# Designing safer climbing pads: The role of foam, covers, and trapped air in pad performance

Erwan Beurienne, Marine Dorsemaine, Claire Bruna-Rosso, Maxime Wylomaski, Nicolas Bailly, Michel Behr

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Erwan Beurienne, Marine Dorsemaine, Claire Bruna-Rosso, Maxime Wylomaski, Nicolas Bailly, et al. Designing safer climbing pads: The role of foam, covers, and trapped air in pad performance. Results in engineering, 2025, 28, 10.1016/j.rineng.2025.107218. hal-05418682

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Submitted on 16 Dec 2025

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# Designing safer climbing pads: The role of foam, covers, and trapped air in pad performance

Erwan Beurienne<sup>a,b,*</sup> <sup>1,2,3</sup>, Marine Dorsemaine<sup>a</sup>, Claire Bruna-Rosso<sup>a,1,2</sup>, Maxime Wylomaski<sup>b,†</sup>, Nicolas Bailly<sup>a,1,2</sup>, Michel Behr<sup>a</sup>

<figure><img src="image_2.png" /></figure>

## ARTICLE INFO

**Keywords:**

Climbing

Crash pad

Safety

Energy absorption

Foam

Impact test

## ABSTRACT

Bouldering is a climbing discipline in which falls are cushioned by pads composed of foam encased in a PVC fabric shell, reducing injury risk. While foam behavior is well-documented, the combined effect of the foam, PVC cover, and trapped air in the pad remains poorly understood. To design safer bouldering pads, this study aims to investigate the distinct roles of the foam, the cover, and the trapped air in pad behavior.

Compression tests, including quasistatic and drop tests, were performed on two types of square samples: uncovered foam blocks (either open-cell or closed-cell) and foam blocks covered with a PVC shell. Force, displacement, and internal pressure (within the cover) were measured. The effects of foam type, PVC cover, and trapped air were assessed on stress, strain, strain rate, and absorbed energy.

During quasistatic compression, both covered and uncovered samples exhibited similar behavior with low, stable internal pressure; the addition of the PVC cover resulted in only a modest increase in stress (1.25 times higher) due to its stiffness. This emphasizes the foam's dominant mechanical contribution under quasistatic conditions. In drop tests, the behavior of covered samples changed considerably compared to uncovered ones: at 40% strain, the stress in closed-cell covered sample was approximately nine times higher, and the energy absorption per cubic meter was five times greater (14 kJ/m³ vs. 2.7 kJ/m³). Concurrently, a substantial rise in internal pressure was observed throughout the compression process, suggesting that trapped air plays a critical role in the pad's response under high-speed loading.

## 1. Introduction

Indoor bouldering, currently one of the most popular climbing disciplines, is associated with the highest number of injuries [1–3]. Indeed, a German report conducted by two German climbing associations on accidentology indicates that bouldering accounts for 76 % of injuries, compared to 19 % for rope climbing [4]. Moreover, injuries sustained during bouldering tend to be more severe than those in other climbing disciplines [5,6]. Bouldering involves climbers ascending walls up to 4.5 m high without the use of ropes or harnesses. Therefore, falls, whether intentional or accidental, are an integral part of the discipline and one of the principal cause of bouldering injuries, accounting for 70 % [5] to 90 % [7] of all reported cases. To prevent these injuries, in Europe, foam pads (or mats) are manufactured and positioned in accordance with the European standard EN 12 572–2. These pads are typically 30 or 40 cm

thick and are designed to offer high energy absorption. They are often composed of two distinct components: a foam block, which consists in one or more layers of polymeric flexible foam, and a polyvinyl chloride (PVC) based fabric shell that covers the foam block.

The mechanical behavior of polymeric foams used in pads is extensively documented in the literature, with much of this understanding rooted in the fundamental findings of Gibson and Ashby on cellular solids [8]. They notably reported that under compression foam behavior is characterized by three phases: linear elastic, plateau, and densification. Furthermore, for flexible foams, the plateau phase corresponds to cell collapsing through buckling, allowing the foam to handle large strains at nearly constant stress. This feature enables the foam to absorb the kinetic energy of an impact while preventing the transmission of high force peak [9]. This behavior is influenced by intrinsic parameters such as the base material, the cell topology and shape and the relative

<footnote><sup>a</sup> Laboratoire de Biomécanique Appliquée, Aix Marseille Université Gustave Eiffel Université, Marseille, France</footnote>

<footnote><sup>b</sup> Tyyny, Context', Le Chambon Feugerolles, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: erwan.beurienne@univ-eiffel.fr (E. Beurienne), marine.dorsemaine@univ-eiffel.fr (M. Dorsemaine), claire.bruna-rosso@univ-eiffel.fr (C. Bruna-Rosso), maxime@tyyny.fr (M. Wylomaski), nicolas.bailly@univ-eiffel.fr (N. Bailly), michel.behr@univ-eiffel.fr (M. Behr).</footnote>
density [8,10,11]. Indeed, the composition and the formulation of the base material determine the base properties of the cellular material [12]. The irregular, stochastic architecture of foam cells [13] contributes to anisotropy and bending-dominated mechanical behavior, resulting in lower elastic modulus [10,11]. Additionally, the mechanical response is influenced by whether the foam is open or closed-cell. In open-cell foams, air escapes freely during compression, whereas closed-cell foams trap air, generating additional resistive forces. Consequently, closed-cell foams typically exhibit a higher elastic modulus and plateau stress compared to open-cell foams of similar density [8,14]. The relative density (defined as the ratio of foam density to the density of the base material) plays a critical role in determining mechanical behavior. Higher relative density results in an increased elastic modulus, elevated plateau stress, and earlier onset of densification, all of which contribute to enhanced energy absorption capacity [15,16]. Foams are also known to be strain rate dependent, resulting in an increase of the stress response of the foam and an earlier densification phase at faster compression speed [17,18]. The understanding of this complex foam behavior has also been improved by both micromechanical models [8], which analyze individual cell geometry and mechanics, and homogenized models, which treat the foam as a continuous medium using phenomenological constitutive laws [11,19]. Among homogenized models, hyperelastic formulations were initially used to describe large deformations but neglected strain-rate effects. Viscoelastic models were later introduced to capture hysteresis and rate-dependent behavior [20], while recent hybrid models [21] combine hyperelastic and viscoelastic features for a more accurate representation of foam behavior. Finally, the behavior of foam and its interaction with other structure upon impact has also been studied in composite structures including sandwich structures [22], nano-reinforced composites [23], and hybrid composites [24]. For instance, [22] showed that, in sandwich structures, choosing the right wire mesh and sheet joining techniques can significantly improve energy absorption while minimizing deformation.

In contrast, the behavior of general safety pads is poorly described. Then, regarding indoor bouldering pads, which combine foam and cover materials, there is only one preliminary study that proposed a methodology for selecting pads based on their intended usage [25]. Few studies in other sports have explored their ability to reduce injuries. For example, the influence of impact velocity on the performance of safety pads has been investigated in skiing, highlighting the strong link between impact speed and foam strain rate dependency [26]. Similarly, in combat sports, the role of pad thickness in preventing full foam densification and bottoming out has been investigated [27]. It was found that increased thickness helps reduce maximum acceleration and the force transmitted during impact. Comparable results have also been observed for foam alone [16]. That said, the literature still lacks comprehensive understanding into the mechanical behavior of pads, particularly regarding how the addition of the surrounding cover influences their overall mechanical properties. While previous studies [28,29] have touched on this subject, their findings remain limited. The effect of cover replacement on cushioning performance of ski pads has been investigated [28], but no significant effect on measured acceleration was found. Impact tests were conducted on pads [29], with and without covers, and no significant differences in maximum deceleration were found. However, these tests were limited to a small number of samples, and the pads tested differ from those used in bouldering. Therefore, they provide little clarity on how the cover interacts with foam across different configurations and loading conditions, leaving a significant knowledge gap in the field.

To contribute on the mechanical knowledge of indoor bouldering pads and to clarify how the addition of a cover influences their behavior, this study investigates three hypotheses:

- The foam has a preponderant contribution to the pad's behavior

- The PVC cover increase in the overall stiffness of the pad

- The trapped air (i.e. the air contained within the pad) has a preponderant contribution to the pad's behavior

## 2. Materials and methods

In this study two types of test commonly used to characterize the mechanical behavior of sports safety foams [30–32] were performed to evaluate the pads:

- Quasistatic compressive tests at a strain rate of $0.0067s^{-1}$

- Drop tests as they are considered the most effective method for simulating the collision or landing of an athlete on a pad [16]. These were performed at 10 different heights, ranging from 0.25 m to 2.5 m with 0.25 m increments, using a 7.5 kg impactor.

Additionally, pressure measurements in the condition of both tests were incorporated to identify the effects of the trapped air.

### 2.1. Samples

Two polyurethane (PU) foams were assessed in this study: an open-cell foam and a closed-cell foam. For each foam 5 samples were prepared. Out of these 5 samples, 3 were covered with a smooth PVC fabric (density: 680 g/m²) sewn during fabrication and closed with a zipper while 2 were left uncovered (Fig. 1a and 1b, respectively). Sample size was $15×15×15$ cm. Table 1 summarizes foam samples characteristics, and which test was performed on each sample.

### 2.2. Quasistatic compressive tests

Quasistatic compressive tests were performed using a hydraulic press (Model Landmark 370.10, MTS System Corporation's, USA) equipped with a 15 kN load cell (Model 661.19h 03, MTS system, USA), a displacement sensor (Model LVDT, MTS system, USA) and an acquisition unit (Model FT40 + 793, MTS system, USA). Given the high degree of repeatability of polyurethane foam's mechanical properties under quasistatic compression [33,34], a single uniaxial compression test was conducted on each sample. The test was performed between two rectangular plates of 35 cm length and 25 cm width (Fig. 1d) at a constant compression speed of 0.001 m/s (equivalent to an engineering strain rate of $0.0067 s^{-1}$) until 90 % of the foam was compressed. Force, time and displacement data were recorded at a sampling rate of 512 Hz. Force data were filtered using a second-order lowpass Butterworth filter with a cutoff frequency of 5 Hz.

### 2.3. Drop tests

In order to mitigate the stress softening when the foam is subjected to several successive compression associated with the Mullins effect [35, 36], the samples were preconditioned following a protocol adapted from [37], and derived from ASTM D395. Specifically, each sample underwent compressions at a constant speed of 1m/s (corresponding to an engineering strain rate of $6.7 s^{-1}$) up to 80 % strain, using the same measurement system and compression tool as for the quasistatic compressive tests. Three consecutive compressions were required to achieve a stable response from the samples.

Then, impact tests were performed using a custom-built drop rig. The samples were placed on a flat surface and subjected to uniaxial compression exerted by square plate measuring $18×18×2.5$ cm and weighing 7.5 kg (Fig. 1e). The system was equipped with a 70 kN load cell (Model 9343A, Kistler, Switzerland) positioned below the flat surface. Data were recorded at 50 kHz using an acquisition unit (Model LabAmp Type 5165A, Kistler, Switzerland). High-speed imaging of the impacts was achieved using a high-speed camera (Model Miro C211, Phantom, USA) sets at 1000 fps for displacement measurement purposes. Each sample underwent 16 impacts: 10 at distinct drop heights,
<figure><img src="image_3.png" /><figcaption>Fig. 1. Samples and experimental setup illustration - (a) Sample without cover, (b) Sample with cover, (c) Sample for pressure measurement, (d) Quasistatic compressive test setup, (e) Drop test setup.</figcaption></figure>

<table><caption>**Table 1**

Samples characteristics and test performed on each sample. A total of 10 samples was used.</caption><thead><tr><th rowspan="2">Sample Type</th><th rowspan="2">Cover</th><th colspan="3">Samples distribution</th></tr><tr><th>Compressive Tests</th><th>Impact Test</th><th>Pressure Measurement</th></tr></thead><tbody><tr><td rowspan="2">Closed-cell –<br/>24kg/m³<br/>(5 samples)</td><td>no</td><td>1</td><td>1</td><td>0</td></tr><tr><td>yes</td><td>1</td><td>1</td><td>1</td></tr><tr><td rowspan="2">Open-cell – 28 kg/<br/>m³<br/>(5 samples)</td><td>no</td><td>1</td><td>1</td><td>0</td></tr><tr><td>yes</td><td>1</td><td>1</td><td>1</td></tr></tbody></table>

incrementally adjusted from 0.25 m to 2.5 m intervals corresponding to the typical height of a fall in bouldering. Additionally, to assess repeatability, two extra impacts were performed at each of the heights 0.25 m, 1.25 m, and 2.5 m. The results demonstrated high repeatability, as evidenced by minimal stress variations, with standard deviations below 1.6 kPa (< 2 % of the mean). Given this consistency, only one test per sample will be presented in the results. Impacts on the same sample were spaced 10 min apart to allow the foam to recover its initial shape. Force data was processed with a CFC1000 filter (i.e. a fourth-order lowpass Butterworth filter with a cutoff frequency of 1650 Hz). Displacement measurements were obtained through a MATLAB (R2024a) routine using Image Processing and Computer Vision Toolbox. These measurements were synchronized with the force signal using an

external laser position sensor (Model AR500–1000, Acuity, USA).

## 2.4. Pressure measurements

To investigate the influence of trapped air on the overall mechanical behavior of the pads, the quasistatic compressive tests and drop tests were replicated on two covered samples with pressure sensor (EPX-N01–3.5b, Measurement Specialties, USA). The internal pressure (i.e. the air pressure within the pad measured between the foam and the cover) was recorded concurrently with force and displacement measurements at a sample rate of 50 kHz via an acquisition unit (Model MiniDAU, Kistler, Switzerland).

## 2.5. Data analysis

To characterize each pad mechanical behavior, four metrics were computed: stress, strain, strain rate and absorbed energy W (corresponding to the area under the stress-strain curve). Applied force and impactor displacement were converted to engineering stress σ (the ratio of force to initial sample area) and engineering strain ε (the ratio of displacement to initial sample height). Engineering strain rate was calculated as the ratio of the impactor speed to the initial height of the sample and the absorbed energy W, was calculated using Equation 1.

$$W = \int_{\varepsilon_0}^{\varepsilon_{\max}} \sigma * d\varepsilon \qquad (1)$$
Finally, to facilitate inter-foam comparison and support future numerical simulations, constant strain rate stress-strain curves were computed from stress-strain curves at variable strain rate retrieved from drop tests. The methodology used is detailed on [38] and involves deriving a linearly interpolated surface by interpolating stress, strain and strain rate data points from all impact tests of a foam, using a MATLAB routine with the Curve Fitting toolbox. From this fitted surface, stress-strain curves at constant strain rates of 13s⁻¹, 20s⁻¹ and 30s⁻¹ were extracted.

The influence of the cover surrounding the foam on mechanical behavior, strain rate dependency and energy absorption capacity was analyzed using: (1) stress vs. strain curves, (2) the maximum stress and strain, (3) stress and energy per unit volume at 40 % strain between samples with and without a cover. Finally, these results were combined with pressure measurements to evaluate the validity of the 3 hypotheses regarding the effect of the foam, the cover and the trapped air on pads behavior.

# 3. Results

## 3.1. Quasistatic compressive tests

In quasistatic compressive tests, both covered and uncovered samples exhibited a three-phase stress-strain behavior: linear elastic, plateau, and densification (Fig. 2a). Covered samples exhibited higher stress levels during the plateau and densification phase. The stress at 40 % strain increased from 5.1 to 6.3 kPa with the addition of the cover for the closed-cell foam and from 4.6 to 5.6 kPa for the open-cell foam (Table 2).

Open-cell foam exhibited an earlier onset of densification at 50 % strain, compared to closed-cell foam, which began densifying at 60 % strain. The addition of a cover did not affect the strain at the onset of densification.

## 3.2. Drop tests

At impact, the stress-strain behavior of uncovered samples remained consistent with that observed in quasistatic compressive tests, maintaining the characteristic three-phase response (Fig. 2b). However, stress levels during the plateau phase were, on average, almost twice as high than in quasistatic compressive tests (Table 2). Covered samples

<table><caption>**Table 2**
Summary of principal metrics at 40 % strain for all samples.</caption><thead><tr><th rowspan="2">Metrics</th><th rowspan="2">Tests</th><th colspan="2">Closed-cell foam</th><th colspan="2">Open-cell foam</th></tr><tr><th>With cover</th><th>Without cover</th><th>With cover</th><th>Without cover</th></tr></thead><tbody><tr><td rowspan="3">Stress (kPa)</td><td>Quasistatic tests (0.0067 s<sup>-1</sup>)</td><td>6.3</td><td>5.1</td><td>5.9</td><td>4.6</td></tr><tr><td>Drop tests (1.5 m)</td><td>73.1</td><td>7.8</td><td>59.6</td><td>9.2</td></tr><tr><td>Constant strain rate (20 s<sup>-1</sup>)</td><td>75.3</td><td>7.8</td><td>60.5</td><td>9.1</td></tr><tr><td rowspan="3">Energy per volume unit (kJ/m<sup>3</sup>)</td><td>Quasistatic tests (0.0067 s<sup>-1</sup>)</td><td>2.2</td><td>1.8</td><td>2.1</td><td>1.7</td></tr><tr><td>Drop tests (1.5 m)</td><td>14.0</td><td>2.7</td><td>11.4</td><td>3.2</td></tr><tr><td>Constant strain rate (20 s<sup>-1</sup>)</td><td>12.6</td><td>2.7</td><td>11.5</td><td>3.2</td></tr><tr><td rowspan="2">Pressure (bar)</td><td>Quasistatic tests (0.0067 s<sup>-1</sup>)</td><td>0.0143</td><td>NA</td><td>0.0086</td><td>NA</td></tr><tr><td>Drop tests (1.5 m)</td><td>0.6250</td><td>NA</td><td>0.3554</td><td>NA</td></tr></tbody></table>

exhibited a more linear stress-strain response, with plateau phase no longer present. At 40 % strain, covered samples exhibited higher stress values compared to uncovered ones, with stress up to 9 times greater for closed-cell foam, and 6.5 times greater for open-cell foam, when dropped from a height of 1.5 m (Table 2). Consequently, covered samples exhibited higher values of energy per unit volume: the absorbed energy per unit volume was, 14 kJ/m³ for covered sample, compared to 2.7 kJ/m³ for uncovered ones in closed-cell foam, and 11.4 kJ/m³ compared to 3.2 kJ/m³ in open-cell foam. Additionally, covered samples compared to uncovered ones exhibited, on average, lower peak forces (86.7 ± 8 kPa vs. 378 ± 84 kPa) and reduced maximal strain (52.8 ± 2.7 % vs. 89.2 ± 2.1 %). This trend was consistently observed across all fall heights.

Fig. 3 presents the stress vs. strain curves at constant strain rates of 13, 20, and 30 s⁻¹, obtained by interpolating the drop test results along with the experimental quasistatic curve. In uncovered samples, increasing the strain rate led to an earlier onset of densification. However, the plateau stress remained the same for strain rates of 13, 20, and 30 s⁻¹, although it was twice as high as in the quasistatic test. In covered samples, the curve shape substantially changes with strain rate: the three-phase response observed in quasistatic conditions was replaced by a more "linear" response for strain rates of 13 s⁻¹ and above. An increase in strain rate was consistently associated with a rise in stress.

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** (a) Stress-strain responses for the four samples tested under quasistatic (0.0067s-1) compression between 0 and 80 % strain; (b) Stress-strain responses of the four samples subjected to a 1.5 m fall height drop test between 0 and 80 % strain.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 3. Stress-strain responses for the four samples tested under quasistatic (0.0067s⁻¹) and dynamic (13s⁻¹, 20s⁻¹ and 30s⁻¹) strain rate between 0 and 80 % strain for a) closed-cell foam and b) open-cell foam.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. Stress-strain behavior of the covered closed-cell sample under a) quasistatic compressive test and b) drop test at fall heights of 2.5 m, along with the associated pressure measurements during compression. Stress-pressure relationship of the covered closed-cell sample under c) quasistatic compressive test and d) drop test at fall height of 2.5 m.</figcaption></figure>
At 40 % strain, the stress measured at a dynamic strain rate of 20s⁻¹ was higher for covered sample compared to uncovered ones resulting in higher values of energy per unit volume for covered samples: 12.6 kJ/m³ vs. 2.7 kJ/m³ for closed-cell foam and 11.5 kJ/m³ vs. 3.2 kJ/m³ for open-cell foam (Table 2).

### 3.3. Pressure measurements

In quasistatic tests, the air pressure measured between the foam and the cover remained low and nearly constant at approximately 0 bar (Fig. 4a; Table 2) and there was no observable relationship between stress and pressure (Fig. 4c). In contrast, the pressure measured during drop tests was higher, reaching 0.63 bar at 40 % strain for closed-cell foam, and 0.36 bar for open-cell foam, when dropped from a height of 1.5 m (Table 2). A pseudo-linear relationship between pressure and stress was observed for strains up to 30 % (Fig. 4b), stress levels up to 6 kPa, and pressures up to 0.7 bar (Fig. 4c). Beyond this point, the relationship transitions into a plateau, where pressure stabilizes despite further increases in stress. Additionally, the slope of the pressure-strain curve between 10 % and 40 % strain increased with higher fall heights. This trend was consistent for both foam types tested.

## 4. Discussion

This study investigates the influence of the foam, the cover and trapped air on the mechanical behavior of bouldering pads. Compression tests, including quasistatic tests and drop tests, were conducted on foam samples, grouped as covered or uncovered. Results show that under low-speed compression, the mechanical behavior of covered and uncovered samples is comparable, with internal pressure measurements remaining low and stable. However, at high-speed compressions, notable changes occur in the covered samples behavior, including a more linear stress-strain response associated with a sharp increase in stress and a noticeable increase in internal pressure during compression. These results highlight the importance of the interaction between the foam, the cover, and the trapped air in the energy absorption of the pad during a bouldering fall.

### 4.1. Quasistatic compressive tests

During quasistatic tests, covered and uncovered samples exhibited comparable behavior (Fig. 2a). This behavior, characteristic of flexible foams, includes a linear elastic region, a plateau phase, and a densification phase [8]. However, covered samples show an increase of the stress response during the plateau and densification phases. Additionally, the internal pressure (measured between the foam and the cover) remained close to zero throughout the compression process (Fig. 4a), suggesting that the air inside the sample is not completely entrapped and can gradually flow outside the cover during the low-speed compression. The similarity in response between covered and uncovered samples, along with the absence of trapped air, indicate a preponderant contribution of the foam to the pad's behavior under low-speed compression. Meanwhile, the cover itself plays a limited role, contributing to the slight increase in stress response observed in covered samples due to its own stiffness.

### 4.2. Drop test

Under drop test conditions, the mechanical behavior of covered and uncovered samples differs greatly. Uncovered samples exhibit a strain-stress response similar to that observed in quasistatic tests, but with the plateau stress being twice as high. In contrast, covered samples display a much more linear stress-strain curve, with the plateau phase no longer observed (Fig. 2b). This shift in behavior coincides with an important rise in internal pressure during compression (Fig. 4b), indicating that air is trapped and compressed within the pad.

In contrast to open-cell foam, closed-cell foam exhibited elevated pressure levels (Table 2). Additionally, this increased pressure was correlated with a higher stress response in the closed-cell foam, high-lighting a strong relationship between these two parameters. The parallel between higher pressure and higher stress response associated with the pseudo-linear relationship (up to 6 kPa stress) between the pressure and the stress (Fig. 4c) suggests that this trapped air actively contributes to the mechanical response of the pad. As a result, the increased stress observed in covered samples can be attributed mostly to the internal pressure buildup, underscoring the preponderant contribution of trapped air in the pad's behavior under high-speed compression.

The compressions were conducted both quasistatically and through drop tests from heights ranging from 0.25 to 2.5 m, consistent with those observed in bouldering falls. Differences in behavior were noted between quasistatic compression and impacts from various heights, underscoring the strain-rate dependency of both the foam and the pad. For uncovered samples an increase of the strain rate is associated with an increase of the stress during the plateau phase and an earlier densification. This result is aligned with precedent work [17,18]. A strain rate effect was also observed for covered samples, in line with previous work showing increased impact acceleration at higher impact speeds [26]. In the present study, the increase in stress with strain rate was even more pronounced for covered samples. This can be explained by the increased air compression inside the cover. Due to the higher impact speed, the air has less time to escape from the cover. Consequently, as the compression speed increases, more air remains trapped inside the cover for a given volume. This increases the internal pressure, thereby amplifies the stress response of the sample, indicating that the rise in stress at higher impact speeds is primarily influenced by the presence of trapped air. This further supports the idea that the trapped air has a preponderant contribution in the pad's behavior under high-speed compression. Nevertheless, these findings should be interpreted with caution, as the small size of the samples (150 mm-sided cubes) may introduce edge effects that amplify internal pressure increases during high-speed compression, potentially leading to an overestimation of the influence of trapped air on mechanical behavior. This could affect all results, including the shift to a more linear stress-strain response as well as changes in the energy absorption of covered samples. Further full-scale pad investigations are necessary to validate these findings for real-world bouldering pads.

Concerning the foam, assessing its contribution to the mechanical behavior of pads during impact remains challenging because both the open-cell foam and the closed-cell foam presented a similar behavior and stress at plateau. To gain further insight, an agglomerated foam with a density of 42 kg/m³ was additionally tested using the same drop test protocol as previously described. This foam was chosen due to its atypical structure, which resulted in distinct behavior compared to the open and closed-cell foams tested earlier. Specifically, it exhibited a lower slope in the linear elastic region, a reduced plateau phase, and an earlier onset of densification, aligns with precedent work [39]. However, when covered the samples behaved similarly to the covered open and closed-cell foams, though it remains slightly stiffer (Fig. 5). These findings suggest that the notable effects of the cover and trapped air limit the foam's contribution to pad behavior under high-speed compression, thereby masking the specific mechanical characteristics of the foam. However, these findings must be interpreted with caution, as the covered samples were only compressed up to 40 % strain, a level at which the three uncovered foams exhibited relatively similar behavior.

The cover used in this study is constructed from a woven PVC fabric, sewed during manufacturing and sealed with a zipper; similar to commercial bouldering crash pads. Unlike a hermetically sealed system, this configuration allows air to escape gradually through the sewing, and zipper interface. Up to 6 kPa (or 30 % strain) the increase in pressure is linearly correlated with increased stress and strain (Fig. 4b and 4d). This suggests a constant and limited escape of air. After this point the internal
<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Stress-strain responses with the addition of the agglomerated foam subjected to a 1.5 m fall height impact test between 0 and 80 % strain.</figcaption></figure>

pressure stabilizes at approximately 0.7 bar (Fig. 4d) while both the compressive strain and stress continue to increase. This plateau suggests that, beyond this pressure, the compression rate balances the air outflow through the fabric and zipper, allowing the trapped air to escape and maintaining a near-constant pressure.

A deeper investigation through modeling, such as a micromechanical or fluid-structure interaction approach, would significantly enhance our understanding of this phenomenon. Such models could elucidate the physical mechanisms governing air confinement and expulsion at the pore, sewing and zipper scales.

### 4.3. Implication for bouldering pads design

Based on the results of this study, it is clear that the design of bouldering pads must carefully consider the foam, the cover and its permeability (i.e. its ability to retain air when compressed). The aim should be to optimize both foam and cover properties to ensure effective protection across a wide range of compression scenarios.

This study shows that unlike uncovered foams, which exhibit a plateau phase that efficiently dissipates energy at a nearly constant stress level [9,40], covered samples exhibit a more linear stress-strain response. Although this linear behavior allows for greater energy absorption (evidenced by the larger area under the stress-strain curve) it also results in higher stress transmission (Fig. 2b, Fig. 3), which must be carefully managed to avoid injuries. Achieving the optimal balance between energy absorption and transmitted stress is crucial to preventing injuries [41,42] and could be fine-tuned by adjusting the permeability of the cover and selecting the most suitable foam. In the design of safety pads, the choice of foam is crucial, particularly for comfort during low-speed compression, such as when climbers walk on them. Then, the second critical aspect lies in the cover's permeability, which can be systematically adjusted through manufacturing and design choices. The method of fabric assembly (whether sewn or welded) significantly affects air escape, as sewn seams inherently permit greater airflow compared to welded joints. Similarly, the choice of enclosure system, such as zippers, Velcro, or fully sealed edges, introduces varying degrees of localized air leakage. Additional features, like strategically placed venting holes, can offer further control over permeability. This selection directly impacts the amount of trapped air during high-speed impacts, thereby influencing the pad's mechanical behavior.

Additionally, the results of this study indicate that impact speed affects the mechanical behavior of bouldering pads. Therefore, it is crucial to gain a better understanding of the actual impact speeds experienced by climbers during falls. This knowledge should be incorporated into regulatory standards for evaluating the effectiveness of bouldering pads and considered by manufacturers during the development process.

## 5. Conclusion

This study demonstrates that at low-speed compression, the mechanical behavior of bouldering pads is preponderantly governed by the foam properties. However, at high-speed compression, the trapped air becomes a critical factor influencing the pad's response. Additionally, the inherent stiffness of the PVC cover slightly contributes to the overall stiffness of the pad. These findings underscore the need to consider not only the foam but also the cover and its permeability when designing bouldering pads. Further research should focus on optimizing parameters such as foam density, cover stiffness, and venting strategies. It should also investigate the specific impact conditions experienced during falls, particularly impact speed, to enhance pads performance.

### Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work the author(s) used Le Chat, a model created by Mistral AI, version 1 October 2023, in order to provided suggestions for phrasing, structure and clarity of the manuscript. After using this tool/service, the author(s) reviewed and edited the content as needed and take(s) full responsibility for the content of the published article.

### Funding

This work was supported by Tyyny and ANRT (Association Nationale Recherche Technologie) and carried out in cooperation with Gustave Eiffel University and Aix-Marseille University.

### CRediT authorship contribution statement

**Erwan Beurienne:** Writing – review & editing, Writing – original draft, Visualization, Methodology, Formal analysis, Data curation, Conceptualization. **Marine Dorsemaine:** Writing – review & editing, Supervision, Methodology, Funding acquisition, Formal analysis, Conceptualization. **Claire Bruna-Rosso:** Writing – review & editing, Supervision, Methodology, Funding acquisition, Formal analysis, Conceptualization. **Maxime Wylomaski:** Supervision, Resources, Funding acquisition, Formal analysis. **Nicolas Bailly:** Writing – review & editing, Supervision, Methodology, Funding acquisition, Formal analysis, Conceptualization. **Michel Behr:** Writing – review & editing, Supervision, Methodology, Funding acquisition, Formal analysis, Conceptualization.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Erwan Beurienne reports financial support and equipment, drugs, or supplies were provided by Tyyny. Maxime Wylomanski reports financial support was provided by Tyyny. Erwan Beurienne reports a relationship with Tyyny that includes: employment. Maxime Wylomanski reports a relationship with Tyyny that includes: employment. If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Data availability

The data that has been used is confidential.
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