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Energy absorption and failure mechanisms of nacre-like structure under low/high-velocity impact loading: a numerical study
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Weitao Gao1, Zihao Wang1, *, Kefeng Peng1, Kehong Wang2, 3, Qi Zhou2, 3, Zhijun Zheng1, 4, *
Acta Mechanica Sinica | 2025, 41(12) : 424560
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Acta Mechanica Sinica | 2025, 41(12): 424560
• RESEARCH PAPER •
Energy absorption and failure mechanisms of nacre-like structure under low/high-velocity impact loading: a numerical study
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Weitao Gao1, Zihao Wang1, *, Kefeng Peng1, Kehong Wang2, 3, Qi Zhou2, 3, Zhijun Zheng1, 4, *
Affiliations
  • 1CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China
  • 2School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
  • 3Key Laboratory of Controlled Arc Intelligent Additive Manufacturing Technology, Ministry of Industry and Information Technology, Nanjing University of Science and Technology, Nanjing 210094, China
  • 4The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
Published: 2025-12-01 doi: 10.1007/s10409-024-24560-x
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Nacre-like structures exhibit excellent mechanical properties under low-velocity impact, but the effectiveness of the nacre-like designs under high-velocity impact remains unclear. In this study, the process of a spherical projectile impacting on a nacre-like plate over a wide range of velocities is simulated using the finite element method. A three-dimensional finite element model is constructed and validated against the test data of the target perforation in terms of residual velocity and fracture morphology. The effects of impact velocity, interface strengths, and geometric sizes on the impact resistance capabilities are systematically investigated, and a dimensionless geometrical parameter is proposed to reveal the mechanism affecting the fracture toughness of nacre-like materials. It is found that the impact resistance of the nacre-like material gradually weakens with impact velocity increasing and is inferior to that of homogeneous plates under high-velocity impact. Moreover, the fracture toughness of nacre-like materials depends on the competition mechanism between interfacial enhancement and strength weakening at different impact velocities. These findings provide significant guidance on applying bio-inspired structures to design protective materials.

Nacre-like material  /  Impact resistance  /  Finite element model  /  Failure mechanism
Weitao Gao, Zihao Wang, Kefeng Peng, Kehong Wang, Qi Zhou, Zhijun Zheng. Energy absorption and failure mechanisms of nacre-like structure under low/high-velocity impact loading: a numerical study[J]. Acta Mechanica Sinica, 2025 , 41 (12) : 424560 - . DOI: 10.1007/s10409-024-24560-x
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1.　Introduction
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Technological advancements and the expansion of human activities across diverse sectors have driven the escalating demand for impact-resistant structures. The applications in aerospace, automotive, construction, and medical equipment require materials and structures with superior impact resistance. For example, in aerospace, aircraft, and spacecraft must withstand impacts and vibrations experienced during flight, while in automotive applications, vehicle structures must protect passengers during collisions. Brittle materi als, such as ceramics [1, 2], glass [3, 4], and concrete [5-7], are commonly used in lightweight impact-resistant structures because they offer excellent hardness relative to their density. These materials exhibit high stiffness and compressive strength but are prone to fracture or breakage in the tension state, thereby constraining their practical applications for high performance. Moreover, the elevated processing cost of these materials restricts their large-scale application.
Organisms have evolved unique microstructures with excellent mechanical properties after long-term natural selection, which can guide the design of impact-resistant structures. These distinctive microstructures have been demonstrated to exhibit superior mechanical properties in specific aspects [8-12]. The properties of biomimetic materials are dominated by the material microstructure instead of only constituents, and the reasonable material distribution gives a more efficient use of the constituents, expanding the property space beyond that of bulk materials. Over the past several decades, many biomimetic protective structures have been developed by emulating natural composites, demonstrating superior mechanical properties to their homogeneous counterparts. The sea mollusk and mantis shrimp are renowned predator-prey pairs known for their unique structural bioarmor in protective design. The nacreous layer of mollusk shells comprises 95% Vol. brittle aragonite tablets (bricks) arranged in interlocked layers, with the remaining 5% Vol. being tough organic matter (mortar) between tablets, serving as an adhesive between these tablets [13]. This brick-mortar configuration facilitates energy dissipation mechanisms such as crack propagation along soft material interfaces [11,14,15] and sliding between layers [10], thereby enhancing the structural toughness under impact loading. Consequently, the claw of mantis shrimp can preserve the integrity of the structure during hammering due to its intricate microscale fibers with helical stacking, known as Bouligand structure [16]. This arrangement enables multilevel crack deflection [17, 18], further promoting energy dissipation.
Despite biological composite structures exhibiting potential for impact resistance, they are not designed to endure higher-velocity impacts due to the limited attack capabilities of their natural predators [19]. The existing studies are about the bending strength, fracture toughness, energy absorption, and crack propagation of bio-inspired structures under quasistatic loads or low-velocity impacts. The research on their performance under high-velocity impact loads is relatively limited. However, the velocity spectrum of impacts is notably broad in real-world conditions, typically spanning approximately 10 m/s for vehicle collisions, 102 m/s to 103 m/s for ballistic impacts, and 103 m/s to 104 m/s for space debris impacts. The dynamic response of materials and structures under high-velocity impact differs significantly from that of low-velocity impact, involving factors such as stress wave effects, thermal effects, and high strain rate behavior of materials. Therefore, future research needs to continue optimizing and improving the performance of bio-inspired structures under low-velocity impacts while expanding their application research under high-velocity impact conditions to enhance their applicability and reliability in real-world engineering scenarios.
In this study, the dynamic toughening mechanism of the nacreous structure subjected to impacts ranging from low to high velocity is investigated. In Sect. 2, a 3D finite element model (FEM) of a nacre-like plate is constructed, and its accuracy is validated through existing experimental results. In Sect. 3, the mechanical responses of the nacre-like plate under projectile impact at varying velocities are presented. The impact resistance of the nacre-like plate under high-velocity impact loading is studied. Furthermore, the effects of impact velocity, interface strengths, and geometric parameters on the impact resistance and fracture mechanisms of the nacre-like structures are explored. Conclusions are presented in Sect. 4.
2.　Finite element model
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2.1　Nacre-like plate
Numerical simulations of a nacre-like plate impacted by a spherical projectile were established to analyze the failure mechanism of the nacreous structure using commercial finite element software ABAQUS/Explicit. In simulations, the square target (60 mm × 60 mm × 6 mm) was supported simply on a rigid frame, as illustrated in Fig. 1. The spherical projectile hit the center of the plate, and its diameter is 6.35 mm, the initial velocity is V0, the mass is M, and the total kinetic energy is Ek. The projectile is regarded as a rigid body according to the results of a spherical projectile impacting a homogeneous glass plate [20]. The nacre-like plate is composed of regular hexagonal glass tablets (edge width Lc and thickness Lt) stacked staggered along the longitudinal direction, with a total number of layers of NL, as depicted in Fig. 1. The deformation and damage were captured to evaluate the impact resistance performance of the nacre-like plate.
2.2　Constitutive model of brittle material
The brittle glass was used as the matrix material of the nacre-like plate to achieve a mechanical behavior close to that of aragonite in natural shells. A dynamic constitutive model [21, 22] was used to describe the mechanical behavior of the brittle material, which comprises mainly an equation of state (EOS), a damage-based strength model, and the strain rate effect.
The EOS defines the polynomial relationship between hydrostatic pressure p and Euler volume strain μ, which can be written as
where K1, K2, K3 are the material constants determined from plate impact tests.
The strength model characterizes the relationship between yield strength σY and hydrostatic pressure p, written as σY = Y(p)rθ, where rθ represents Lode effect [21], and Y is expressed as
where fcc = ηcfcψc and ftt = ηt ftψt are respective dynamic strengths of brittle materials in uniaxial compression and tension; fc and ft denote quasi-static uniaxial compressive and tensile strengths, respectively; ηc and ηt are shape functions which describe shear and tensile damage [21]. ψc and ψt are respective dynamic increase factors (DIF) due to strain rate effect only in uniaxial compression and tension, which can be written as [21, 23, 24]
and
where is the dimensionless strain rate, and is the reference strain rate usually taken to be 1:0 s−1; Fm, Wx, Wy, and S are constants determined from experimental tests.
The residual strength of the crushed ceramics is still high under the confining pressure. The residual yield surface for ceramics materials can be written as
where fr = fcr represents the residual strength under quasistatic uniaxial compression. Meanwhile, fcl corresponds to the initial yield strength. r and l are material constants.
The constitutive model was incorporated into the software ABAQUS by coding subroutine VUMAT to simulate the mechanical response of glass under impact load. In the constitutive model, the EOS parameters of glass are taken from Ref. [25]. The strength parameters were estimated by curve-fitting experimental data [26], as illustrated in Fig. 2. The strain rate effect parameters were obtained by fitting (Fig. 3) to the experimental data in Ref. [25]. The values of all the other parameters were estimated using the guidelines outlined in Ref. [22]. The main material parameters of the glass used in this study are given in Table 1, and additional parameters follow with Refs. [21, 22].
2.3　Interface model
The cohesive zone model (CZM) was employed to describe the dynamic mechanical behavior of the adhesive layer between tablets. The CZM was widely used to simulate the adhesive layer bonding ceramics to metal or fiber [27]. The organic matter that acts as a binder in the nacreous structure makes up only about 5% of the total volume [13]. Hence, a cohesive contact method (without solid material) is adopted for numerical simulations. The traction-separation law describes the relationship between the cohesive nominal traction stress vector T = [tn, ts, tt]T and the corresponding separations δ = [δn, δs, δt]T, where the subscripts n, s, and t denote the normal and two tangential components, respectively. K = [Kn, Ks, Kt]T is defined as the stiffness along the normal and tangential directions and satisfies T = (1 − D) Kδ, where D is the damage variable. A simple bilinear traction-separation law is depicted in Fig. 4, where represents the peak values of the traction stress when the separation is either purely normal to the interface or purely in the first or the second shear direction, respectively. Likewise, represents the values corresponding to the peak values of the traction. Damage begins to occur when the following criterion is satisfied:
where 〈tn〉= tn if tn > 0 (tension) and 〈tn〉= 0 otherwise (compression), which signifies that a purely compressive stress state does not initiate damage. The Benzeggagh-Kenane fracture criterion [28] was adopted to describe damage evolution and failure of the interface. The fracture energy GC required to cause failure in mixed-mode loading is defined as
where GI = Gn,GII = Gs+Gt, and η is a cohesive property parameter; Gn,Gs,Gt denote the work done by the tractions and their conjugate separations in the normal, first and second-shear directions, respectively; the superscript C refers to the fracture energy required to cause failure in the corresponding directions. In this study, the mechanical behaviors along two shear directions are assumed to be the same and with specific parameters detailed in Table 2.
2.4　Validation of the finite element model
The reliability of the finite element model (FEM) was validated by comparing the numerical simulation and experimental results of the spherical projectile impacting homogeneous glass plate [20]. The process of a spherical projectile with a diameter of 6.35 mm impacting a square glass plate with a dimension of 100 mm × 100 mm × 12 mm was simulated. Crack propagation is a crucial mechanical behavior during the failure of brittle materials, which significantly impacts the failure zone and fragments of the material. Unfortunately, limited by computer computing capacity, it is difficult to simulate cracks accurately and efficiently due to the huge number of elements when the mesh size is close to the feature size of the crack. The local encryption of the mesh may alter the crack propagation pattern in the transition region from coarse to fine mesh. Therefore, a uniform mesh size of 0.4 mm (≈ 2 × 106 solid elements) was ultimately selected, taking into account the mesh sensitivity and the computational time. The velocity of projectile ranges from 500 m/s to 800 m/s. The surroundings of the glass target plate are approximately free according to the experimental tests of Sathananthan et al. [20].
The deformation of the glass plate at the initial velocities of 500 m/s and 800 m/s are shown in Fig. 5. Under the projectile impact, cracks in plates mainly propagate in two forms: radial large cracks and circumferential small cracks. The distribution of the circumferential cracks is more extensive at the velocity of 500 m/s, while the size of the resulting fragments is smaller at 800 m/s. Figure 6 show the crack evolution of the plate during the impact process in experiments and numerical simulations. The overall distribution of the cracks obtained from the numerical simulations is consistent with the experimental results, but the number of cracks cannot be simulated accurately due to the mesh size of 0.4 mm, which is larger than the characteristic size of the crack. However, numerical simulations can accurately capture the velocity variation before and after the impact of the projectile (Fig. 7). The ballistic limit of 598 m/s can be approximated through the numerical simulation results, which closely align with 585 m/s predicted by the experimental results. When the projectile velocity surpasses this ballistic limit, the relative error between the numerical calculated residual velocity and the experimental results remains below 5%.
3.　Results and discussion
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3.1　Impact resistance of nacre-like plate at high velocity
Crack propagation patterns in the nacre-like plate and homogeneous plates at an initial velocity of 200 m/s are distin guished, as shown in Figs. 8 and 9. The dimensions of the nacre-like plate are NL = 5 and Lc = 6:4 mm in the numerical simulation. A large number of short cracks appear in the circumferential direction first, followed by fewer large cracks along the radial direction in the front of the plate (Fig. 8a), while cracks propagate mainly along the radial direction in the back of the plate (Fig. 9a) when a homogeneous plate is subjected to a spherical projectile. However, for the nacre-like plate, a large number of short cracks are concentrated in a single hexagonal cell, and no large cracks propagate (Figs. 8b and 9b), thus the damage region in the nacre-like plate is much smaller than that in the homogeneous plate. These results indicate that stress propagation and crack extension will be blocked by the interfaces in a nacre-like plate.
The cross-sectional crack pattern of the nacre-like and homogeneous plates shows varying sensitivity to velocity, as shown in Figs. 10 and 11. The typical conical failure pattern is observed in both nacre-like and homogeneous plates subjected to a spherical projectile, a phenomenon also noted in brittle target [29,30]. The failure zone of the nacre-like plate exhibited a conical shape at an impact velocity of 100 m/s and 200 m/s, and the cater in the back decreases with impact velocity increasing. In contrast, the homogeneous plate displays a conical crack pattern at an impact velocity of 200 m/s, but a large dominated crack occurs in the cross-section at 100 m/s due to no penetration in the target. The perforation of a homogeneous plate was also observed in experimental tests [20], but at a higher impact velocity (> 500 m/s). This suggests that the impact velocity of the failure pattern transition is lower for the nacre-like plate compared to the homogeneous plate.
The energy absorption curves of the nacre-like plate with the impact velocity of 200 m/s are shown in Fig. 12. Due to the presence of the hourglass, the total energy of the system may increase during the impact process, but the increase can be ignored, ensuring the reliability of the obtained results. Spherical projectiles with different initial velocities were launched against both the nacre-like and homogeneous plates and the residual velocities are illustrated in Fig. 13. The ballistic limit for the nacre-like plate is determined to be 97.6 m/s, a value lower than that of the homogeneous plate (136.8 m/s). Besides, it can also be observed that the residual velocity of the projectile is higher for the nacre-like plate at different impact velocities, which indicates a poorer impact resistance performance. These findings above suggest that the nacre-like plate does not enhance the protective efficacy at impact velocities exceeding 100 m/s.
3.2　Effects of impact velocity on the impact resistance
The impact resistance performance of the nacre-like plate may be affected by the impact velocity. Under quasi-static tests [31,32] and low-velocity impact [33,34], the efficacy of nacre-like structures in enhancing toughness has been substantiated. These results demonstrate a significant improvement compared to a homogeneous plate. While under high-velocity impact, the nacre-like plate does not enhance the protective efficacy. This discrepancy may arise from the variance in the mass of the impactor. In reality, the mass of an impactor for high-velocity impact is typically small, e.g., projectile impacting from a gun, whereas it is generally large for low-velocity impact, e.g., vehicle collisions. The mass of the projectile can be implicitly determined by the initial impact velocity V0 and kinetic energy, denoted as Ek. The resistance of the nacre-like plate to impact was assessed under conditions of varying projectile velocities, all maintaining the same kinetic energy by manipulating the density of the projectile material rather than volume to avoid dimension mismatch between the projectile and the plate.
The deformation patterns observed in a plate subjected to a projectile impact at a velocity of 10 m/s differed significantly from those observed under high-velocity impacts, applicable to both homogeneous and nacre-like plates, as shown in Fig. 14. For a homogeneous plate, the cracks stop propagation along the toroidal direction, and there is a reduction in the number of radial cracks compared to the deformation depicted in Fig. 9a. A pronounced longitudinal deflection of the plate was noted, culminating in the collapse of the entire structure, as compared to the section deformation depicted in Fig. 11a. For the nacre-like plate, distinct radial cracks were observed on the rear surface of the plate. Additionally, the dimensions of the fragments within the fractured region area increased significantly (see Figs. 11b and 14b).
The impact resistance of the plate was assessed by calculating the absorbed energy, which represents the difference between the initial and final kinetic energies of the projectile. When V0 = 200 m/s, the absorbed energy of the nacre-like plate is 14.74 J, which is lower than that of the homogeneous plate (20.51 J). However, when the velocity is reduced to 10 m/s, the absorbed energy of the nacre-like plate equals to 3.41 J, surpassing that of the homogeneous plate (1.68 J). This finding agrees with the results of the literature regarding the high toughness of the nacre-like plate compared to homogeneous plates at low-velocity impacts [33, 34]. Based on the analysis above, it is evident that the impact velocity of the projectile also influences the toughening capability of the nacre-like plate.
Comparing the history of the resistance force exerted on the projectile, it is evident that the nacre-like plate markedly extends the impact duration at lower velocities. This leads to superior energy absorption compared to the homogeneous plate despite its reduced resistance force. At an impact velocity of 10 m/s, the peak resistance force of the nacre-like plate is merely 20% of that of the homogeneous plate. However, the impact duration increases from 0.09 ms to 0.6 ms, as depicted in Fig. 15. During the impact process, the crack propagation path within a nacre-like plate is altered to extend solely along pre-designed paths (interfaces). The interfaces present in the plane impede the radial propagation of the crack, which limits the size of the failure region. The staggered stacking design of hexagonal tablets offers structural support, preventing the material adjacent to the projectile from being ejected in a plug-like manner. These factors collectively prevent the abrupt collapse of brittle materials, leading to a marked increase in the duration of impact. When the impact velocity is 200 m/s, the peak resistance force experienced by the projectile is about 50% of that of the homogeneous plate, but the duration of the impact is close to that of the homogeneous plate (about 0.06 ms), leading to a reduced energy absorption capacity. This suggests that the interface is unable to react to the impact of the projectile in such a short time. Notably, the rate at which stress is transferred between the interfaces is significantly slower than the speed of stress waves within a homogeneous plate. This results in a smaller failure area for the nacre-like plate, as illustrated in Fig. 11. It becomes evident that under high-velocity impact loading, structural design plays a limited role, with the performance of the matrix material being more critical.
Figure 16 illustrates the energy absorption ratio Ea of the plate at varying impact velocities V0, with Ek of 5.17 J, 11.64 J, 20.70 J and 46.57 J (equal to that of the projectile with the velocity of 100 m/s, 150 m/s, 200 m/s and 300 m/s and the density of 7850 kg/m3), respectively. The results indicate that as the kinetic energy of the projectile remains constant, the value of Ea increases with V0. The magnitude of Ea for the nacre-like plate is notably larger at a relatively low velocity. However, once the velocity of the projectile reaches a sufficient level, the Ea of the homogeneous plate surpasses that of the nacre-like plate. From the force-displacement curve in Fig. 15, we can infer that as the impact velocity decreases, the duration of the impact process increases. This longer impact duration dissipates more kinetic energy of the projectile, off-setting the negative impact of reduced resistance. When these two effects balance each other out, the corresponding impact speed is defined as the critical velocity. Then, the critical velocity can be obtained by the intersection of curves in Fig. 16. It is found that the critical velocity decreases as the projectile kinetic energy increases, as detailed in Fig. 17. When Ek falls below 10 J, Vc experiences a swift decay. However, as Ek exceeds 10 J, Vc declines very slowly in alignment with the rise in Ek. For a specified mass (M) and initial velocity (V0) of the impactor striking both the nacre-like plate and the homogeneous plate, Fig. 18 illustrates which plate has greater impact resistance, and an approximate boundary line is delineated. The lower left region signifies that the nacre-like plate exhibits superior resistance, and the upper right indicates that the homogeneous plate is much greater. The results also indicate that when the impact velocity of the projectile is reduced to the order of 10 m/s, the nacre-like plate consistently exhibits superior anti-impact capabilities.
3.3　Effects of the interface strengths
The interface, a prevalent feature in biocomposites, is an efficient energy dissipation structure. The strength of the interface significantly influences the propagation of cracks within it, with tensile and shear strength emerging as crucial factors [35]. The numerical simulations of a nacre-like plate subjected to a spherical projectile were conducted with different ts and tn in equal proportions (tn=ts = 0:6). The failure separation displacement of the interface remained constant (δn = 0:2 mm, δs = 0:4 mm). The crack distributions observed in the nacre-like and homogeneous plates are similar when ts reaches 1600 MPa (see Figs. 8, 9, 14 and 19). At low impact velocities, only radial cracks emerge, which results in the overall collapse of the nacre-like target. The phenomenon is distinguished from that observed in Fig. 14b (ts = 25 MPa) where the damage zone is approximately 1 to 2 hexagonal cell. At elevated impact velocities, the nacrelike plate exhibits circumferential cracks in conjunction with the radial crack, as depicted in Fig. 8a, which can not occur at low interface strength, as shown in Figs. 8b and 9b. In conclusion, the dynamic mechanical behavior of the nacrelike plate under impact load progressively aligns with that of a homogeneous plate with increasing interface strength.
The energy absorption ratio Ea varies with interface strength, as illustrated in Fig. 20. The energy absorption ratio of the nacre-like plate decreases at low impact velocity; nevertheless, that increases at high impact velocity with the increase of interface strength, which will converge towards that of the homogeneous plate (black line in Fig. 20) when it approaches infinite. The critical velocity (Vc) of the nacre-like plate demonstrates insensitivity to interface strength (see Fig. 21). In other words, the weaker the interface, the better at low impact velocity, while a stronger interface is preferable at high impact velocity.
3.4　Effects of the geometric dimension of the hexagonal cell
The energy absorption ratios of the nacre-like plates with cell sizes Lc of 2.4 mm, 3.6 mm, 4.8 mm, 6.4 mm and 10.8 mm subjected to projectile impacts are shown in Fig. 22. The results indicate that at an impact velocity of 10 m/s, the energy absorption ratio decreases slightly from 0.25 to 0.17 as Lc escalates from 2.4 mm to 10.8 mm. However, at a relatively high impact velocity, the alterations in the energy absorption ratio are relatively insignificant, with variations of less than 3.5% across different Lc values. Thus, the energy absorption ratio is insensitive to the cell sizes.
The effects of the number of layers NL of the nacre-like plates on the energy absorption ratio were also analyzed, and the results of the nacre-like plates with NL of 1, 3, 5, and 15 were displayed in Fig. 23. In particular, NL = 1 represents the homogeneous plate. It is observed that for the plates with different NL, the energy absorption ratio exhibits significant variations and demonstrates distinct patterns under both low and high impact velocities. For plates with less than 5 layers, the energy absorption ratio experiences a slight increase at low impact velocities as the number of layers increases. Conversely, at high impact velocity, this ratio significantly decreases. However, for plates with more than 5 layers, the energy absorption ratio consistently increases with the number of layers. The results also indicate that only the nacrelike plate, with low impact velocities (10 m/s and 20 m/s), exhibits a higher energy absorption ratio compared to the homogeneous plate. This further suggests that the nacre-like structure does not confer an advantage at high velocities.
To further explore the intrinsic relationship between the energy absorption ratio of a nacre-like plate and the geometric dimensions of its unit cell, a dimensionless number termed α as the “interface area density” (IAD) was introduced. This factor represents the relative proportion of the total area of all material interfaces within the nacre-like plate to the cross-sectional area. The IAD includes two components: the intra-layer IAD (denoted as α1) and the inter-layer IAD (denoted as α2). Given that Lc can be inferred that IAD for a single layer equates to that of the triangle region in Fig.24, which is expressed as , thus α1 can be determined to be ). When the nacre-like plate comprises NL layers, the inter-layer IAD (α2)is determined as NL−1. Consequently, the relationship between α and the geometric parameters of the nacre-like plate can be expressed as
Upon reorganizing the resultant data, we derived the Ea-α curves, which depict the relationship between the energy absorption ratio of the nacre-like plate and the IAD at different impact velocities, as illustrated in Fig. 25. The trend of the curve aligns closely with the results presented in Fig. 23. This is attributed to the fact that Lc employed in the numerical simulation is relatively large, which results in the effect of α1 having a significantly less effect than α2. This observation also explains the insignificant effect of Lc on the energy absorption ratio, as seen in Fig. 22. It is interesting to note that the energy absorption ratio increases at low impact velocity (V0≤20 m/s), first decreases, and then increases at high impact velocity (V0≥50 m/s) with α increasing. This phenomenon indicates that the factors affecting the fracture toughness of nacre-like materials are not singular, and a competitive mechanism exists.
The resistance to a projectile of a target depends on the material strength and impact velocity [36,37]. Given that the density of the target plate and the velocity of the projectile remain constant, the resistance encountered by the projectile is contingent upon the material strength of the target plate. A projectile striking a sufficiently thick ceramic-like material at high velocities results in a conical region ahead of the projectile, as shown in Fig. 11a. This region experiences elevated confining pressure, which substantially increases material strength. In contrast, the presence of the interface in the nacre-like plate affects or even prevents the formation of the conical zone. The contour of hydrostatic pressure within the target plate (Fig. 26) during initial penetration reveals that the peak hydrostatic pressure within the nacre-like plate is merely 50% of that observed in the homogeneous plate, which is very aligned the results in Fig. 15. Much lower hydrostatic pressure corresponds to smaller material strength, called strength-weakening. At low impact velocities, interfaces increase the duration of impact and offer an additional energy dissipation by crack propagation between them, rendering the nacre-like plate more impact-resistant. The feature could be called interface-enhancement, but its significance diminishes at high impact velocities.
Based on the analysis presented, the energy absorption ratio of the nacre-like plate can be expressed as Ea = E1 + E2. Here, E1 denotes the portion toughened by the interface, while E2 pertains to the impact velocity. As observed in Fig.25, it is hypothesized that E1 varies linearly with α, represented as E1 = kα. The velocity-dependent term comprises two components: one component represents the enhancement in energy absorption as the impact velocity increases(denoted as g1(V0)), as shown in Fig. 16. This enhancement arises because a higher impact velocity results in a lower projectile mass for a fixed impact energy, allowing the same resistance force to impart larger deceleration. The second component represents the reduction in energy absorption due to the diminished dynamic strength of the materials, denoted as−g2 · h(α). Here, g2 is a function of the impact velocity, and h(α) increases with the rise in α. Assuming g1 = g2 = g, we can write Ea = kα + g(V0)[1−h(α)]. The final equation derived from this analysis is fitted as follows:
where k = 0.01, a = 1.02, b = 0.40, and c = 0.31; Vs represents standard velocity (200 m/s here, the velocity corresponding to Ek = 20.70 J and the projectile density of 7850 kg/m3), as shown in Fig. 25.
When the value of V0 is small, resulting in a very small V0/Vs and it suggests that the interface-enhancement predominates at lower impact velocities. A larger α implies a greater interface, which can dissipate more kinetic energy of the projectile. This is confirmed by the curves for V0 = 10 m/s and 20 m/s in Fig. 25. However, as impact velocity increases, the V0/Vs enlarges, making the value of tanh (cα) non-negligible. Consequently, strength weakening begins to dominate. It is evident from the characteristics of tanh(cα) that as α increases, Ea initially decreases until α reaches a sufficient value, at which point This is in agreement with Fig.25, where Ea increases linearly with α for large values of α.
4.　Conclusions
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This study employs the finite element method to simulate the dynamic mechanical behavior of nacre-like plates subjected to projectile impact, thereby validating the efficacy of these structures under various impact velocities. Furthermore, the effects of impact velocity, interface strengths, and geometric sizes on the impact resistance performance and mechanisms were investigated. Our study suggests that:
• The plate with a nacre-like structure shows excellent resistance to low-velocity impacts but does not provide any advantage over a homogeneous plate under high-velocity impacts.
• There is a critical velocity describing the transition of fracture toughness from enhancement to weakening in nacre-like structures. This transition is attributed to the prolongation of the impact process at low impact velocities. Additionally, the critical velocity decreases rapidly as projectile impact energy increases, eventually stabilizing to the value of about 20 m/s in this study.
• The influence of the strength of interfaces in the nacre-like plate on impact resistance is different at different impact velocities. For low-velocity impact, the weak interface is instrumental in energy absorption. The strong interface is preferable for high-velocity impact.
• The competition of the interface-enhancement and strength-weakening of the nacre-like structure controls the impact resistance of the plate. The weakening effect of strength-weakening at low impact velocity is insignificant compared to the enhanced effect of the interface-enhancement, but becomes obvious at high impact velocity, leading to a substantial decrease in impact resistance compared to the homogeneous plate.
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doi: 10.1007/s10409-024-24560-x
  • Receive Date：2024-09-26
  • Online Date：2026-03-24
  • Published：2025-12-01
Article Data
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  • Received：2024-09-26
  • Accepted：2024-10-16
Affiliations
    1CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China
    2School of Materials Science and Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
    3Key Laboratory of Controlled Arc Intelligent Additive Manufacturing Technology, Ministry of Industry and Information Technology, Nanjing University of Science and Technology, Nanjing 210094, China
    4The State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

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* E-mail addresses: (Zihao Wang);
(Zhijun Zheng)
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表12种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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