Development and Dynamic Numerical Evaluation of a Lightweight Sports Helmet Using Topology Optimization and Advanced Architected Materials

Abstract

Sports activities often carry a high risk of injury, varying in severity, making the use of protective equipment, such as helmets and kneecaps, essential in many cases. Among all potential injuries, head injuries are the most crucial due to their severity. Hence, in the last decades, the scientific interest has been focused on establishing head injury criteria and improving the helmet design with the ultimate goal of the reduction in injury probability and increasing the athlete’s performance. In this context, the current study aims to develop a lightweight sports helmet with increased safety performance, utilizing topology optimization processes and advanced architected materials. In detail, the design of a conventional helmet was developed and modified applying in specific regions advanced architected materials, such as triply periodic minimal surfaces (TPMS) and hybrid structures, with functionally graded configurations to produce sandwich-like structures capable of absorbing mechanical energy from impacts. The developed helmet’s designs were numerically evaluated through dynamic finite element analyses (FEA), simulating the helmet’s impact on a wall with a specific velocity. Through these analyses, the plastic deformation of the designed helmets was observed, coupled with the stress concentration contours. Furthermore, the results of FEAs were utilized in order to calculate the values of the head injury criterion (HIC). Finally, the developed topologically optimized helmet design incorporating the hybrid lattice structure revealed increased energy absorption, reaching a HIC of 1618, improved by around 14% compared to the conventional design configuration.

1. Introduction

Main sports activities have a high probability of causing injury with variable severity; thus, in many cases, protective equipment is required, such as helmets, kneecaps, etc. Of all possible injuries, head injuries are the most crucial, as they reveal the most severe cases. The type and severity of an injury are classified based on the Abbreviated Injury Scale (AIS), created by the Association for the Advancement of Automotive Medicine (AAAM) [1]. In

Table 1. Abbreviated Injury Scale (AIS) [1].

Level	Severity	Type of Injury
0	None	No injury
1	Minor	Superficial injury
2	Moderate	Reversible injury, medical attention required
3	Serious	Reversible injury, and hospitalization required
4	Severe	Life-threatening, not fully recoverable without care
5	Critical	Non-reversible injury, not fully recoverable even with medical care
6	Fatal	Unsurvivable injury

, the AIS is presented with a short description for each level. Based on the aforementioned classification of injuries, a special criterion has been established focused on head injuries, namely the head injury criterion (HIC). The HIC was first introduced by Henn in 1998 [2] to measure quantitatively the head injury risk in crash situations. HIC concerns impact/crash scenarios with a linear velocity between 5.6 m/s (20 km/h) and 11.1 m/s (40 km/h) and a duration ranging from 15 ms to 36 ms [3]. It is worth mentioning that, for acceleration values with a duration shorter than 3 ms, there is no effect on the human brain [2].

Hence, in recent years, significant advancements have been made in helmet design, materials, wearable sensors, and testing methodologies to enhance safety and improve athlete performance by reducing injury probability and enhancing helmet characteristics [4,5,6,7,8]. Modern helmet designs increasingly incorporate biomimetic approaches. For example, the work by Chen et al. [9] simulates real-world impact conditions, as demonstrated by finite element models, such as those developed by Mustafa et al. [4]. These models enable the precise analysis of impact dynamics, providing valuable insights for optimizing helmet structures to mitigate injury risks. Researchers like Fernandes and de Sousa [6] and Li et al. [10] have further explored helmet performance under oblique impacts, emphasizing the critical role of acceleration in head injuries and integrated human head dummies in the simulation. Their studies reveal that integrating energy-dissipating layers and advanced geometries can reduce the rotational forces transmitted to the head. Material innovation also plays a crucial role in modern helmet technology. The use of lightweight, high-performance composites and multi-density foams has allowed designers to enhance energy absorption without compromising comfort or aerodynamics. These materials adapt to various impact severities, improving overall protective capabilities. Willinger et al. [5] have highlighted the importance of advanced testing methods, proposing improvements to existing standards by incorporating oblique and multidirectional impact scenarios that better reflect real-world accidents.

Towards this direction, architected materials have emerged as promising candidates for applications requiring enhanced energy absorption. These materials, characterized by their engineered microstructures, offer superior mechanical performance compared to traditional solid materials. Their lightweight nature, combined with tailored energy-absorption properties, makes them particularly suitable for managing the complex dynamics of impact scenarios [11] and providing high crashworthiness [12]. The crashworthiness of a structure, especially of an architected material, has a high value for industrial and commercial applications, and for this reason, it has been investigated extensively during the last few years. More specifically, Novak et al. [13] demonstrated that the specific energy absorption (SEA) and peak strength of architected material specimens (with consistent geometry and relative density) could be increased by up to 12.3% and 16.4%, respectively, under high strain rate loading conditions. This enhancement in energy absorption and strength quantifies the strain rate hardening effect, which arises from the material’s intrinsic hardening properties and the applied deformation mode influenced by inertia effects. Moreover, the studies of Abueidda et al. [14] and Abou-Ali et al. [15] showed that advanced architected materials, such as triply periodic minimal surfaces (TPMS), constructed by PA12 can exhibit remarkable energy absorption performance, which makes them suitable for crashworthiness applications, such as protective equipment.

For this reason, in the context of this paper, the current study aims to develop a lightweight sports helmet constructed from polymeric material with increased safety performance, utilizing topology optimization processes and advanced architected materials. The novelty of the current case study can be reviewed in the following bullet points.

• Lightweight sports helmet with relatively low-cost materials, i.e., PA12;
• Additively manufactured sports helmet with enhanced structural integrity and increased energy absorption capability utilizing only one construction material;
• Significant reduction in probability of injury from impact compared to a solid helmet;
• Further improvement of the helmet’s energy absorption performance by filling the porosity of the structure with foam material (polyurethane foam).

In detail, the design of a conventional helmet was developed and modified, applying advanced architected materials in specific regions, such as TPMS and hybrid lattice structures, with functionally graded and conformal configurations to produce sandwich-like structures capable of absorbing high amounts of mechanical energy from impacts [16]. The developed helmet’s designs were numerically evaluated through dynamic finite element analyses (FEA), simulating the helmet’s impact on a wall with a specific velocity. Through these analyses, the plastic deformation of the designed helmets was observed coupled with the stress concentration contours. Figure 1 shows the representative flowchart of this study. The first step was the creation of the initial design of the helmet, utilizing international standards and exploiting an anthropometric dummy head to accurately size the helmet. The next step was the topology optimization of the helmet by integrating conformal and functionally graded architected materials within the structure and developing a sandwich-like configuration. The last step was the computational evaluation of the developed helmet through non-linear FEA. Finally, the current paper is structured in four sections, the first deals with the introductory elements and literature review and highlights the necessity and the novelty of this study. Section 2 analyses the methodology around the design and applies FEA, along with a description of the construction and architected materials. Section 3 presents the results of this study both in terms of design and in terms of computation mechanics, and Section 4 summarizes the conclusion of this paper.

2. Materials and Methods

2.1. HIC Evaluation

As it is presented in the following formulation, HIC is exponentially related to the average acceleration $\left(\overline{a}\right)$ measured in gs and changes in velocity (Δv) during the crash for a time interval (Δt = t₂ − t₁) measured in seconds [2].

$$\overline{a}={\displaystyle \frac{\Delta v}{Dt}}={\displaystyle \frac{1}{t_2-t_1}}{{\displaystyle \int }}_{t_1}^{t_2}a\left(t\right)dt$$

(1)

$$HIC=\left(t_2-t_1\right)·{\overline{a}}^{2.5}$$

(2)

$$HIC=\underset{t_1,t_2}{\max }\left[\left(t_2-t_1\right)·{\left({\displaystyle \frac{1}{t_2-t_1}}{{\displaystyle \int }}_{t_1}^{t_2}a\left(t\right)dt\right)}^{2.5}\right]$$

(3)

The mathematical expression of $\left(t_2-t_1\right)·{\overline{a}}^{2.5}$ includes both the duration and weighted value of the deceleration for the corresponding time interval. Moreover, the following conditions need to be fulfilled in order to obtain reliable and practical data. First, the condition 0 ≤ t₁ < t₂ ≤ T, where T is the total duration of the deceleration affecting the head, is necessary. Also, 15 ms ≤ Δt ≤ 36 ms must be applied in order to extract practical data. When Δt is lower than 15 ms, this could cause unsurvivable injuries, and when Δt is higher than 36 ms, the injury risk decreases rapidly. It is worth mentioning that, for acceleration values with a duration shorter than 3 ms, there is no effect on the human brain [5]. Furthermore, the HIC values are directly connected with the probability of injury and the levels of AIS. Figure 2 graphically shows the connection between these three entities. From Figure 2, it is evident that a lower HIC value corresponds to a higher probability of minor injuries [17]. Also, it is observed that, for HIC values above 2500, the survival probability is almost zero. Hence, in the automotive industry, especially in motorcycling, an HIC value smaller than 2400 is essential for the qualification of products.

2.2. Design Process of the Sport’s Helmet

The design process of the helmet was based on the International Society for the Advancement of Kinanthropometry (ISAK) and on the empirical standards for helmet design. The developed helmet was designed to exploit the dimensions and morphology of the ISAK head of adult males, as is shown in Figure 3, along with the main dimensions [18].

Also, a sports helmet should sufficiently cover the head area above the ears, extending from the upper part of the neck to the forehead, including the temples, top, sides, and back of the head. It should be lightweight (<2 kg) to ensure comfort, increase performance, and enhance maneuverability and safety. It is essential to provide the necessary ventilation for the head to reduce the risk of head overheating during the activity. Finally, helmets must be constructed of rigid and durable materials with superior energy absorption capabilities to provide optimal protection.

Figure 4 depicts the 3D model bulk helmet design on a 3D model head showing the sufficient fitting of the external design with an average human head morphology. The above-presented helmet had a bulk design with numerous ventilation holes; however, the overall weight of the object was 1.67 kg, which is marginally below the specifications. It is worth mentioning that the design of the solid helmet was performed with SolidWorks™ 2023 design software (Systèmes SolidWorks Corp., Waltham, MA, USA). In addition, the energy absorbability of the developed helmet is questionable, due to the bulkiness of the structure. Thus, it was decided to replace the solid regions between the inner and the outer surfaces with advanced architected materials, creating a novel sandwich-like configuration. In detail, functionally graded and conformal, according to the shape of the helmet, lattice structures were designed and applied in order to obtain the maximum possible performance. Two different lattice structures were derived employing two different architected materials, i.e., the sheet-based Schwarz diamond (SD) and SD–FCC [19,20]. Indicative images of these lattice unit cells are depicted in Figure 5. It is worth noting that the SD–FCC is derived through the hybridization process of combining the Schwarz diamond and face-centered cubic (FCC) structures in order to maintain its structural integrity and improve its strength. Generally, according to the existing literature [20,21], hybrid unit cells of TPMS structures can exhibit extreme mechanical behavior.

These architected materials were selected due to their strength and energy absorption performance and the ability to be transformed into IPCs, further improving their energy absorption capability [19,21]. The mean relative density of the functionally graded lattice structures was chosen at 40%, with linear gradation for both architected materials, due to its enhanced energy absorption performance [13,22,23]. More specifically, the denser structures were close to the head (helmet’s inner surface) by up to 60%, and the lighter ones were positioned close to the helmet’s outer surface with a relative density of almost 20%. The employed architected materials had a constant mean unit cell length of 10 mm, and gradation was achieved through the modification of wall/strut thickness. The wall thickness for the SD architected material ranged from 0.86 mm to 1.58 mm, and the wall/strut thickness for the SD–FCC hybrid architected material ranged from 0.7/0.8 mm (SD/FCC) to 2.5/1.5 mm (SD/FCC). Regarding the conformalization process, the upper and lower inner surfaces were selected as boundary surfaces for the cell maps, where the lattice structures were developed. Finally, for the overall redesign process of the helmet, the nTopology software version 5.9.2. was used to extract high-fidelity 3D models for the topologically optimized helmet.

2.3. Evaluation Methodology

The evaluation of the developed helmet designs was performed through dynamic computation studies, utilizing the explicit dynamic module of the ANSYS™ (ANSYS, Inc., Canonsburg, PA, USA) simulation platform. Due to the extensive elasticity and plasticity of the architected materials [24,25], non-linear hyperelastic finite element models were developed utilizing the hyperelastic 3rd order material model. This model can describe materials with non-linear hyperelastic behavior, large deformations, and plastic strain, which are common characteristics of lattice structures [26]. The Yeoh material model utilizes the mathematical formula of Equation (4), where W_Y is the strain energy density, I₁ is the first variant, J is the volume ratio, d_i is the incompressibility factor, and C_i is the materials constant. It is worth noting that i is referring to the order of the Yeoh model. For the evaluation of the constants for this material model, the experimental data from previous studies were utilized and curve-fitted with the model’s diagram [19,20].

$$W_Y={{\displaystyle \sum }}_i^3{C}_i{\left(I_1-3\right)}^i+{{\displaystyle \sum }}_i^3{\displaystyle \frac{1}{d_i}}{\left(J-1\right)}^{2i}$$

(4)

The analysis meshes were created with tetrahedral elements, and

Table 2. Main sizing properties for the mesh of each design.

Design	Total Elements	Minimum Edge Length
Solid	129,200	0.15 mm
SD	412,278	0.12 mm
SD–FCC	444,808	0.15

lists the total number of elements and the minimum edge length for each examined design. It was worth noting that the final meshes were derived after comprehensive mesh sensitivity analyses to ensure mesh-independent results.

Regarding the loading conditions, a crash-like scenario was employed, simulating the impact of a rider with a vertical wall at a certain speed. In detail, the analyses simulated the vertical impacts of the helmets in a solid wall with a linear velocity of 11 m/s (≈40 km/h worst-case scenario for a bicycle rider). The impacts were simulated until a stable rebound velocity was achieved, with an overall T of 40 ms. Regarding the analysis setup, for all three designs, only half of each helmet design (solid, SD, and SD–FCC) was modeled, with symmetric boundary conditions applied to simulate the other half through mirroring. As a construction material, the PA12 material was employed with the physical and mechanical properties derived from the previous experimental study [27] and listed in

Table 3. Main properties of PA12 material.

Properties	Values
Density	0.95 g/cm3
Elastic modulus	938 ± 30 MPa
Yield strength	22.7 ± 0.5 MPa
Ultimate tensile strength	31.8 ± 0.5 MPa
Elongation at break	10% ± 1%

.

3. Results

3.1. Final Design of the Helmet

Figure 6 shows the developed designs created using the nTopology™ design platform. The images clearly demonstrate the sandwich-like configuration of the employed architected materials, featuring inner and outer surfaces of 3 mm. Moreover, the superimposed images present the conformal and functionally graded configurations of the employed lattice structures.

In addition, the lattice structures are uncovered in the sides in order to easily release the applied stress and allow the filling of the structure with expanding foam (polyurethane foam) for further structure improvement. The overall volume and dimension of the designed helmet remained unchanged. However, a significant weight reduction was achieved with an overall weight of 0.86 kg for both designs due to the same mean relative density for both applied architected materials.

3.2. Dynamic FEA Results

The results of the numerical analyses are illustrated in Figure 7. In detail, Figure 7 presents the stress contour for the developed helmet design, i.e., solid, SD, and SD–FCC, at three different impact stages. In detail, it presents the initial stage where there are zero displacements and maximum velocity (left side), the impact stage where the maximum acceleration (v = 0 m/s) is observed (middle), and the rebound stage where the rebound velocity has been stabilized (right side). The following qualitative conclusions can be derived concerning all the conducted impact analyses.

Initially, prior to the impact, all three analyses shared identical metrics. During the second stage, the maximum stresses and corresponding maximum strains were observed within the structures. Moreover, as was expected, the regions of the impact experienced the maximum stresses that were distributed within the structure’s volume. Finally, in the rebound stage, internal stresses from the impact were released in the rest of the structure with significantly lower magnitude; furthermore, a constant rebound velocity occurred in the opposite direction of the initial velocity. This rebound velocity of each structure is directly linked with their absorbed energy, which is dependent on the structure’s stresses and strains. It is also worth noting that, during the rebound stage, the impact stresses are relieved in the entire body of the helmet resulting in minor stress loading on the specific self-stressed regions. More specifically, the solid helmet showed better performance in terms of structural integrity, exhibiting lower stress concentration within its structure, with a maximum value of 24.62 MPa. However, this led to increased elastic strain, which was released during the rebound stage, with a rebound velocity of 10.9 m/s, resulting in decreased mechanical energy absorption. On the other hand, the helmet with the SD structure revealed a maximum stress of 33.84 MPa, with increased plastic strains for the internal lattice structure and the fraction of the external structure, as it surpassed the material’s ultimate strength (32 MPa). These resulted in compromised structural integrity and a reduced rebound velocity of 10.2 m/s. A similar pattern with the helmet with the SD structure was observed for the helmet with the SD–FCC structure. This helmet’s design revealed a maximum stress of 30.48 MPa and a rebound velocity of 9.6 m/s. Given that the rebound velocity is inversely proportional to the energy absorbed during the impact, the SD–FCC structure, with its lower rebound velocity of 9.6 m/s, suggests the highest energy absorption among the designs. This is primarily due to the extensive fracture in the FCC region, which significantly dissipates energy. As a result, the energy absorption of the SD–FCC structure is greater compared to the solid and SD helmets, which exhibit higher rebound velocities and lower energy absorption, as their structures stay more intact, leading to less energy dissipation and a higher rebound velocity. The unique characteristic of this case is that the hybrid architected material experienced a significant fracture on the low relative density region for the FCC part of the structure, with the complete breakage of the strut, which led to extensive energy absorption. In contrast, the SD part of the hybrid structure maintained the structural integrity of the overall helmet.

Having described qualitative impact characteristics and the stress distribution for the examined designs of this case study, the next step is the evaluation of each design through specific performance indicators, namely the average acceleration, the HIC values, the factor of safety (FOS) values, and the weight of each structure.

Table 4. Main impact indicators for each helmet design.

Design	Average Acceleration (gs)	Impact Duration (s)	HIC	FOS	Weight (kg)
Solid	89.33	0.025	1885	0.93	1.67
SD	86.47		1738	0.68	0.86
SD–FCC	84.02		1618	0.76	0.86

lists the values of each of these indications for all examined helmet designs. First of all, the designs with the integrated lattice structure led to a mass reduction of 48.5%, achieving final lightweight designs. Then, through the FEAs, the FOS values for each design were derived, i.e., how much stronger the structure is, compared to what it needs to be for the applied load. All three designs exceeded their yield point due to the increased initial velocity, but only the helmet with the SD structure surpassed the ultimate strength of the construction material. The other two values, i.e., the average acceleration and HIC, concerning the overall performance of each helmet and their ability to protect the human’s head in case of impact, were numerically evaluated. It is commonly known that both of these values should be as low as possible according to standards [2]. According to Table 4, the design with the lattice structure revealed lower average accelerations and HIC values due to their increased energy absorption.

Finally, the last result of this case study is the representation of the calculated HIC value on the AIS diagram (Figure 8). Based on Figure 8, in a crash with an impact velocity of 11 m/s (≈40 km), the solid helmet revealed a high probability of fatal injury nearly 20%, with a 35% probability of critical injury, 25% probability of severe injury, 17% probability of serious injury, and a negligible 3% probability of moderate injury. On the other hand, the helmet with the SD structure reduced the probability of fatal injury by half (10%), while the other probability scores were evaluated at 30% for critical injury, 35% for severe injury, 20% for serious injury, and 5% for moderate injury. Finally, the helmet with SD–FCC almost eliminated the probability of fatal injury with a probability below 5% and significantly increased the probability of moderate injury (>10%), while showing a 25% probability for critical injury, 45% probability for severe injury, and 15% probability for serious injury. Generally, the integration of architected materials in helmet designs revealed superior impact performance compared to solid designs. In addition, the design of the architected material possesses a crucial role in the observed impact performance, as it can lead to sufficient the improvement of the helmet’s crashworthiness.

4. Conclusions

This paper focused on the development of a lightweight sports helmet, integrating advanced architected materials constructed with PA12, designed to enhance energy absorption and crashworthiness. In detail, three helmet configurations were designed, employing conformal and functionally graded architected materials and were evaluated in terms of crashworthiness with the assistance of dynamic finite element analyses and advanced evaluation tools and indicators. The helmet with the SD–FCC structure revealed the optimum performance by almost eliminating the probability of fatal injury for an impact with a vertical velocity of 11 m/s (≈40 km), while the helmet with the SD structure also sufficiently improved the impact performance of the helmet. To conclude, topology optimization design processes through the employment of novel structures consisting of advanced architected materials can enhance the overall helmet efficiency both in terms of performance and crashworthiness. By only applying a specific design methodology and without changing the construction, it is possible to positively affect the final helmet design. Thus, in the future, it is essential to exploit the developed design methodology of this paper in combination with pure material science in order to further improve the performance of the designed helmet. In detail, the helmet with the integrated lattice structures can be further improved by employing interpenetrating phase composites (IPCs), utilizing the developed designs as core phases and specialized energy absorption foams (i.e., polyurethane) as filling material. This could result in an HIC value below 1000, which is a safety landmark for protective equipment. However, numerous aspects still require further investigation and development, especially regarding their implementation in real-world pilot applications. Finally, the commercial production of this type of helmet may face key challenges related to mass production and commercialization. Nevertheless, recent advancements in 3D printing have significantly enhanced productivity, and the development of industrial farms and manufacturing hubs has enabled the mass customization of such products. These advancements make the production of these complex designs feasible and drive the shift toward Industry 5.0, as defined by European directives.