amplitude of the force-time curve increase with higher energy levels. In addition, the energy absorption rate, the slope of the energy-time curve, the peak impact displacement, and the residual displacement after impact all show a rising trend with increasing impact energy. Although these results comprehensively reveal the influence of impact energy on the structural response, it should be noted that the experimental investigation in this study was limited to 500 J. The analyses at 600 J and 700 J were therefore conducted through numerical simulations. Even so, the simulation results effectively complement the experimental observations, offering broader insight into the deformation and failure behavior under more severe impact conditions. Future work will involve higher-energy impact experiments to further validate the numerical predictions and achieve a more complete understanding of TSV-CML structural behavior.